var bibbase_data = {"data":"<img src=\"//bibbase.org/img/ajax-loader.gif\" id=\"spinner\"\n  style=\"display: none;\" alt=\"Loading..\" />\n\n<div id=\"bibbase\">\n\n  <script type=\"text/javascript\">\n    var bibbase = {\n      params: {\"bib\":\"https://api.zotero.org/users/5612529/collections/2NUUABGE/items?key=aiprMlXOSKe71AbbxNPHHfe7&format=bibtex&limit=100\",\"jsonp\":\"1\",\"host\":\"bibbase.org\"},\n      data: [{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"address\":\"Portland, OR, USA\",\"title\":\"Robust model predictive control with imperfect information\",\"isbn\":\"978-0-7803-9098-0\",\"url\":\"http://ieeexplore.ieee.org/document/1469944/\",\"doi\":\"10.1109/ACC.2005.1469944\",\"abstract\":\"This paper presents two extensions to robust Model Predictive Control (MPC) involving imperfect information. Previous work developed a form of MPC guaranteeing feasibility and constraint satisfaction given an unknown but bounded disturbance and perfect state information. In the first extension, this controller is modified to account for an unknown but bounded state estimation error. As an example, a simple estimator is proposed and analyzed to provide the necessary error bounds. Furthermore, it is shown that delayed state information can be handled using the same method. These analyses depend on knowledge of bounds on the measurement and disturbance uncertainties. The second extension provides a method of estimating these bounds using available data, providing an adaptive form of the controller for cases where the error levels are poorly known a priori.\",\"language\":\"en\",\"urldate\":\"2021-02-01\",\"booktitle\":\"Proceedings of the 2005, American Control Conference, 2005.\",\"publisher\":\"IEEE\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Richards\"],\"firstnames\":[\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"How\"],\"firstnames\":[\"J.\"],\"suffixes\":[]}],\"year\":\"2005\",\"pages\":\"268–273\",\"bibtex\":\"@inproceedings{richards_robust_2005,\\n\\taddress = {Portland, OR, USA},\\n\\ttitle = {Robust model predictive control with imperfect information},\\n\\tisbn = {978-0-7803-9098-0},\\n\\turl = {http://ieeexplore.ieee.org/document/1469944/},\\n\\tdoi = {10.1109/ACC.2005.1469944},\\n\\tabstract = {This paper presents two extensions to robust Model Predictive Control (MPC) involving imperfect information. Previous work developed a form of MPC guaranteeing feasibility and constraint satisfaction given an unknown but bounded disturbance and perfect state information. In the first extension, this controller is modified to account for an unknown but bounded state estimation error. As an example, a simple estimator is proposed and analyzed to provide the necessary error bounds. Furthermore, it is shown that delayed state information can be handled using the same method. These analyses depend on knowledge of bounds on the measurement and disturbance uncertainties. The second extension provides a method of estimating these bounds using available data, providing an adaptive form of the controller for cases where the error levels are poorly known a priori.},\\n\\tlanguage = {en},\\n\\turldate = {2021-02-01},\\n\\tbooktitle = {Proceedings of the 2005, {American} {Control} {Conference}, 2005.},\\n\\tpublisher = {IEEE},\\n\\tauthor = {Richards, A. and How, J.},\\n\\tyear = {2005},\\n\\tpages = {268--273},\\n}\\n\\n\",\"author_short\":[\"Richards, A.\",\"How, J.\"],\"key\":\"richards_robust_2005\",\"id\":\"richards_robust_2005\",\"bibbaseid\":\"richards-how-robustmodelpredictivecontrolwithimperfectinformation-2005\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://ieeexplore.ieee.org/document/1469944/\"},\"metadata\":{\"authorlinks\":{}},\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control\",\"doi\":\"10.1109/IROS.2018.8594448\",\"abstract\":\"This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20-30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.\",\"booktitle\":\"2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Carlo\"],\"firstnames\":[\"J.\",\"Di\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wensing\"],\"firstnames\":[\"P.\",\"M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Katz\"],\"firstnames\":[\"B.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Bledt\"],\"firstnames\":[\"G.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Kim\"],\"firstnames\":[\"S.\"],\"suffixes\":[]}],\"month\":\"October\",\"year\":\"2018\",\"note\":\"ISSN: 2153-0866\",\"keywords\":\"Convex functions, Dynamics, Legged locomotion, MIT cheetah 3, Predictive control, Predictive models, Robot kinematics, convex model-predictive control, convex optimization, convex programming, dynamic locomotion, ground reaction force planning problems, legged locomotion, predictive control, robot dynamics, torque control, torque-controlled quadruped robot\",\"pages\":\"1–9\",\"bibtex\":\"@inproceedings{carlo_dynamic_2018,\\n\\ttitle = {Dynamic {Locomotion} in the {MIT} {Cheetah} 3 {Through} {Convex} {Model}-{Predictive} {Control}},\\n\\tdoi = {10.1109/IROS.2018.8594448},\\n\\tabstract = {This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20-30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.},\\n\\tbooktitle = {2018 {IEEE}/{RSJ} {International} {Conference} on {Intelligent} {Robots} and {Systems} ({IROS})},\\n\\tauthor = {Carlo, J. Di and Wensing, P. M. and Katz, B. and Bledt, G. and Kim, S.},\\n\\tmonth = oct,\\n\\tyear = {2018},\\n\\tnote = {ISSN: 2153-0866},\\n\\tkeywords = {Convex functions, Dynamics, Legged locomotion, MIT cheetah 3, Predictive control, Predictive models, Robot kinematics, convex model-predictive control, convex optimization, convex programming, dynamic locomotion, ground reaction force planning problems, legged locomotion, predictive control, robot dynamics, torque control, torque-controlled quadruped robot},\\n\\tpages = {1--9},\\n}\\n\\n\",\"author_short\":[\"Carlo, J. D.\",\"Wensing, P. M.\",\"Katz, B.\",\"Bledt, G.\",\"Kim, S.\"],\"key\":\"carlo_dynamic_2018\",\"id\":\"carlo_dynamic_2018\",\"bibbaseid\":\"carlo-wensing-katz-bledt-kim-dynamiclocomotioninthemitcheetah3throughconvexmodelpredictivecontrol-2018\",\"role\":\"author\",\"urls\":{},\"keyword\":[\"Convex functions\",\"Dynamics\",\"Legged locomotion\",\"MIT cheetah 3\",\"Predictive control\",\"Predictive models\",\"Robot kinematics\",\"convex model-predictive control\",\"convex optimization\",\"convex programming\",\"dynamic locomotion\",\"ground reaction force planning problems\",\"legged locomotion\",\"predictive control\",\"robot dynamics\",\"torque control\",\"torque-controlled quadruped robot\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Learning a Contact-Adaptive Controller for Robust, Efficient Legged Locomotion\",\"url\":\"http://arxiv.org/abs/2009.10019\",\"abstract\":\"We present a hierarchical framework that combines model-based control and reinforcement learning (RL) to synthesize robust controllers for a quadruped (the Unitree Laikago). The system consists of a high-level controller that learns to choose from a set of primitives in response to changes in the environment and a low-level controller that utilizes an established control method to robustly execute the primitives. Our framework learns a controller that can adapt to challenging environmental changes on the fly, including novel scenarios not seen during training. The learned controller is up to 85 percent more energy efficient and is more robust compared to baseline methods. We also deploy the controller on a physical robot without any randomization or adaptation scheme.\",\"language\":\"en\",\"urldate\":\"2021-01-10\",\"journal\":\"arXiv:2009.10019 [cs]\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Da\"],\"firstnames\":[\"Xingye\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Xie\"],\"firstnames\":[\"Zhaoming\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Hoeller\"],\"firstnames\":[\"David\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Boots\"],\"firstnames\":[\"Byron\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Anandkumar\"],\"firstnames\":[\"Animashree\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Zhu\"],\"firstnames\":[\"Yuke\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Babich\"],\"firstnames\":[\"Buck\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Garg\"],\"firstnames\":[\"Animesh\"],\"suffixes\":[]}],\"month\":\"November\",\"year\":\"2020\",\"note\":\"arXiv: 2009.10019\",\"keywords\":\"Computer Science - Machine Learning, Computer Science - Robotics\",\"bibtex\":\"@article{da_learning_2020,\\n\\ttitle = {Learning a {Contact}-{Adaptive} {Controller} for {Robust}, {Efficient} {Legged} {Locomotion}},\\n\\turl = {http://arxiv.org/abs/2009.10019},\\n\\tabstract = {We present a hierarchical framework that combines model-based control and reinforcement learning (RL) to synthesize robust controllers for a quadruped (the Unitree Laikago). The system consists of a high-level controller that learns to choose from a set of primitives in response to changes in the environment and a low-level controller that utilizes an established control method to robustly execute the primitives. Our framework learns a controller that can adapt to challenging environmental changes on the fly, including novel scenarios not seen during training. The learned controller is up to 85 percent more energy efficient and is more robust compared to baseline methods. We also deploy the controller on a physical robot without any randomization or adaptation scheme.},\\n\\tlanguage = {en},\\n\\turldate = {2021-01-10},\\n\\tjournal = {arXiv:2009.10019 [cs]},\\n\\tauthor = {Da, Xingye and Xie, Zhaoming and Hoeller, David and Boots, Byron and Anandkumar, Animashree and Zhu, Yuke and Babich, Buck and Garg, Animesh},\\n\\tmonth = nov,\\n\\tyear = {2020},\\n\\tnote = {arXiv: 2009.10019},\\n\\tkeywords = {Computer Science - Machine Learning, Computer Science - Robotics},\\n}\\n\\n\",\"author_short\":[\"Da, X.\",\"Xie, Z.\",\"Hoeller, D.\",\"Boots, B.\",\"Anandkumar, A.\",\"Zhu, Y.\",\"Babich, B.\",\"Garg, A.\"],\"key\":\"da_learning_2020\",\"id\":\"da_learning_2020\",\"bibbaseid\":\"da-xie-hoeller-boots-anandkumar-zhu-babich-garg-learningacontactadaptivecontrollerforrobustefficientleggedlocomotion-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://arxiv.org/abs/2009.10019\"},\"keyword\":[\"Computer Science - Machine Learning\",\"Computer Science - Robotics\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"address\":\"Chicago, IL, USA\",\"title\":\"An invariance principle for nonlinear hybrid and impulsive dynamical systems\",\"isbn\":\"978-0-7803-5519-4\",\"url\":\"http://ieeexplore.ieee.org/document/879139/\",\"doi\":\"10.1109/ACC.2000.879139\",\"abstract\":\"In this paper we develop an invariance principle for dynamical systems possessing leftcontinuous ows. Speciÿcally, we show that left-continuity of the system trajectories in time for each ÿxed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi-inÿnite interval are su cient for establishing an invariance principle for hybrid and impulsive dynamical systems. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.\",\"language\":\"en\",\"urldate\":\"2020-12-31\",\"booktitle\":\"Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334)\",\"publisher\":\"IEEE\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Chellaboina\"],\"firstnames\":[\"V.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Bhat\"],\"firstnames\":[\"S.P.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Haddad\"],\"firstnames\":[\"W.M.\"],\"suffixes\":[]}],\"year\":\"2000\",\"pages\":\"3116–3122 vol.5\",\"bibtex\":\"@inproceedings{chellaboina_invariance_2000,\\n\\taddress = {Chicago, IL, USA},\\n\\ttitle = {An invariance principle for nonlinear hybrid and impulsive dynamical systems},\\n\\tisbn = {978-0-7803-5519-4},\\n\\turl = {http://ieeexplore.ieee.org/document/879139/},\\n\\tdoi = {10.1109/ACC.2000.879139},\\n\\tabstract = {In this paper we develop an invariance principle for dynamical systems possessing leftcontinuous ows. Speciÿcally, we show that left-continuity of the system trajectories in time for each ÿxed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi-inÿnite interval are su cient for establishing an invariance principle for hybrid and impulsive dynamical systems. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.},\\n\\tlanguage = {en},\\n\\turldate = {2020-12-31},\\n\\tbooktitle = {Proceedings of the 2000 {American} {Control} {Conference}. {ACC} ({IEEE} {Cat}. {No}.{00CH36334})},\\n\\tpublisher = {IEEE},\\n\\tauthor = {Chellaboina, V. and Bhat, S.P. and Haddad, W.M.},\\n\\tyear = {2000},\\n\\tpages = {3116--3122 vol.5},\\n}\\n\\n\",\"author_short\":[\"Chellaboina, V.\",\"Bhat, S.\",\"Haddad, W.\"],\"key\":\"chellaboina_invariance_2000\",\"id\":\"chellaboina_invariance_2000\",\"bibbaseid\":\"chellaboina-bhat-haddad-aninvarianceprinciplefornonlinearhybridandimpulsivedynamicalsystems-2000\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://ieeexplore.ieee.org/document/879139/\"},\"metadata\":{\"authorlinks\":{}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models\",\"volume\":\"49\",\"issn\":\"1558-2523\",\"doi\":\"10.1109/TAC.2004.831175\",\"abstract\":\"A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented. Both fixed and fast sampling are considered. In each case, sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete-time plant models also stabilizes the exact discrete-time plant model for sufficiently small integration and/or sampling periods. Previous results in the literature are extended to cover: 1) continuous-time plants modeled as differential inclusions; 2) general approximate discrete-time plant models; 3) dynamical discontinuous controllers modeled as difference inclusions; and 4) stability with respect to closed arbitrary (not necessarily compact) sets.\",\"number\":\"7\",\"journal\":\"IEEE Transactions on Automatic Control\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Nesic\"],\"firstnames\":[\"D.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Teel\"],\"firstnames\":[\"A.\",\"R.\"],\"suffixes\":[]}],\"month\":\"July\",\"year\":\"2004\",\"note\":\"Conference Name: IEEE Transactions on Automatic Control\",\"keywords\":\"Australia Council, Control design, Feedback control, Hardware, Lyapunov method, Lyapunov methods, Military computing, Robustness, Sampling methods, Stability, Sufficient conditions, continuous time systems, continuous-time plants, control system synthesis, discrete time systems, discrete-time models, dynamical discontinuous controllers, fast sampling, fixed sampling, nonlinear control systems, nonlinear sampled-data systems stability, sampled data systems, sampled-data differential inclusions, stability\",\"pages\":\"1103–1122\",\"bibtex\":\"@article{nesic_framework_2004,\\n\\ttitle = {A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models},\\n\\tvolume = {49},\\n\\tissn = {1558-2523},\\n\\tdoi = {10.1109/TAC.2004.831175},\\n\\tabstract = {A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented. Both fixed and fast sampling are considered. In each case, sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete-time plant models also stabilizes the exact discrete-time plant model for sufficiently small integration and/or sampling periods. Previous results in the literature are extended to cover: 1) continuous-time plants modeled as differential inclusions; 2) general approximate discrete-time plant models; 3) dynamical discontinuous controllers modeled as difference inclusions; and 4) stability with respect to closed arbitrary (not necessarily compact) sets.},\\n\\tnumber = {7},\\n\\tjournal = {IEEE Transactions on Automatic Control},\\n\\tauthor = {Nesic, D. and Teel, A. R.},\\n\\tmonth = jul,\\n\\tyear = {2004},\\n\\tnote = {Conference Name: IEEE Transactions on Automatic Control},\\n\\tkeywords = {Australia Council, Control design, Feedback control, Hardware, Lyapunov method, Lyapunov methods, Military computing, Robustness, Sampling methods, Stability, Sufficient conditions, continuous time systems, continuous-time plants, control system synthesis, discrete time systems, discrete-time models, dynamical discontinuous controllers, fast sampling, fixed sampling, nonlinear control systems, nonlinear sampled-data systems stability, sampled data systems, sampled-data differential inclusions, stability},\\n\\tpages = {1103--1122},\\n}\\n\\n\",\"author_short\":[\"Nesic, D.\",\"Teel, A. R.\"],\"key\":\"nesic_framework_2004\",\"id\":\"nesic_framework_2004\",\"bibbaseid\":\"nesic-teel-aframeworkforstabilizationofnonlinearsampleddatasystemsbasedontheirapproximatediscretetimemodels-2004\",\"role\":\"author\",\"urls\":{},\"keyword\":[\"Australia Council\",\"Control design\",\"Feedback control\",\"Hardware\",\"Lyapunov method\",\"Lyapunov methods\",\"Military computing\",\"Robustness\",\"Sampling methods\",\"Stability\",\"Sufficient conditions\",\"continuous time systems\",\"continuous-time plants\",\"control system synthesis\",\"discrete time systems\",\"discrete-time models\",\"dynamical discontinuous controllers\",\"fast sampling\",\"fixed sampling\",\"nonlinear control systems\",\"nonlinear sampled-data systems stability\",\"sampled data systems\",\"sampled-data differential inclusions\",\"stability\"],\"metadata\":{\"authorlinks\":{}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations\",\"volume\":\"38\",\"issn\":\"0167-6911\",\"url\":\"http://www.sciencedirect.com/science/article/pii/S0167691199000730\",\"doi\":\"10.1016/S0167-6911(99)00073-0\",\"abstract\":\"Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.\",\"language\":\"en\",\"number\":\"4\",\"urldate\":\"2020-12-29\",\"journal\":\"Systems & Control Letters\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Nešić\"],\"firstnames\":[\"D.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Teel\"],\"firstnames\":[\"A.\",\"R.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Kokotović\"],\"firstnames\":[\"P.\",\"V.\"],\"suffixes\":[]}],\"month\":\"December\",\"year\":\"1999\",\"keywords\":\"Discrete time, Nonlinear, Sampled data, Stabilization\",\"pages\":\"259–270\",\"bibtex\":\"@article{nesic_sufficient_1999,\\n\\ttitle = {Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations},\\n\\tvolume = {38},\\n\\tissn = {0167-6911},\\n\\turl = {http://www.sciencedirect.com/science/article/pii/S0167691199000730},\\n\\tdoi = {10.1016/S0167-6911(99)00073-0},\\n\\tabstract = {Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.},\\n\\tlanguage = {en},\\n\\tnumber = {4},\\n\\turldate = {2020-12-29},\\n\\tjournal = {Systems \\\\& Control Letters},\\n\\tauthor = {Nešić, D. and Teel, A. R. and Kokotović, P. V.},\\n\\tmonth = dec,\\n\\tyear = {1999},\\n\\tkeywords = {Discrete time, Nonlinear, Sampled data, Stabilization},\\n\\tpages = {259--270},\\n}\\n\\n\",\"author_short\":[\"Nešić, D.\",\"Teel, A. R.\",\"Kokotović, P. V.\"],\"key\":\"nesic_sufficient_1999\",\"id\":\"nesic_sufficient_1999\",\"bibbaseid\":\"nei-teel-kokotovi-sufficientconditionsforstabilizationofsampleddatanonlinearsystemsviadiscretetimeapproximations-1999\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://www.sciencedirect.com/science/article/pii/S0167691199000730\"},\"keyword\":[\"Discrete time\",\"Nonlinear\",\"Sampled data\",\"Stabilization\"],\"metadata\":{\"authorlinks\":{}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"At the Interface of Algebra and Statistics\",\"url\":\"http://arxiv.org/abs/2004.05631\",\"abstract\":\"This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture \\\"concepts\\\" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the \\\"fixed points\\\" of a morphism with its adjoint encode interesting information.\",\"language\":\"en\",\"urldate\":\"2020-12-28\",\"journal\":\"arXiv:2004.05631 [quant-ph, stat]\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Bradley\"],\"firstnames\":[\"Tai-Danae\"],\"suffixes\":[]}],\"month\":\"April\",\"year\":\"2020\",\"note\":\"arXiv: 2004.05631\",\"keywords\":\"Computer Science - Machine Learning, Mathematics - Category Theory, Quantum Physics, Statistics - Machine Learning\",\"bibtex\":\"@article{bradley_at_2020,\\n\\ttitle = {At the {Interface} of {Algebra} and {Statistics}},\\n\\turl = {http://arxiv.org/abs/2004.05631},\\n\\tabstract = {This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture \\\"concepts\\\" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the \\\"fixed points\\\" of a morphism with its adjoint encode interesting information.},\\n\\tlanguage = {en},\\n\\turldate = {2020-12-28},\\n\\tjournal = {arXiv:2004.05631 [quant-ph, stat]},\\n\\tauthor = {Bradley, Tai-Danae},\\n\\tmonth = apr,\\n\\tyear = {2020},\\n\\tnote = {arXiv: 2004.05631},\\n\\tkeywords = {Computer Science - Machine Learning, Mathematics - Category Theory, Quantum Physics, Statistics - Machine Learning},\\n}\\n\\n\",\"author_short\":[\"Bradley, T.\"],\"key\":\"bradley_at_2020\",\"id\":\"bradley_at_2020\",\"bibbaseid\":\"bradley-attheinterfaceofalgebraandstatistics-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://arxiv.org/abs/2004.05631\"},\"keyword\":[\"Computer Science - Machine Learning\",\"Mathematics - Category Theory\",\"Quantum Physics\",\"Statistics - Machine Learning\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"book\",\"type\":\"book\",\"title\":\"Towards a Geometric Theory of Hybrid Systems.\",\"volume\":\"12\",\"abstract\":\"We propose a framework for a geometric theory of hybrid systems. Given a deterministic, non-blocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non-smooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it is due to nonsmoothness of the hybrid flow. We introduce the notion of topological equivalence of hybrid systems and locally classify isolated Zeno states in dimension two.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Simic\"],\"firstnames\":[\"Slobodan\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Johansson\"],\"firstnames\":[\"Karl\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Sastry\"],\"firstnames\":[\"Shankar\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Lygeros\"],\"firstnames\":[\"John\"],\"suffixes\":[]}],\"month\":\"January\",\"year\":\"2000\",\"note\":\"Journal Abbreviation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Pages: 436 Publication Title: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms\",\"bibtex\":\"@book{simic_towards_2000,\\n\\ttitle = {Towards a {Geometric} {Theory} of {Hybrid} {Systems}.},\\n\\tvolume = {12},\\n\\tabstract = {We propose a framework for a geometric theory of hybrid systems. Given a deterministic, non-blocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non-smooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it is due to nonsmoothness of the hybrid flow. We introduce the notion of topological equivalence of hybrid systems and locally classify isolated Zeno states in dimension two.},\\n\\tauthor = {Simic, Slobodan and Johansson, Karl and Sastry, Shankar and Lygeros, John},\\n\\tmonth = jan,\\n\\tyear = {2000},\\n\\tnote = {Journal Abbreviation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms\\nPages: 436\\nPublication Title: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms},\\n}\\n\\n\",\"author_short\":[\"Simic, S.\",\"Johansson, K.\",\"Sastry, S.\",\"Lygeros, J.\"],\"key\":\"simic_towards_2000\",\"id\":\"simic_towards_2000\",\"bibbaseid\":\"simic-johansson-sastry-lygeros-towardsageometrictheoryofhybridsystems-2000\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Global controllability tests for geometric hybrid control systems\",\"url\":\"http://arxiv.org/abs/1905.02490\",\"abstract\":\"This paper introduces a novel geometric framework to define and study hybrid systems. We exploit the geometry and topology of the set of jump points, where the instantaneous change of dynamics takes place, in order to gain controllability for the system. This approach allows us to describe new global controllability tests for hybrid control systems. We illustrate these results with several examples where none of the continuous control systems are controllable, but the associated hybrid system is controllable because of the characteristics of the jump set.\",\"language\":\"en\",\"urldate\":\"2020-12-28\",\"journal\":\"arXiv:1905.02490 [math]\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Liñán\"],\"firstnames\":[\"M.\",\"Barbero\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cortés\"],\"firstnames\":[\"J.\"],\"suffixes\":[]},{\"propositions\":[\"de\"],\"lastnames\":[\"Diego\"],\"firstnames\":[\"D.\",\"Martín\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Martínez\"],\"firstnames\":[\"S.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Lecanda\"],\"firstnames\":[\"M.\",\"C.\",\"Muñoz\"],\"suffixes\":[]}],\"month\":\"June\",\"year\":\"2020\",\"note\":\"arXiv: 1905.02490\",\"keywords\":\"93C30, 93B05, 93B27, Mathematics - Differential Geometry, Mathematics - Optimization and Control\",\"bibtex\":\"@article{linan_global_2020,\\n\\ttitle = {Global controllability tests for geometric hybrid control systems},\\n\\turl = {http://arxiv.org/abs/1905.02490},\\n\\tabstract = {This paper introduces a novel geometric framework to define and study hybrid systems. We exploit the geometry and topology of the set of jump points, where the instantaneous change of dynamics takes place, in order to gain controllability for the system. This approach allows us to describe new global controllability tests for hybrid control systems. We illustrate these results with several examples where none of the continuous control systems are controllable, but the associated hybrid system is controllable because of the characteristics of the jump set.},\\n\\tlanguage = {en},\\n\\turldate = {2020-12-28},\\n\\tjournal = {arXiv:1905.02490 [math]},\\n\\tauthor = {Liñán, M. Barbero and Cortés, J. and de Diego, D. Martín and Martínez, S. and Lecanda, M. C. Muñoz},\\n\\tmonth = jun,\\n\\tyear = {2020},\\n\\tnote = {arXiv: 1905.02490},\\n\\tkeywords = {93C30, 93B05, 93B27, Mathematics - Differential Geometry, Mathematics - Optimization and Control},\\n}\\n\\n\",\"author_short\":[\"Liñán, M. B.\",\"Cortés, J.\",\"de Diego, D. M.\",\"Martínez, S.\",\"Lecanda, M. C. M.\"],\"key\":\"linan_global_2020\",\"id\":\"linan_global_2020\",\"bibbaseid\":\"lin-corts-dediego-martnez-lecanda-globalcontrollabilitytestsforgeometrichybridcontrolsystems-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://arxiv.org/abs/1905.02490\"},\"keyword\":[\"93C30\",\"93B05\",\"93B27\",\"Mathematics - Differential Geometry\",\"Mathematics - Optimization and Control\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"A unified geometric approach to modeling and control of constrained mechanical systems\",\"volume\":\"18\",\"issn\":\"2374-958X\",\"doi\":\"10.1109/TRA.2002.802207\",\"abstract\":\"Dynamic control of constrained mechanical systems, such as robotic manipulators under end-effector constraints, parallel manipulators, and multifingered robotic hands under closure constraints have been classic problems in robotics research. In this paper, we provide a unified geometric framework for modeling, analysis, and control of constrained mechanical systems. Starting with the constraint, we define two canonical subspaces, namely the subspace of constraint forces and the tangent space of the constraint manifold for holonomic constraint. Using the kinetic energy metric, we define the remaining subspaces and show explicitly the relations among these subspaces. We project the Euler-Lagrange equation of a constrained mechanical system into two orthogonal components and give geometric and physical interpretations of the projected equations. Based on the projected equations, a unified and asymptotically stable hybrid position/force-control algorithm is proposed, along with experimental results for several practical examples. In the case of nonholonomic constraints, we show that the equations can be projected to the distribution/codistribution associated with the constraints and the control law reduces to hybrid velocity/force control.\",\"number\":\"4\",\"journal\":\"IEEE Transactions on Robotics and Automation\",\"author\":[{\"firstnames\":[\"Guanfeng\"],\"propositions\":[],\"lastnames\":[\"Liu\"],\"suffixes\":[]},{\"firstnames\":[\"Zexiang\"],\"propositions\":[],\"lastnames\":[\"Li\"],\"suffixes\":[]}],\"month\":\"August\",\"year\":\"2002\",\"note\":\"1000\",\"keywords\":\"Control system analysis, Control systems, Equations, Euler-Lagrange equation, Force control, Manipulator dynamics, Mechanical systems, Orbital robotics, Parallel robots, Solid modeling, Subspace constraints, asymptotic stability, canonical subspaces, closure constraints, constrained mechanical systems, constraint forces subspace, constraint manifold tangent space, constraint theory, control, control system analysis, dexterous manipulators, distribution/codistribution, dynamic control, end-effector constraints, force control, holonomic constraint, hybrid velocity/force control, industrial manipulators, kinetic energy metric, manipulator dynamics, modeling, multifingered robotic hands, nonholonomic constraints, orthogonal components, parallel manipulators, position control, robotic manipulators, unified asymptotically stable hybrid position/force-control algorithm, unified geometric approach, velocity control\",\"pages\":\"574–587\",\"bibtex\":\"@article{guanfeng_liu_unified_2002,\\n\\ttitle = {A unified geometric approach to modeling and control of constrained mechanical systems},\\n\\tvolume = {18},\\n\\tissn = {2374-958X},\\n\\tdoi = {10.1109/TRA.2002.802207},\\n\\tabstract = {Dynamic control of constrained mechanical systems, such as robotic manipulators under end-effector constraints, parallel manipulators, and multifingered robotic hands under closure constraints have been classic problems in robotics research. In this paper, we provide a unified geometric framework for modeling, analysis, and control of constrained mechanical systems. Starting with the constraint, we define two canonical subspaces, namely the subspace of constraint forces and the tangent space of the constraint manifold for holonomic constraint. Using the kinetic energy metric, we define the remaining subspaces and show explicitly the relations among these subspaces. We project the Euler-Lagrange equation of a constrained mechanical system into two orthogonal components and give geometric and physical interpretations of the projected equations. Based on the projected equations, a unified and asymptotically stable hybrid position/force-control algorithm is proposed, along with experimental results for several practical examples. In the case of nonholonomic constraints, we show that the equations can be projected to the distribution/codistribution associated with the constraints and the control law reduces to hybrid velocity/force control.},\\n\\tnumber = {4},\\n\\tjournal = {IEEE Transactions on Robotics and Automation},\\n\\tauthor = {Guanfeng Liu and Zexiang Li},\\n\\tmonth = aug,\\n\\tyear = {2002},\\n\\tnote = {1000},\\n\\tkeywords = {Control system analysis, Control systems, Equations, Euler-Lagrange equation, Force control, Manipulator dynamics, Mechanical systems, Orbital robotics, Parallel robots, Solid modeling, Subspace constraints, asymptotic stability, canonical subspaces, closure constraints, constrained mechanical systems, constraint forces subspace, constraint manifold tangent space, constraint theory, control, control system analysis, dexterous manipulators, distribution/codistribution, dynamic control, end-effector constraints, force control, holonomic constraint, hybrid velocity/force control, industrial manipulators, kinetic energy metric, manipulator dynamics, modeling, multifingered robotic hands, nonholonomic constraints, orthogonal components, parallel manipulators, position control, robotic manipulators, unified asymptotically stable hybrid position/force-control algorithm, unified geometric approach, velocity control},\\n\\tpages = {574--587},\\n}\\n\\n\",\"author_short\":[\"Liu, G.\",\"Li, Z.\"],\"key\":\"guanfeng_liu_unified_2002\",\"id\":\"guanfeng_liu_unified_2002\",\"bibbaseid\":\"liu-li-aunifiedgeometricapproachtomodelingandcontrolofconstrainedmechanicalsystems-2002\",\"role\":\"author\",\"urls\":{},\"keyword\":[\"Control system analysis\",\"Control systems\",\"Equations\",\"Euler-Lagrange equation\",\"Force control\",\"Manipulator dynamics\",\"Mechanical systems\",\"Orbital robotics\",\"Parallel robots\",\"Solid modeling\",\"Subspace constraints\",\"asymptotic stability\",\"canonical subspaces\",\"closure constraints\",\"constrained mechanical systems\",\"constraint forces subspace\",\"constraint manifold tangent space\",\"constraint theory\",\"control\",\"control system analysis\",\"dexterous manipulators\",\"distribution/codistribution\",\"dynamic control\",\"end-effector constraints\",\"force control\",\"holonomic constraint\",\"hybrid velocity/force control\",\"industrial manipulators\",\"kinetic energy metric\",\"manipulator dynamics\",\"modeling\",\"multifingered robotic hands\",\"nonholonomic constraints\",\"orthogonal components\",\"parallel manipulators\",\"position control\",\"robotic manipulators\",\"unified asymptotically stable hybrid position/force-control algorithm\",\"unified geometric approach\",\"velocity control\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"incollection\",\"type\":\"incollection\",\"address\":\"Dordrecht\",\"title\":\"FLOER HOMOLOGY, DYNAMICS AND GROUPS\",\"volume\":\"217\",\"isbn\":\"978-1-4020-4272-0\",\"url\":\"http://link.springer.com/10.1007/1-4020-4266-3_09\",\"abstract\":\"We discuss some recent results on algebraic properties of the group of Hamiltonian diffeomorphisms of a symplectic manifold. We focus on two topics which lie at the interface between Floer theory and dynamics: 1) Restrictions on Hamiltonian actions of finitely generated groups, including a Hamiltonian version of the Zimmer program dealing with actions of lattices; 2) Quasi-morphisms on the group of Hamiltonian diffeomorphisms. The unifying theme is the study of distortion of cyclic and one-parameter subgroups with respect to various metrics on the group of Hamiltonian diffeomorphisms.\",\"language\":\"en\",\"urldate\":\"2020-11-13\",\"booktitle\":\"Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology\",\"publisher\":\"Kluwer Academic Publishers\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Polterovich\"],\"firstnames\":[\"Leonid\"],\"suffixes\":[]}],\"editor\":[{\"propositions\":[],\"lastnames\":[\"Biran\"],\"firstnames\":[\"Paul\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cornea\"],\"firstnames\":[\"Octav\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Lalonde\"],\"firstnames\":[\"François\"],\"suffixes\":[]}],\"year\":\"2006\",\"doi\":\"10.1007/1-4020-4266-3_09\",\"note\":\"Series Title: NATO Science Series II: Mathematics, Physics and Chemistry\",\"pages\":\"417–438\",\"bibtex\":\"@incollection{biran_floer_2006,\\n\\taddress = {Dordrecht},\\n\\ttitle = {{FLOER} {HOMOLOGY}, {DYNAMICS} {AND} {GROUPS}},\\n\\tvolume = {217},\\n\\tisbn = {978-1-4020-4272-0},\\n\\turl = {http://link.springer.com/10.1007/1-4020-4266-3_09},\\n\\tabstract = {We discuss some recent results on algebraic properties of the group of Hamiltonian diffeomorphisms of a symplectic manifold. We focus on two topics which lie at the interface between Floer theory and dynamics: 1) Restrictions on Hamiltonian actions of finitely generated groups, including a Hamiltonian version of the Zimmer program dealing with actions of lattices; 2) Quasi-morphisms on the group of Hamiltonian diffeomorphisms. The unifying theme is the study of distortion of cyclic and one-parameter subgroups with respect to various metrics on the group of Hamiltonian diffeomorphisms.},\\n\\tlanguage = {en},\\n\\turldate = {2020-11-13},\\n\\tbooktitle = {Morse {Theoretic} {Methods} in {Nonlinear} {Analysis} and in {Symplectic} {Topology}},\\n\\tpublisher = {Kluwer Academic Publishers},\\n\\tauthor = {Polterovich, Leonid},\\n\\teditor = {Biran, Paul and Cornea, Octav and Lalonde, François},\\n\\tyear = {2006},\\n\\tdoi = {10.1007/1-4020-4266-3_09},\\n\\tnote = {Series Title: NATO Science Series II: Mathematics, Physics and Chemistry},\\n\\tpages = {417--438},\\n}\\n\\n\",\"author_short\":[\"Polterovich, L.\"],\"editor_short\":[\"Biran, P.\",\"Cornea, O.\",\"Lalonde, F.\"],\"key\":\"biran_floer_2006\",\"id\":\"biran_floer_2006\",\"bibbaseid\":\"polterovich-floerhomologydynamicsandgroups-2006\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://link.springer.com/10.1007/1-4020-4266-3_09\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"HOMOLOGY THEORY AND DYNAMICAL SYSTEMS\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Sullivan\"],\"firstnames\":[\"D\"],\"suffixes\":[]}],\"pages\":\"24\",\"bibtex\":\"@article{sullivan_homology_nodate,\\n\\ttitle = {{HOMOLOGY} {THEORY} {AND} {DYNAMICAL} {SYSTEMS}},\\n\\tlanguage = {en},\\n\\tauthor = {Sullivan, D},\\n\\tpages = {24},\\n}\\n\\n\",\"author_short\":[\"Sullivan, D\"],\"key\":\"sullivan_homology_nodate\",\"id\":\"sullivan_homology_nodate\",\"bibbaseid\":\"sullivan-homologytheoryanddynamicalsystems\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Sequential Composition of Dynamically Dexterous Robot Behaviors\",\"volume\":\"18\",\"issn\":\"0278-3649, 1741-3176\",\"url\":\"http://journals.sagepub.com/doi/10.1177/02783649922066385\",\"doi\":\"10.1177/02783649922066385\",\"abstract\":\"We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.\",\"language\":\"en\",\"number\":\"6\",\"urldate\":\"2020-10-20\",\"journal\":\"The International Journal of Robotics Research\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Burridge\"],\"firstnames\":[\"R.\",\"R.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Rizzi\"],\"firstnames\":[\"A.\",\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Koditschek\"],\"firstnames\":[\"D.\",\"E.\"],\"suffixes\":[]}],\"month\":\"June\",\"year\":\"1999\",\"pages\":\"534–555\",\"bibtex\":\"@article{burridge_sequential_1999,\\n\\ttitle = {Sequential {Composition} of {Dynamically} {Dexterous} {Robot} {Behaviors}},\\n\\tvolume = {18},\\n\\tissn = {0278-3649, 1741-3176},\\n\\turl = {http://journals.sagepub.com/doi/10.1177/02783649922066385},\\n\\tdoi = {10.1177/02783649922066385},\\n\\tabstract = {We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.},\\n\\tlanguage = {en},\\n\\tnumber = {6},\\n\\turldate = {2020-10-20},\\n\\tjournal = {The International Journal of Robotics Research},\\n\\tauthor = {Burridge, R. R. and Rizzi, A. A. and Koditschek, D. E.},\\n\\tmonth = jun,\\n\\tyear = {1999},\\n\\tpages = {534--555},\\n}\\n\\n\",\"author_short\":[\"Burridge, R. R.\",\"Rizzi, A. A.\",\"Koditschek, D. E.\"],\"key\":\"burridge_sequential_1999\",\"id\":\"burridge_sequential_1999\",\"bibbaseid\":\"burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://journals.sagepub.com/doi/10.1177/02783649922066385\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Sequential Composition of Dynamically Dexterous Robot Behaviors\",\"volume\":\"18\",\"issn\":\"0278-3649, 1741-3176\",\"url\":\"http://journals.sagepub.com/doi/10.1177/02783649922066385\",\"doi\":\"10.1177/02783649922066385\",\"abstract\":\"We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.\",\"language\":\"en\",\"number\":\"6\",\"urldate\":\"2020-07-10\",\"journal\":\"The International Journal of Robotics Research\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Burridge\"],\"firstnames\":[\"R.\",\"R.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Rizzi\"],\"firstnames\":[\"A.\",\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Koditschek\"],\"firstnames\":[\"D.\",\"E.\"],\"suffixes\":[]}],\"month\":\"June\",\"year\":\"1999\",\"note\":\"5\",\"pages\":\"534–555\",\"bibtex\":\"@article{burridge_sequential_1999-1,\\n\\ttitle = {Sequential {Composition} of {Dynamically} {Dexterous} {Robot} {Behaviors}},\\n\\tvolume = {18},\\n\\tissn = {0278-3649, 1741-3176},\\n\\turl = {http://journals.sagepub.com/doi/10.1177/02783649922066385},\\n\\tdoi = {10.1177/02783649922066385},\\n\\tabstract = {We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.},\\n\\tlanguage = {en},\\n\\tnumber = {6},\\n\\turldate = {2020-07-10},\\n\\tjournal = {The International Journal of Robotics Research},\\n\\tauthor = {Burridge, R. R. and Rizzi, A. A. and Koditschek, D. E.},\\n\\tmonth = jun,\\n\\tyear = {1999},\\n\\tnote = {5},\\n\\tpages = {534--555},\\n}\\n\\n\",\"author_short\":[\"Burridge, R. R.\",\"Rizzi, A. A.\",\"Koditschek, D. E.\"],\"key\":\"burridge_sequential_1999-1\",\"id\":\"burridge_sequential_1999-1\",\"bibbaseid\":\"burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://journals.sagepub.com/doi/10.1177/02783649922066385\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Adaptive Safety with Control Barrier Functions\",\"abstract\":\"Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunovbased methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the system’s state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an Adaptive Cruise Control (ACC) simulation.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Taylor\"],\"firstnames\":[\"Andrew\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ames\"],\"firstnames\":[\"Aaron\",\"D\"],\"suffixes\":[]}],\"pages\":\"7\",\"bibtex\":\"@article{taylor_adaptive_nodate,\\n\\ttitle = {Adaptive {Safety} with {Control} {Barrier} {Functions}},\\n\\tabstract = {Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunovbased methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the system’s state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an Adaptive Cruise Control (ACC) simulation.},\\n\\tlanguage = {en},\\n\\tauthor = {Taylor, Andrew and Ames, Aaron D},\\n\\tpages = {7},\\n}\\n\\n\",\"author_short\":[\"Taylor, A.\",\"Ames, A. D\"],\"key\":\"taylor_adaptive_nodate\",\"id\":\"taylor_adaptive_nodate\",\"bibbaseid\":\"taylor-ames-adaptivesafetywithcontrolbarrierfunctions\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"An Inverse Dynamics Approach to Control Lyapunov Functions\",\"abstract\":\"With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots. The primary focus of this paper is on the development of an alternative approach to the implementation of controllers utilizing control Lyapunov function based quadratic programs. This approach utilizes many of the desirable aspects from successful inverse dynamics based controllers in the literature, while also incorporating a variant of control Lyapunov functions that renders better convergence in the context of tracking outputs. The principal benefits of this formulation include a greater ability to add costs which regulate the resulting behavior of the robot. In addition, the model error-prone inertia matrix is used only once, in a non-inverted form. The result is a successful demonstration of the controller for walking in simulation, and applied on hardware in real-time for dynamic crouching.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Reher\"],\"firstnames\":[\"Jenna\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Kann\"],\"firstnames\":[\"Claudia\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ames\"],\"firstnames\":[\"Aaron\",\"D\"],\"suffixes\":[]}],\"pages\":\"8\",\"bibtex\":\"@article{reher_inverse_nodate,\\n\\ttitle = {An {Inverse} {Dynamics} {Approach} to {Control} {Lyapunov} {Functions}},\\n\\tabstract = {With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots. The primary focus of this paper is on the development of an alternative approach to the implementation of controllers utilizing control Lyapunov function based quadratic programs. This approach utilizes many of the desirable aspects from successful inverse dynamics based controllers in the literature, while also incorporating a variant of control Lyapunov functions that renders better convergence in the context of tracking outputs. The principal benefits of this formulation include a greater ability to add costs which regulate the resulting behavior of the robot. In addition, the model error-prone inertia matrix is used only once, in a non-inverted form. The result is a successful demonstration of the controller for walking in simulation, and applied on hardware in real-time for dynamic crouching.},\\n\\tlanguage = {en},\\n\\tauthor = {Reher, Jenna and Kann, Claudia and Ames, Aaron D},\\n\\tpages = {8},\\n}\\n\\n\",\"author_short\":[\"Reher, J.\",\"Kann, C.\",\"Ames, A. D\"],\"key\":\"reher_inverse_nodate\",\"id\":\"reher_inverse_nodate\",\"bibbaseid\":\"reher-kann-ames-aninversedynamicsapproachtocontrollyapunovfunctions\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Density Functions for Guaranteed Safety on Robotic Systems\",\"abstract\":\"The recent study on density functions as the dual of value functions for optimal control gives a new method for synthesizing safe controllers. A density function describes the state distribution in the state space, and its evolution follows the Liouville Partial Differential Equation (PDE). The duality between the density function and the value function in optimal control can be utilized to solve constrained optimal control problems with a primal-dual algorithm. This paper focuses on the application of the method on robotic systems and proposes an implementation of the primal-dual algorithm that is less computationally demanding than the method used in the literature. To be specific, we use kernel density estimation to estimate the density function, which scales better than the ODE approach in the literature and only requires a simulator instead of a dynamic model. The Hamilton Jacobi Bellman (HJB) PDE is solved with the finite element method in an implicit form, which accelerates the value iteration process. We show an application of the safe control synthesis with density functions on a segway control problem demonstrated experimentally.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Chen\"],\"firstnames\":[\"Yuxiao\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Singletary\"],\"firstnames\":[\"Andrew\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ames\"],\"firstnames\":[\"Aaron\",\"D\"],\"suffixes\":[]}],\"pages\":\"6\",\"bibtex\":\"@article{chen_density_nodate,\\n\\ttitle = {Density {Functions} for {Guaranteed} {Safety} on {Robotic} {Systems}},\\n\\tabstract = {The recent study on density functions as the dual of value functions for optimal control gives a new method for synthesizing safe controllers. A density function describes the state distribution in the state space, and its evolution follows the Liouville Partial Differential Equation (PDE). The duality between the density function and the value function in optimal control can be utilized to solve constrained optimal control problems with a primal-dual algorithm. This paper focuses on the application of the method on robotic systems and proposes an implementation of the primal-dual algorithm that is less computationally demanding than the method used in the literature. To be specific, we use kernel density estimation to estimate the density function, which scales better than the ODE approach in the literature and only requires a simulator instead of a dynamic model. The Hamilton Jacobi Bellman (HJB) PDE is solved with the finite element method in an implicit form, which accelerates the value iteration process. We show an application of the safe control synthesis with density functions on a segway control problem demonstrated experimentally.},\\n\\tlanguage = {en},\\n\\tauthor = {Chen, Yuxiao and Singletary, Andrew and Ames, Aaron D},\\n\\tpages = {6},\\n}\\n\\n\",\"author_short\":[\"Chen, Y.\",\"Singletary, A.\",\"Ames, A. D\"],\"key\":\"chen_density_nodate\",\"id\":\"chen_density_nodate\",\"bibbaseid\":\"chen-singletary-ames-densityfunctionsforguaranteedsafetyonroboticsystems\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"On a Converse Theorem for Finite-Time Lyapunov Functions to Estimate Domains of Attraction\",\"abstract\":\"The main result of the paper is a new converse theorem for finite-time Lyapunov functions. We show the existence of a finite-time Lyapunov function for an autonomous continuoustime nonlinear dynamical system if the origin of the system is asymptotically stable. Our proof extends the recent results in finite-time Lyapunov function theory by providing an alternative converse proof for the existence of finite-time Lyapunov functions. In particular, we show that given asymptotic stability of the origin, the linearized dynamics satisfy global finitetime Lyapunov function conditions hence proving the converse theorem. Using our results, we present a consolidated theory for using and constructing Lyapunov functions to certify system stability properties. We also propose a constructive algorithm to efficiently compute non-conservative estimates of the domain of attraction for nonlinear dynamical systems.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Pandey\"],\"firstnames\":[\"Ayush\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ames\"],\"firstnames\":[\"Aaron\",\"D\"],\"suffixes\":[]}],\"pages\":\"7\",\"bibtex\":\"@article{pandey_converse_nodate,\\n\\ttitle = {On a {Converse} {Theorem} for {Finite}-{Time} {Lyapunov} {Functions} to {Estimate} {Domains} of {Attraction}},\\n\\tabstract = {The main result of the paper is a new converse theorem for finite-time Lyapunov functions. We show the existence of a finite-time Lyapunov function for an autonomous continuoustime nonlinear dynamical system if the origin of the system is asymptotically stable. Our proof extends the recent results in finite-time Lyapunov function theory by providing an alternative converse proof for the existence of finite-time Lyapunov functions. In particular, we show that given asymptotic stability of the origin, the linearized dynamics satisfy global finitetime Lyapunov function conditions hence proving the converse theorem. Using our results, we present a consolidated theory for using and constructing Lyapunov functions to certify system stability properties. We also propose a constructive algorithm to efficiently compute non-conservative estimates of the domain of attraction for nonlinear dynamical systems.},\\n\\tlanguage = {en},\\n\\tauthor = {Pandey, Ayush and Ames, Aaron D},\\n\\tpages = {7},\\n}\\n\\n\",\"author_short\":[\"Pandey, A.\",\"Ames, A. D\"],\"key\":\"pandey_converse_nodate\",\"id\":\"pandey_converse_nodate\",\"bibbaseid\":\"pandey-ames-onaconversetheoremforfinitetimelyapunovfunctionstoestimatedomainsofattraction\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Invariant Sets for Integrators and Quadrotor Obstacle Avoidance\",\"abstract\":\"Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nthorder integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n ≤ 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Doeser\"],\"firstnames\":[\"Ludvig\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Nilsson\"],\"firstnames\":[\"Petter\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ames\"],\"firstnames\":[\"Aaron\",\"D\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Murray\"],\"firstnames\":[\"Richard\",\"M\"],\"suffixes\":[]}],\"pages\":\"8\",\"bibtex\":\"@article{doeser_invariant_nodate,\\n\\ttitle = {Invariant {Sets} for {Integrators} and {Quadrotor} {Obstacle} {Avoidance}},\\n\\tabstract = {Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nthorder integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n ≤ 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.},\\n\\tlanguage = {en},\\n\\tauthor = {Doeser, Ludvig and Nilsson, Petter and Ames, Aaron D and Murray, Richard M},\\n\\tpages = {8},\\n}\\n\\n\",\"author_short\":[\"Doeser, L.\",\"Nilsson, P.\",\"Ames, A. D\",\"Murray, R. M\"],\"key\":\"doeser_invariant_nodate\",\"id\":\"doeser_invariant_nodate\",\"bibbaseid\":\"doeser-nilsson-ames-murray-invariantsetsforintegratorsandquadrotorobstacleavoidance\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Lyapunov-Like Conditions for Tight Exit Probability Bounds through Comparison Theorems for SDEs\",\"abstract\":\"Computing upper bounds on exit probabilities—the probability that a system reaches certain “bad” sets—may assist decision-making in control of stochastic systems. Existing analytical bounds for systems described by stochastic differential equations are quite loose, especially for low-probability events, which limits their applicability in practical situations. In this paper we analyze why existing bounds are loose, and conclude that it is a fundamental issue with the underlying techniques based on martingale inequalities. As an alternative, we give comparison results for stochastic differential equations that via a Lyapunov-like function allow exit probabilities of an ndimensional system to be upper-bounded by an exit probability of a one-dimensional Ornstein-Uhlenbeck process. Even though no closed-form expression is known for the latter, it depends on three or four parameters and can be a priori tabulated for applications. We extend these ideas to the controlled setting and state a stochastic analogue of control barrier functions. The bounds are illustrated on numerical examples and are shown to be much tighter than those based on martingale inequalities.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Nilsson\"],\"firstnames\":[\"Petter\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ames\"],\"firstnames\":[\"Aaron\",\"D\"],\"suffixes\":[]}],\"pages\":\"7\",\"bibtex\":\"@article{nilsson_lyapunov-like_nodate,\\n\\ttitle = {Lyapunov-{Like} {Conditions} for {Tight} {Exit} {Probability} {Bounds} through {Comparison} {Theorems} for {SDEs}},\\n\\tabstract = {Computing upper bounds on exit probabilities—the probability that a system reaches certain “bad” sets—may assist decision-making in control of stochastic systems. Existing analytical bounds for systems described by stochastic differential equations are quite loose, especially for low-probability events, which limits their applicability in practical situations. In this paper we analyze why existing bounds are loose, and conclude that it is a fundamental issue with the underlying techniques based on martingale inequalities. As an alternative, we give comparison results for stochastic differential equations that via a Lyapunov-like function allow exit probabilities of an ndimensional system to be upper-bounded by an exit probability of a one-dimensional Ornstein-Uhlenbeck process. Even though no closed-form expression is known for the latter, it depends on three or four parameters and can be a priori tabulated for applications. We extend these ideas to the controlled setting and state a stochastic analogue of control barrier functions. The bounds are illustrated on numerical examples and are shown to be much tighter than those based on martingale inequalities.},\\n\\tlanguage = {en},\\n\\tauthor = {Nilsson, Petter and Ames, Aaron D},\\n\\tpages = {7},\\n}\\n\\n\",\"author_short\":[\"Nilsson, P.\",\"Ames, A. D\"],\"key\":\"nilsson_lyapunov-like_nodate\",\"id\":\"nilsson_lyapunov-like_nodate\",\"bibbaseid\":\"nilsson-ames-lyapunovlikeconditionsfortightexitprobabilityboundsthroughcomparisontheoremsforsdes\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Distributed Feedback Controllers for Stable Cooperative Locomotion of Quadrupedal Robots: A Virtual Constraint Approach\",\"abstract\":\"This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. The paper then generates modified and local virtual constraints for each agent that allow stable collaborative locomotion. Optimal distributed feedback controllers, based on nonlinear control and quadratic programming, are developed to impose the local virtual constraints. To demonstrate the power of the analytical foundation, an extensive numerical simulation for cooperative locomotion of two quadrupedal robots with robotic manipulators is presented. The numerical complex hybrid model has 64 continuous-time domains, 192 discretetime transitions, 96 state variables, and 36 control inputs.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Hamed\"],\"firstnames\":[\"Kaveh\",\"Akbari\"],\"suffixes\":[]}],\"pages\":\"8\",\"bibtex\":\"@article{hamed_distributed_nodate,\\n\\ttitle = {Distributed {Feedback} {Controllers} for {Stable} {Cooperative} {Locomotion} of {Quadrupedal} {Robots}: {A} {Virtual} {Constraint} {Approach}},\\n\\tabstract = {This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. The paper then generates modified and local virtual constraints for each agent that allow stable collaborative locomotion. Optimal distributed feedback controllers, based on nonlinear control and quadratic programming, are developed to impose the local virtual constraints. To demonstrate the power of the analytical foundation, an extensive numerical simulation for cooperative locomotion of two quadrupedal robots with robotic manipulators is presented. The numerical complex hybrid model has 64 continuous-time domains, 192 discretetime transitions, 96 state variables, and 36 control inputs.},\\n\\tlanguage = {en},\\n\\tauthor = {Hamed, Kaveh Akbari},\\n\\tpages = {8},\\n}\\n\\n\",\"author_short\":[\"Hamed, K. A.\"],\"key\":\"hamed_distributed_nodate\",\"id\":\"hamed_distributed_nodate\",\"bibbaseid\":\"hamed-distributedfeedbackcontrollersforstablecooperativelocomotionofquadrupedalrobotsavirtualconstraintapproach\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Optimal Safe Controller Synthesis: A Density Function Approach\",\"abstract\":\"This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value function. The density function follows the Liouville equation and is the dual of the value function, which satisfies Bellman’s optimality principle. Thanks to density functions, constraints over the distribution of states, such as safety constraints, can be posed straightforwardly in an optimal control problem. The constrained optimal control problem is then solved with a primal-dual algorithm. This formulation is extended to the case with external disturbances, and we show that the robust constrained optimal control can be solved with a modified primal-dual algorithm. We apply this formulation to the problem of finding the optimal safe controller that minimizes the cumulative intervention. An adaptive cruise control (ACC) example is used to demonstrate the efficacy of the proposed, wherein we compare the result of the density function approach with the conventional control barrier function (CBF) method.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Chen\"],\"firstnames\":[\"Yuxiao\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ahmadi\"],\"firstnames\":[\"Mohamadreza\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ames\"],\"firstnames\":[\"Aaron\",\"D\"],\"suffixes\":[]}],\"pages\":\"6\",\"bibtex\":\"@article{chen_optimal_nodate,\\n\\ttitle = {Optimal {Safe} {Controller} {Synthesis}: {A} {Density} {Function} {Approach}},\\n\\tabstract = {This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value function. The density function follows the Liouville equation and is the dual of the value function, which satisfies Bellman’s optimality principle. Thanks to density functions, constraints over the distribution of states, such as safety constraints, can be posed straightforwardly in an optimal control problem. The constrained optimal control problem is then solved with a primal-dual algorithm. This formulation is extended to the case with external disturbances, and we show that the robust constrained optimal control can be solved with a modified primal-dual algorithm. We apply this formulation to the problem of finding the optimal safe controller that minimizes the cumulative intervention. An adaptive cruise control (ACC) example is used to demonstrate the efficacy of the proposed, wherein we compare the result of the density function approach with the conventional control barrier function (CBF) method.},\\n\\tlanguage = {en},\\n\\tauthor = {Chen, Yuxiao and Ahmadi, Mohamadreza and Ames, Aaron D},\\n\\tpages = {6},\\n}\\n\\n\",\"author_short\":[\"Chen, Y.\",\"Ahmadi, M.\",\"Ames, A. D\"],\"key\":\"chen_optimal_nodate\",\"id\":\"chen_optimal_nodate\",\"bibbaseid\":\"chen-ahmadi-ames-optimalsafecontrollersynthesisadensityfunctionapproach\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Continuous-Time Optimization of Time-Varying Cost Functions Via Finite-Time Stability with Pre-Defined Convergence Time\",\"abstract\":\"In this paper, we propose a new family of continuous-time optimization algorithms for time-varying, locally strongly convex cost functions, based on discontinuous second-order gradient optimization flows with provable finite-time convergence to local optima. To analyze our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of arbitrary time-varying differential inclusions, particularly of the Filippov type. We then prove the convergence of our proposed flows in finite time. We illustrate the performance of our proposed flows on a quadratic cost function to track a decaying sinusoid.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Romero\"],\"firstnames\":[\"Orlando\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Benosman\"],\"firstnames\":[\"Mouhacine\"],\"suffixes\":[]}],\"pages\":\"6\",\"bibtex\":\"@article{romero_continuous-time_nodate,\\n\\ttitle = {Continuous-{Time} {Optimization} of {Time}-{Varying} {Cost} {Functions} {Via} {Finite}-{Time} {Stability} with {Pre}-{Defined} {Convergence} {Time}},\\n\\tabstract = {In this paper, we propose a new family of continuous-time optimization algorithms for time-varying, locally strongly convex cost functions, based on discontinuous second-order gradient optimization flows with provable finite-time convergence to local optima. To analyze our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of arbitrary time-varying differential inclusions, particularly of the Filippov type. We then prove the convergence of our proposed flows in finite time. We illustrate the performance of our proposed flows on a quadratic cost function to track a decaying sinusoid.},\\n\\tlanguage = {en},\\n\\tauthor = {Romero, Orlando and Benosman, Mouhacine},\\n\\tpages = {6},\\n}\\n\\n\",\"author_short\":[\"Romero, O.\",\"Benosman, M.\"],\"key\":\"romero_continuous-time_nodate\",\"id\":\"romero_continuous-time_nodate\",\"bibbaseid\":\"romero-benosman-continuoustimeoptimizationoftimevaryingcostfunctionsviafinitetimestabilitywithpredefinedconvergencetime\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version)\",\"copyright\":\"5\",\"shorttitle\":\"Robust Adaptive Control Barrier Functions\",\"url\":\"http://arxiv.org/abs/2003.10028\",\"abstract\":\"A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive control algorithm for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as closed-loop contraction does not require the system be invertible or in a particular form. Additionally, the approach is less expensive than nonlinear model predictive control as it does not require a full desired trajectory, but rather only a desired terminal state. The approach is illustrated on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.\",\"language\":\"en\",\"urldate\":\"2020-07-02\",\"journal\":\"arXiv:2003.10028 [cs, eess]\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Lopez\"],\"firstnames\":[\"Brett\",\"T.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Slotine\"],\"firstnames\":[\"Jean-Jacques\",\"E.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"How\"],\"firstnames\":[\"Jonathan\",\"P.\"],\"suffixes\":[]}],\"month\":\"May\",\"year\":\"2020\",\"note\":\"arXiv: 2003.10028\",\"keywords\":\"Electrical Engineering and Systems Science - Systems and Control\",\"bibtex\":\"@article{lopez_robust_2020,\\n\\ttitle = {Robust {Adaptive} {Control} {Barrier} {Functions}: {An} {Adaptive} \\\\& {Data}-{Driven} {Approach} to {Safety} ({Extended} {Version})},\\n\\tcopyright = {5},\\n\\tshorttitle = {Robust {Adaptive} {Control} {Barrier} {Functions}},\\n\\turl = {http://arxiv.org/abs/2003.10028},\\n\\tabstract = {A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive control algorithm for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as closed-loop contraction does not require the system be invertible or in a particular form. Additionally, the approach is less expensive than nonlinear model predictive control as it does not require a full desired trajectory, but rather only a desired terminal state. The approach is illustrated on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.},\\n\\tlanguage = {en},\\n\\turldate = {2020-07-02},\\n\\tjournal = {arXiv:2003.10028 [cs, eess]},\\n\\tauthor = {Lopez, Brett T. and Slotine, Jean-Jacques E. and How, Jonathan P.},\\n\\tmonth = may,\\n\\tyear = {2020},\\n\\tnote = {arXiv: 2003.10028},\\n\\tkeywords = {Electrical Engineering and Systems Science - Systems and Control},\\n}\\n\\n\",\"author_short\":[\"Lopez, B. T.\",\"Slotine, J. E.\",\"How, J. P.\"],\"key\":\"lopez_robust_2020\",\"id\":\"lopez_robust_2020\",\"bibbaseid\":\"lopez-slotine-how-robustadaptivecontrolbarrierfunctionsanadaptivedatadrivenapproachtosafetyextendedversion-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://arxiv.org/abs/2003.10028\"},\"keyword\":[\"Electrical Engineering and Systems Science - Systems and Control\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Nonlinear Control Using Coordinate-Free and Euler Formulations: An Empirical Evaluation on a 3D Pendulum\",\"abstract\":\"Pendulum dynamics are widely utilized in robotics control literature to test and evaluate novel control design techniques. They exhibit many interesting features commonly seen in real-world nonlinear systems and yet they are simple enough for quick prototyping, further analysis, and benchmarking. In this work, we study the impact of a 3D pendulum’s orientation parametrization on stabilization performance. Mainly, we show that using a global or coordinate-free formulation for dynamics and control is not only singularity-free but also more input-efficient. We validate this empirically by running over 700 stabilization simulations across the full configuration space of a 3D pendulum and compare the performance of a geometric and a Euler-parametrized controller. We show that the geometric controller is able to leverage the inherent manifold curvature and flow along geodesics for efficient stabilization.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Siravuru\"],\"firstnames\":[\"Avinash\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Sreenath\"],\"firstnames\":[\"Koushil\"],\"suffixes\":[]}],\"pages\":\"6\",\"bibtex\":\"@article{siravuru_nonlinear_nodate,\\n\\ttitle = {Nonlinear {Control} {Using} {Coordinate}-{Free} and {Euler} {Formulations}: {An} {Empirical} {Evaluation} on a {3D} {Pendulum}},\\n\\tabstract = {Pendulum dynamics are widely utilized in robotics control literature to test and evaluate novel control design techniques. They exhibit many interesting features commonly seen in real-world nonlinear systems and yet they are simple enough for quick prototyping, further analysis, and benchmarking. In this work, we study the impact of a 3D pendulum’s orientation parametrization on stabilization performance. Mainly, we show that using a global or coordinate-free formulation for dynamics and control is not only singularity-free but also more input-efficient. We validate this empirically by running over 700 stabilization simulations across the full configuration space of a 3D pendulum and compare the performance of a geometric and a Euler-parametrized controller. We show that the geometric controller is able to leverage the inherent manifold curvature and flow along geodesics for efficient stabilization.},\\n\\tlanguage = {en},\\n\\tauthor = {Siravuru, Avinash and Sreenath, Koushil},\\n\\tpages = {6},\\n}\\n\\n\",\"author_short\":[\"Siravuru, A.\",\"Sreenath, K.\"],\"key\":\"siravuru_nonlinear_nodate\",\"id\":\"siravuru_nonlinear_nodate\",\"bibbaseid\":\"siravuru-sreenath-nonlinearcontrolusingcoordinatefreeandeulerformulationsanempiricalevaluationona3dpendulum\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions\",\"url\":\"http://arxiv.org/abs/2006.01229\",\"abstract\":\"The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process.\",\"language\":\"en\",\"urldate\":\"2020-06-25\",\"journal\":\"arXiv:2006.01229 [cs, eess]\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Grandia\"],\"firstnames\":[\"Ruben\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Taylor\"],\"firstnames\":[\"Andrew\",\"J.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Singletary\"],\"firstnames\":[\"Andrew\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Hutter\"],\"firstnames\":[\"Marco\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ames\"],\"firstnames\":[\"Aaron\",\"D.\"],\"suffixes\":[]}],\"month\":\"June\",\"year\":\"2020\",\"note\":\"arXiv: 2006.01229\",\"keywords\":\"Computer Science - Robotics, Electrical Engineering and Systems Science - Systems and Control\",\"bibtex\":\"@article{grandia_nonlinear_2020,\\n\\ttitle = {Nonlinear {Model} {Predictive} {Control} of {Robotic} {Systems} with {Control} {Lyapunov} {Functions}},\\n\\turl = {http://arxiv.org/abs/2006.01229},\\n\\tabstract = {The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process.},\\n\\tlanguage = {en},\\n\\turldate = {2020-06-25},\\n\\tjournal = {arXiv:2006.01229 [cs, eess]},\\n\\tauthor = {Grandia, Ruben and Taylor, Andrew J. and Singletary, Andrew and Hutter, Marco and Ames, Aaron D.},\\n\\tmonth = jun,\\n\\tyear = {2020},\\n\\tnote = {arXiv: 2006.01229},\\n\\tkeywords = {Computer Science - Robotics, Electrical Engineering and Systems Science - Systems and Control},\\n}\\n\\n\",\"author_short\":[\"Grandia, R.\",\"Taylor, A. J.\",\"Singletary, A.\",\"Hutter, M.\",\"Ames, A. D.\"],\"key\":\"grandia_nonlinear_2020\",\"id\":\"grandia_nonlinear_2020\",\"bibbaseid\":\"grandia-taylor-singletary-hutter-ames-nonlinearmodelpredictivecontrolofroboticsystemswithcontrollyapunovfunctions-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://arxiv.org/abs/2006.01229\"},\"keyword\":[\"Computer Science - Robotics\",\"Electrical Engineering and Systems Science - Systems and Control\"],\"metadata\":{\"authorlinks\":{\"ames, a\":\"http://www.bipedalrobotics.com/publications.html\"}},\"downloads\":15,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"A Topological Approach to Gait Generation for Biped Robots\",\"url\":\"http://arxiv.org/abs/2006.03785\",\"abstract\":\"This paper describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2D and 3D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g., closed chains), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly-defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2D and 3D biped walkers.\",\"language\":\"en\",\"urldate\":\"2020-06-25\",\"journal\":\"arXiv:2006.03785 [cs]\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Rosa\",\"Jr.\"],\"firstnames\":[\"Nelson\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Lynch\"],\"firstnames\":[\"Kevin\",\"M.\"],\"suffixes\":[]}],\"month\":\"June\",\"year\":\"2020\",\"note\":\"arXiv: 2006.03785\",\"keywords\":\"Computer Science - Robotics\",\"bibtex\":\"@article{rosa_jr_topological_2020,\\n\\ttitle = {A {Topological} {Approach} to {Gait} {Generation} for {Biped} {Robots}},\\n\\turl = {http://arxiv.org/abs/2006.03785},\\n\\tabstract = {This paper describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2D and 3D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g., closed chains), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly-defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2D and 3D biped walkers.},\\n\\tlanguage = {en},\\n\\turldate = {2020-06-25},\\n\\tjournal = {arXiv:2006.03785 [cs]},\\n\\tauthor = {Rosa Jr., Nelson and Lynch, Kevin M.},\\n\\tmonth = jun,\\n\\tyear = {2020},\\n\\tnote = {arXiv: 2006.03785},\\n\\tkeywords = {Computer Science - Robotics},\\n}\\n\\n\",\"author_short\":[\"Rosa Jr., N.\",\"Lynch, K. M.\"],\"key\":\"rosa_jr_topological_2020\",\"id\":\"rosa_jr_topological_2020\",\"bibbaseid\":\"rosajr-lynch-atopologicalapproachtogaitgenerationforbipedrobots-2020\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://arxiv.org/abs/2006.03785\"},\"keyword\":[\"Computer Science - Robotics\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Lagrangian coherent structures in n-dimensional systems\",\"volume\":\"48\",\"issn\":\"0022-2488, 1089-7658\",\"url\":\"http://aip.scitation.org/doi/10.1063/1.2740025\",\"doi\":\"10.1063/1.2740025\",\"language\":\"en\",\"number\":\"6\",\"urldate\":\"2020-06-25\",\"journal\":\"Journal of Mathematical Physics\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Lekien\"],\"firstnames\":[\"Francois\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Shadden\"],\"firstnames\":[\"Shawn\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Marsden\"],\"firstnames\":[\"Jerrold\",\"E.\"],\"suffixes\":[]}],\"month\":\"June\",\"year\":\"2007\",\"pages\":\"065404\",\"bibtex\":\"@article{lekien_lagrangian_2007,\\n\\ttitle = {Lagrangian coherent structures in n-dimensional systems},\\n\\tvolume = {48},\\n\\tissn = {0022-2488, 1089-7658},\\n\\turl = {http://aip.scitation.org/doi/10.1063/1.2740025},\\n\\tdoi = {10.1063/1.2740025},\\n\\tlanguage = {en},\\n\\tnumber = {6},\\n\\turldate = {2020-06-25},\\n\\tjournal = {Journal of Mathematical Physics},\\n\\tauthor = {Lekien, Francois and Shadden, Shawn C. and Marsden, Jerrold E.},\\n\\tmonth = jun,\\n\\tyear = {2007},\\n\\tpages = {065404},\\n}\\n\\n\",\"author_short\":[\"Lekien, F.\",\"Shadden, S. C.\",\"Marsden, J. E.\"],\"key\":\"lekien_lagrangian_2007\",\"id\":\"lekien_lagrangian_2007\",\"bibbaseid\":\"lekien-shadden-marsden-lagrangiancoherentstructuresinndimensionalsystems-2007\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://aip.scitation.org/doi/10.1063/1.2740025\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"misc\",\"type\":\"misc\",\"title\":\"STABILIZATION WITH RELAXED CONTROLS\",\"shorttitle\":\"PII\",\"url\":\"https://reader.elsevier.com/reader/sd/pii/0362546X83900494?token=B88DBE74ECF120DBA01EA046831622DD7E545B033FA36243E3552AA41910AC40C4AC00AEF64C05628DED2123DF4CD220\",\"language\":\"en\",\"urldate\":\"2020-06-22\",\"author\":[{\"firstnames\":[],\"propositions\":[],\"lastnames\":[\"Artstein\"],\"suffixes\":[]}],\"doi\":\"10.1016/0362-546X(83)90049-4\",\"note\":\"ISSN: 10.1016/0362-546X(83)90049-4 Library Catalog: reader.elsevier.com\",\"bibtex\":\"@misc{artstein_stabilization_nodate,\\n\\ttitle = {{STABILIZATION} {WITH} {RELAXED} {CONTROLS}},\\n\\tshorttitle = {{PII}},\\n\\turl = {https://reader.elsevier.com/reader/sd/pii/0362546X83900494?token=B88DBE74ECF120DBA01EA046831622DD7E545B033FA36243E3552AA41910AC40C4AC00AEF64C05628DED2123DF4CD220},\\n\\tlanguage = {en},\\n\\turldate = {2020-06-22},\\n\\tauthor = {Artstein},\\n\\tdoi = {10.1016/0362-546X(83)90049-4},\\n\\tnote = {ISSN: 10.1016/0362-546X(83)90049-4\\nLibrary Catalog: reader.elsevier.com},\\n}\\n\\n\",\"author_short\":[\"Artstein\"],\"key\":\"artstein_stabilization_nodate\",\"id\":\"artstein_stabilization_nodate\",\"bibbaseid\":\"artstein-stabilizationwithrelaxedcontrols\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://reader.elsevier.com/reader/sd/pii/0362546X83900494?token=B88DBE74ECF120DBA01EA046831622DD7E545B033FA36243E3552AA41910AC40C4AC00AEF64C05628DED2123DF4CD220\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"On characterizations of the input-to-state stability property\",\"volume\":\"24\",\"issn\":\"01676911\",\"url\":\"https://linkinghub.elsevier.com/retrieve/pii/0167691194000506\",\"doi\":\"10.1016/0167-6911(94)00050-6\",\"abstract\":\"We show that the well-known Lyapunov sufficient condition for “input-to-state stability” is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.\",\"language\":\"en\",\"number\":\"5\",\"urldate\":\"2020-06-22\",\"journal\":\"Systems & Control Letters\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Sontag\"],\"firstnames\":[\"Eduardo\",\"D.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wang\"],\"firstnames\":[\"Yuan\"],\"suffixes\":[]}],\"month\":\"April\",\"year\":\"1995\",\"pages\":\"351–359\",\"bibtex\":\"@article{sontag_characterizations_1995,\\n\\ttitle = {On characterizations of the input-to-state stability property},\\n\\tvolume = {24},\\n\\tissn = {01676911},\\n\\turl = {https://linkinghub.elsevier.com/retrieve/pii/0167691194000506},\\n\\tdoi = {10.1016/0167-6911(94)00050-6},\\n\\tabstract = {We show that the well-known Lyapunov sufficient condition for “input-to-state stability” is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.},\\n\\tlanguage = {en},\\n\\tnumber = {5},\\n\\turldate = {2020-06-22},\\n\\tjournal = {Systems \\\\& Control Letters},\\n\\tauthor = {Sontag, Eduardo D. and Wang, Yuan},\\n\\tmonth = apr,\\n\\tyear = {1995},\\n\\tpages = {351--359},\\n}\\n\\n\",\"author_short\":[\"Sontag, E. D.\",\"Wang, Y.\"],\"key\":\"sontag_characterizations_1995\",\"id\":\"sontag_characterizations_1995\",\"bibbaseid\":\"sontag-wang-oncharacterizationsoftheinputtostatestabilityproperty-1995\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://linkinghub.elsevier.com/retrieve/pii/0167691194000506\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"A general result on the stabilization of linear systems using bounded controls\",\"doi\":\"10.1109/CDC.1993.325264\",\"abstract\":\"We present two constructions of controllers that globally stabilize linear systems subject to control saturation. The only conditions imposed are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition holds. We use essentially arbitrary saturations /spl sigma/, subject only to the requirement that: (i) /spl sigma/ is locally Lipschitz, (ii) s/spl sigma/(s)\\\\textgreater0 whenever s/spl ne/0, (iii) /spl sigma/ is differentiable at 0 and /spl sigma/'(0)\\\\textgreater0, and (iv) lim inf/sub \\\\textbars\\\\textbar/spl rarr//spl infin//\\\\textbar/spl sigma/(s)\\\\textbar\\\\textgreater0.\\\\textless\\\\textgreater\",\"booktitle\":\"Proceedings of 32nd IEEE Conference on Decision and Control\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Sussmann\"],\"firstnames\":[\"H.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Sontag\"],\"firstnames\":[\"E.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Yang\"],\"firstnames\":[\"Y.\"],\"suffixes\":[]}],\"month\":\"December\",\"year\":\"1993\",\"keywords\":\"Actuators, Control systems, Control theory, Eigenvalues and eigenfunctions, Linear systems, Mathematics, Negative feedback, Open loop systems, Power engineering and energy, Power supplies, bounded controls, control saturation, control system analysis, eigenvalues, eigenvalues and eigenfunctions, global stability, linear systems, linear time invariant continuous time systems, stability, stabilization\",\"pages\":\"1802–1807 vol.2\",\"bibtex\":\"@inproceedings{sussmann_general_1993,\\n\\ttitle = {A general result on the stabilization of linear systems using bounded controls},\\n\\tdoi = {10.1109/CDC.1993.325264},\\n\\tabstract = {We present two constructions of controllers that globally stabilize linear systems subject to control saturation. The only conditions imposed are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition holds. We use essentially arbitrary saturations /spl sigma/, subject only to the requirement that: (i) /spl sigma/ is locally Lipschitz, (ii) s/spl sigma/(s){\\\\textgreater}0 whenever s/spl ne/0, (iii) /spl sigma/ is differentiable at 0 and /spl sigma/'(0){\\\\textgreater}0, and (iv) lim inf/sub {\\\\textbar}s{\\\\textbar}/spl rarr//spl infin//{\\\\textbar}/spl sigma/(s){\\\\textbar}{\\\\textgreater}0.{\\\\textless}{\\\\textgreater}},\\n\\tbooktitle = {Proceedings of 32nd {IEEE} {Conference} on {Decision} and {Control}},\\n\\tauthor = {Sussmann, H. and Sontag, E. and Yang, Y.},\\n\\tmonth = dec,\\n\\tyear = {1993},\\n\\tkeywords = {Actuators, Control systems, Control theory, Eigenvalues and eigenfunctions, Linear systems, Mathematics, Negative feedback, Open loop systems, Power engineering and energy, Power supplies, bounded controls, control saturation, control system analysis, eigenvalues, eigenvalues and eigenfunctions, global stability, linear systems, linear time invariant continuous time systems, stability, stabilization},\\n\\tpages = {1802--1807 vol.2},\\n}\\n\\n\",\"author_short\":[\"Sussmann, H.\",\"Sontag, E.\",\"Yang, Y.\"],\"key\":\"sussmann_general_1993\",\"id\":\"sussmann_general_1993\",\"bibbaseid\":\"sussmann-sontag-yang-ageneralresultonthestabilizationoflinearsystemsusingboundedcontrols-1993\",\"role\":\"author\",\"urls\":{},\"keyword\":[\"Actuators\",\"Control systems\",\"Control theory\",\"Eigenvalues and eigenfunctions\",\"Linear systems\",\"Mathematics\",\"Negative feedback\",\"Open loop systems\",\"Power engineering and energy\",\"Power supplies\",\"bounded controls\",\"control saturation\",\"control system analysis\",\"eigenvalues\",\"eigenvalues and eigenfunctions\",\"global stability\",\"linear systems\",\"linear time invariant continuous time systems\",\"stability\",\"stabilization\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Nonlinear regulation: The piecewise linear approach\",\"volume\":\"26\",\"issn\":\"1558-2523\",\"shorttitle\":\"Nonlinear regulation\",\"doi\":\"10.1109/TAC.1981.1102596\",\"abstract\":\"This paper approaches nonlinear control problems through the use of (discrete-time) piecewise linear systems. These are systems whose next-state and output maps are both described by PL maps, i.e., by maps which are affine on each of the components of a finite polyhedral partition. Various results on state and output feedback, observers, and inverses, standard for linear systems, are proved for PL systems. Many of these results are then used in the study of more general (both discrete- and continuous-time) systems, using suitable approximations.\",\"number\":\"2\",\"journal\":\"IEEE Transactions on Automatic Control\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Sontag\"],\"firstnames\":[\"E.\"],\"suffixes\":[]}],\"month\":\"April\",\"year\":\"1981\",\"note\":\"Conference Name: IEEE Transactions on Automatic Control\",\"keywords\":\"Arithmetic, Control systems, Digital control, Linear programming, Linear systems, Logic, Microprocessors, Nonlinear control systems, Piecewise linear approximation, Piecewise linear techniques, Piecewise-linear approximation, Regulators, nonlinear systems, State feedback, nonlinear systems\",\"pages\":\"346–358\",\"bibtex\":\"@article{sontag_nonlinear_1981,\\n\\ttitle = {Nonlinear regulation: {The} piecewise linear approach},\\n\\tvolume = {26},\\n\\tissn = {1558-2523},\\n\\tshorttitle = {Nonlinear regulation},\\n\\tdoi = {10.1109/TAC.1981.1102596},\\n\\tabstract = {This paper approaches nonlinear control problems through the use of (discrete-time) piecewise linear systems. These are systems whose next-state and output maps are both described by PL maps, i.e., by maps which are affine on each of the components of a finite polyhedral partition. Various results on state and output feedback, observers, and inverses, standard for linear systems, are proved for PL systems. Many of these results are then used in the study of more general (both discrete- and continuous-time) systems, using suitable approximations.},\\n\\tnumber = {2},\\n\\tjournal = {IEEE Transactions on Automatic Control},\\n\\tauthor = {Sontag, E.},\\n\\tmonth = apr,\\n\\tyear = {1981},\\n\\tnote = {Conference Name: IEEE Transactions on Automatic Control},\\n\\tkeywords = {Arithmetic, Control systems, Digital control, Linear programming, Linear systems, Logic, Microprocessors, Nonlinear control systems, Piecewise linear approximation, Piecewise linear techniques, Piecewise-linear approximation, Regulators, nonlinear systems, State feedback, nonlinear systems},\\n\\tpages = {346--358},\\n}\\n\\n\",\"author_short\":[\"Sontag, E.\"],\"key\":\"sontag_nonlinear_1981\",\"id\":\"sontag_nonlinear_1981\",\"bibbaseid\":\"sontag-nonlinearregulationthepiecewiselinearapproach-1981\",\"role\":\"author\",\"urls\":{},\"keyword\":[\"Arithmetic\",\"Control systems\",\"Digital control\",\"Linear programming\",\"Linear systems\",\"Logic\",\"Microprocessors\",\"Nonlinear control systems\",\"Piecewise linear approximation\",\"Piecewise linear techniques\",\"Piecewise-linear approximation\",\"Regulators\",\"nonlinear systems\",\"State feedback\",\"nonlinear systems\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"incollection\",\"type\":\"incollection\",\"address\":\"Berlin, Heidelberg\",\"title\":\"Input to State Stability: Basic Concepts and Results\",\"volume\":\"1932\",\"isbn\":\"978-3-540-77644-4 978-3-540-77653-6\",\"shorttitle\":\"Input to State Stability\",\"url\":\"http://link.springer.com/10.1007/978-3-540-77653-6_3\",\"language\":\"en\",\"urldate\":\"2020-06-22\",\"booktitle\":\"Nonlinear and Optimal Control Theory\",\"publisher\":\"Springer Berlin Heidelberg\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Sontag\"],\"firstnames\":[\"Eduardo\",\"D.\"],\"suffixes\":[]}],\"editor\":[{\"propositions\":[],\"lastnames\":[\"Morel\"],\"firstnames\":[\"J.\",\"-M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Takens\"],\"firstnames\":[\"F.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Teissier\"],\"firstnames\":[\"B.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Nistri\"],\"firstnames\":[\"Paolo\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Stefani\"],\"firstnames\":[\"Gianna\"],\"suffixes\":[]}],\"collaborator\":\"Agrachev, Andrei A. and Morse, A. Stephen and Sontag, Eduardo D. and Sussmann, Héctor J. and Utkin, Vadim I.\",\"year\":\"2008\",\"doi\":\"10.1007/978-3-540-77653-6_3\",\"note\":\"Series Title: Lecture Notes in Mathematics\",\"pages\":\"163–220\",\"bibtex\":\"@incollection{morel_input_2008,\\n\\taddress = {Berlin, Heidelberg},\\n\\ttitle = {Input to {State} {Stability}: {Basic} {Concepts} and {Results}},\\n\\tvolume = {1932},\\n\\tisbn = {978-3-540-77644-4 978-3-540-77653-6},\\n\\tshorttitle = {Input to {State} {Stability}},\\n\\turl = {http://link.springer.com/10.1007/978-3-540-77653-6_3},\\n\\tlanguage = {en},\\n\\turldate = {2020-06-22},\\n\\tbooktitle = {Nonlinear and {Optimal} {Control} {Theory}},\\n\\tpublisher = {Springer Berlin Heidelberg},\\n\\tauthor = {Sontag, Eduardo D.},\\n\\teditor = {Morel, J. -M. and Takens, F. and Teissier, B. and Nistri, Paolo and Stefani, Gianna},\\n\\tcollaborator = {Agrachev, Andrei A. and Morse, A. Stephen and Sontag, Eduardo D. and Sussmann, Héctor J. and Utkin, Vadim I.},\\n\\tyear = {2008},\\n\\tdoi = {10.1007/978-3-540-77653-6_3},\\n\\tnote = {Series Title: Lecture Notes in Mathematics},\\n\\tpages = {163--220},\\n}\\n\\n\",\"author_short\":[\"Sontag, E. D.\"],\"editor_short\":[\"Morel, J. -.\",\"Takens, F.\",\"Teissier, B.\",\"Nistri, P.\",\"Stefani, G.\"],\"key\":\"morel_input_2008\",\"id\":\"morel_input_2008\",\"bibbaseid\":\"sontag-inputtostatestabilitybasicconceptsandresults-2008\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://link.springer.com/10.1007/978-3-540-77653-6_3\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":1,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"A ‘universal’ construction of Artstein's theorem on nonlinear stabilization\",\"volume\":\"13\",\"issn\":\"01676911\",\"url\":\"https://linkinghub.elsevier.com/retrieve/pii/0167691189900285\",\"doi\":\"10.1016/0167-6911(89)90028-5\",\"abstract\":\"This note presents an explicit proof of the theorem due to Artstein - which states that the existence of a smooth control-Lyapunov function implies smooth stabilizabifity. Moreover, the result is extended to the real-analytic and rational cases as well. The proof uses a \\\"universal' formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation.\",\"language\":\"en\",\"number\":\"2\",\"urldate\":\"2020-06-22\",\"journal\":\"Systems & Control Letters\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Sontag\"],\"firstnames\":[\"Eduardo\",\"D.\"],\"suffixes\":[]}],\"month\":\"August\",\"year\":\"1989\",\"pages\":\"117–123\",\"bibtex\":\"@article{sontag_universal_1989,\\n\\ttitle = {A ‘universal’ construction of {Artstein}'s theorem on nonlinear stabilization},\\n\\tvolume = {13},\\n\\tissn = {01676911},\\n\\turl = {https://linkinghub.elsevier.com/retrieve/pii/0167691189900285},\\n\\tdoi = {10.1016/0167-6911(89)90028-5},\\n\\tabstract = {This note presents an explicit proof of the theorem due to Artstein - which states that the existence of a smooth control-Lyapunov function implies smooth stabilizabifity. Moreover, the result is extended to the real-analytic and rational cases as well. The proof uses a \\\"universal' formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation.},\\n\\tlanguage = {en},\\n\\tnumber = {2},\\n\\turldate = {2020-06-22},\\n\\tjournal = {Systems \\\\& Control Letters},\\n\\tauthor = {Sontag, Eduardo D.},\\n\\tmonth = aug,\\n\\tyear = {1989},\\n\\tpages = {117--123},\\n}\\n\\n\",\"author_short\":[\"Sontag, E. D.\"],\"key\":\"sontag_universal_1989\",\"id\":\"sontag_universal_1989\",\"bibbaseid\":\"sontag-auniversalconstructionofartsteinstheoremonnonlinearstabilization-1989\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://linkinghub.elsevier.com/retrieve/pii/0167691189900285\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Hybrid Invariant Manifolds in Systems With Impulse Effects With Application to Periodic Locomotion in Bipedal Robots\",\"volume\":\"54\",\"issn\":\"1558-2523\",\"doi\":\"10.1109/TAC.2009.2024563\",\"abstract\":\"Motivated by the problem of controlling walking in a biped with series compliant actuation, this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects. The first main result shows that when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold, there exist local coordinate transforms under which the Jacobian linearization of the Poincare return map has a block upper triangular structure. One diagonal block is the linearization of the system as restricted to the hybrid invariant manifold, also called the hybrid zero dynamics. The other is the product of two sensitivity matrices related to the transverse dynamics-one pertaining to the impact map and the other pertaining to the closed-loop vector field. When either of these sensitivity matrices is sufficiently close to zero, the stability of the return map is determined solely by the stability of the hybrid zero dynamics. The second main result of the paper details the construction of a hybrid invariant manifold, such as that required by the first main theorem. Forward invariance follows from the methods of Byrnes and Isidori, and impact invariance is achieved by a novel construction of impact-updated control parameters. In addition to providing impact invariance, the construction allows entries of the impact sensitivity matrix of the transverse dynamics to be made arbitrarily small. A simulation example is provided where stable walking is achieved in a 5-link biped with series compliant actuation.\",\"number\":\"8\",\"journal\":\"IEEE Transactions on Automatic Control\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Morris\"],\"firstnames\":[\"Benjamin\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Grizzle\"],\"firstnames\":[\"Jessy\",\"W.\"],\"suffixes\":[]}],\"month\":\"August\",\"year\":\"2009\",\"note\":\"Conference Name: IEEE Transactions on Automatic Control\",\"keywords\":\"Bipedal robots, Control systems, Differential equations, Feedback, Jacobian linearization, Jacobian matrices, Legged locomotion, Nonlinear systems, Orbital robotics, Orbits, Poincare invariance, Poincare return map, Robot kinematics, Stability, bipedal robot, closed loop systems, closed-loop vector field, forward invariance, hybrid invariant manifold, hybrid systems, hybrid zero dynamics, impact invariance, impact map, impact-updated control parameter, impulse effects, legged locomotion, linearisation techniques, local coordinate transforms, periodic control, periodic locomotion, periodic orbit, sensitivity analysis, sensitivity matrix, stability, stabilization, stable walking, transverse dynamics, underactuated systems, walking control, zero assignment, zero dynamics\",\"pages\":\"1751–1764\",\"bibtex\":\"@article{morris_hybrid_2009,\\n\\ttitle = {Hybrid {Invariant} {Manifolds} in {Systems} {With} {Impulse} {Effects} {With} {Application} to {Periodic} {Locomotion} in {Bipedal} {Robots}},\\n\\tvolume = {54},\\n\\tissn = {1558-2523},\\n\\tdoi = {10.1109/TAC.2009.2024563},\\n\\tabstract = {Motivated by the problem of controlling walking in a biped with series compliant actuation, this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects. The first main result shows that when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold, there exist local coordinate transforms under which the Jacobian linearization of the Poincare return map has a block upper triangular structure. One diagonal block is the linearization of the system as restricted to the hybrid invariant manifold, also called the hybrid zero dynamics. The other is the product of two sensitivity matrices related to the transverse dynamics-one pertaining to the impact map and the other pertaining to the closed-loop vector field. When either of these sensitivity matrices is sufficiently close to zero, the stability of the return map is determined solely by the stability of the hybrid zero dynamics. The second main result of the paper details the construction of a hybrid invariant manifold, such as that required by the first main theorem. Forward invariance follows from the methods of Byrnes and Isidori, and impact invariance is achieved by a novel construction of impact-updated control parameters. In addition to providing impact invariance, the construction allows entries of the impact sensitivity matrix of the transverse dynamics to be made arbitrarily small. A simulation example is provided where stable walking is achieved in a 5-link biped with series compliant actuation.},\\n\\tnumber = {8},\\n\\tjournal = {IEEE Transactions on Automatic Control},\\n\\tauthor = {Morris, Benjamin and Grizzle, Jessy W.},\\n\\tmonth = aug,\\n\\tyear = {2009},\\n\\tnote = {Conference Name: IEEE Transactions on Automatic Control},\\n\\tkeywords = {Bipedal robots, Control systems, Differential equations, Feedback, Jacobian linearization, Jacobian matrices, Legged locomotion, Nonlinear systems, Orbital robotics, Orbits, Poincare invariance, Poincare return map, Robot kinematics, Stability, bipedal robot, closed loop systems, closed-loop vector field, forward invariance, hybrid invariant manifold, hybrid systems, hybrid zero dynamics, impact invariance, impact map, impact-updated control parameter, impulse effects, legged locomotion, linearisation techniques, local coordinate transforms, periodic control, periodic locomotion, periodic orbit, sensitivity analysis, sensitivity matrix, stability, stabilization, stable walking, transverse dynamics, underactuated systems, walking control, zero assignment, zero dynamics},\\n\\tpages = {1751--1764},\\n}\\n\\n\",\"author_short\":[\"Morris, B.\",\"Grizzle, J. W.\"],\"key\":\"morris_hybrid_2009\",\"id\":\"morris_hybrid_2009\",\"bibbaseid\":\"morris-grizzle-hybridinvariantmanifoldsinsystemswithimpulseeffectswithapplicationtoperiodiclocomotioninbipedalrobots-2009\",\"role\":\"author\",\"urls\":{},\"keyword\":[\"Bipedal robots\",\"Control systems\",\"Differential equations\",\"Feedback\",\"Jacobian linearization\",\"Jacobian matrices\",\"Legged locomotion\",\"Nonlinear systems\",\"Orbital robotics\",\"Orbits\",\"Poincare invariance\",\"Poincare return map\",\"Robot kinematics\",\"Stability\",\"bipedal robot\",\"closed loop systems\",\"closed-loop vector field\",\"forward invariance\",\"hybrid invariant manifold\",\"hybrid systems\",\"hybrid zero dynamics\",\"impact invariance\",\"impact map\",\"impact-updated control parameter\",\"impulse effects\",\"legged locomotion\",\"linearisation techniques\",\"local coordinate transforms\",\"periodic control\",\"periodic locomotion\",\"periodic orbit\",\"sensitivity analysis\",\"sensitivity matrix\",\"stability\",\"stabilization\",\"stable walking\",\"transverse dynamics\",\"underactuated systems\",\"walking control\",\"zero assignment\",\"zero dynamics\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"misc\",\"type\":\"misc\",\"title\":\"Frobenius theorem (differential topology)\",\"copyright\":\"Creative Commons Attribution-ShareAlike License\",\"url\":\"https://en.wikipedia.org/w/index.php?title=Frobenius_theorem_(differential_topology)&oldid=938445316\",\"abstract\":\"In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an underdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds. The theorem is foundational in differential topology and calculus on manifolds.\",\"language\":\"en\",\"urldate\":\"2020-06-16\",\"journal\":\"Wikipedia\",\"month\":\"January\",\"year\":\"2020\",\"note\":\"Page Version ID: 938445316\",\"bibtex\":\"@misc{noauthor_frobenius_2020,\\n\\ttitle = {Frobenius theorem (differential topology)},\\n\\tcopyright = {Creative Commons Attribution-ShareAlike License},\\n\\turl = {https://en.wikipedia.org/w/index.php?title=Frobenius_theorem_(differential_topology)&oldid=938445316},\\n\\tabstract = {In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an underdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds.  The theorem is foundational in differential topology and calculus on manifolds.},\\n\\tlanguage = {en},\\n\\turldate = {2020-06-16},\\n\\tjournal = {Wikipedia},\\n\\tmonth = jan,\\n\\tyear = {2020},\\n\\tnote = {Page Version ID: 938445316},\\n}\\n\\n\",\"key\":\"noauthor_frobenius_2020\",\"id\":\"noauthor_frobenius_2020\",\"bibbaseid\":\"anonymous-frobeniustheoremdifferentialtopology-2020\",\"role\":\"\",\"urls\":{\"Paper\":\"https://en.wikipedia.org/w/index.php?title=Frobenius_theorem_(differential_topology)&oldid=938445316\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"On the construction of Lyapunov functions using the sum of squares decomposition\",\"volume\":\"3\",\"copyright\":\"5\",\"doi\":\"10.1109/CDC.2002.1184414\",\"abstract\":\"A relaxation of Lyapunov's direct method has been proposed elsewhere that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In the paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certain non-polynomial nonlinearities in the vector field to be handled exactly and the constructed Lyapunov functions to contain non-polynomial terms. It also allows robustness analysis to be performed. Some examples are given to illustrate how this is done.\",\"booktitle\":\"Proceedings of the 41st IEEE Conference on Decision and Control, 2002.\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Papachristodoulou\"],\"firstnames\":[\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Prajna\"],\"firstnames\":[\"S.\"],\"suffixes\":[]}],\"month\":\"December\",\"year\":\"2002\",\"note\":\"ISSN: 0191-2216\",\"keywords\":\"Biological system modeling, Control systems, Lyapunov functions, Lyapunov method, Lyapunov methods, Nonlinear control systems, Nonlinear systems, Polynomials, Robust stability, Robustness, Sufficient conditions, Uncertainty, control system analysis, equality constraints, inequality constraints, integral constraints, nonlinear control systems, nonlinear dynamical systems, nonlinear systems, nonpolynomial nonlinearities, polynomials, robust control, robustness analysis, stability of equilibria, sum of squares decomposition, vectors\",\"pages\":\"3482–3487 vol.3\",\"bibtex\":\"@inproceedings{papachristodoulou_construction_2002,\\n\\ttitle = {On the construction of {Lyapunov} functions using the sum of squares decomposition},\\n\\tvolume = {3},\\n\\tcopyright = {5},\\n\\tdoi = {10.1109/CDC.2002.1184414},\\n\\tabstract = {A relaxation of Lyapunov's direct method has been proposed elsewhere that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In the paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certain non-polynomial nonlinearities in the vector field to be handled exactly and the constructed Lyapunov functions to contain non-polynomial terms. It also allows robustness analysis to be performed. Some examples are given to illustrate how this is done.},\\n\\tbooktitle = {Proceedings of the 41st {IEEE} {Conference} on {Decision} and {Control}, 2002.},\\n\\tauthor = {Papachristodoulou, A. and Prajna, S.},\\n\\tmonth = dec,\\n\\tyear = {2002},\\n\\tnote = {ISSN: 0191-2216},\\n\\tkeywords = {Biological system modeling, Control systems, Lyapunov functions, Lyapunov method, Lyapunov methods, Nonlinear control systems, Nonlinear systems, Polynomials, Robust stability, Robustness, Sufficient conditions, Uncertainty, control system analysis, equality constraints, inequality constraints, integral constraints, nonlinear control systems, nonlinear dynamical systems, nonlinear systems, nonpolynomial nonlinearities, polynomials, robust control, robustness analysis, stability of equilibria, sum of squares decomposition, vectors},\\n\\tpages = {3482--3487 vol.3},\\n}\\n\\n\",\"author_short\":[\"Papachristodoulou, A.\",\"Prajna, S.\"],\"key\":\"papachristodoulou_construction_2002\",\"id\":\"papachristodoulou_construction_2002\",\"bibbaseid\":\"papachristodoulou-prajna-ontheconstructionoflyapunovfunctionsusingthesumofsquaresdecomposition-2002\",\"role\":\"author\",\"urls\":{},\"keyword\":[\"Biological system modeling\",\"Control systems\",\"Lyapunov functions\",\"Lyapunov method\",\"Lyapunov methods\",\"Nonlinear control systems\",\"Nonlinear systems\",\"Polynomials\",\"Robust stability\",\"Robustness\",\"Sufficient conditions\",\"Uncertainty\",\"control system analysis\",\"equality constraints\",\"inequality constraints\",\"integral constraints\",\"nonlinear control systems\",\"nonlinear dynamical systems\",\"nonlinear systems\",\"nonpolynomial nonlinearities\",\"polynomials\",\"robust control\",\"robustness analysis\",\"stability of equilibria\",\"sum of squares decomposition\",\"vectors\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Composing limit cycles for motion planning of 3D bipedal walkers\",\"doi\":\"10.1109/CDC.2016.7799249\",\"abstract\":\"This paper presents a framework for navigation of 3D dynamically walking bipeds. The framework is based on extracting gait primitives in the form of limit-cycle locomotion behaviors, which are then composed by a higher-level planning algorithm with the purpose of navigating the biped to a goal location while avoiding obstacles. By formulating motion planning as a discrete-time switched system with multiple equilibria - each corresponding to a gait primitive - we provide analytical conditions that constrain the frequency of the switching signal so that the biped is guaranteed to stably execute a suggested plan. Effectively, these conditions distill the stability limitations of the system dynamics in a form that can be readily incorporated to the planning algorithm. We demonstrate the feasibility of the method in the context of a 3D bipedal model, walking dynamically under the influence of a Hybrid Zero Dynamics (HZD) controller. It is shown that the dimensional reduction afforded by HZD greatly facilitates the application of the method by allowing certificates of stability for gait primitives using sums-of-squares programming.\",\"booktitle\":\"2016 IEEE 55th Conference on Decision and Control (CDC)\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Motahar\"],\"firstnames\":[\"Mohamad\",\"Shafiee\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Veer\"],\"firstnames\":[\"Sushant\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Poulakakis\"],\"firstnames\":[\"Ioannis\"],\"suffixes\":[]}],\"month\":\"December\",\"year\":\"2016\",\"keywords\":\"3D bipedal walker motion planning, 3D dynamically walking biped navigation, HZD, Legged locomotion, Limit-cycles, Navigation, Planning, Switched systems, Switches, Three-dimensional displays, collision avoidance, discrete time systems, discrete-time switched system, gait analysis, gait primitive, gait primitive extraction, higher-level planning algorithm, hybrid zero dynamic controller, legged locomotion, limit-cycle locomotion behaviors, obstacle avoidance, path planning, stability, stability limitations, sums-of-squares programming, switching signal, switching systems (control)\",\"pages\":\"6368–6374\",\"bibtex\":\"@inproceedings{motahar_composing_2016,\\n\\ttitle = {Composing limit cycles for motion planning of {3D} bipedal walkers},\\n\\tdoi = {10.1109/CDC.2016.7799249},\\n\\tabstract = {This paper presents a framework for navigation of 3D dynamically walking bipeds. The framework is based on extracting gait primitives in the form of limit-cycle locomotion behaviors, which are then composed by a higher-level planning algorithm with the purpose of navigating the biped to a goal location while avoiding obstacles. By formulating motion planning as a discrete-time switched system with multiple equilibria - each corresponding to a gait primitive - we provide analytical conditions that constrain the frequency of the switching signal so that the biped is guaranteed to stably execute a suggested plan. Effectively, these conditions distill the stability limitations of the system dynamics in a form that can be readily incorporated to the planning algorithm. We demonstrate the feasibility of the method in the context of a 3D bipedal model, walking dynamically under the influence of a Hybrid Zero Dynamics (HZD) controller. It is shown that the dimensional reduction afforded by HZD greatly facilitates the application of the method by allowing certificates of stability for gait primitives using sums-of-squares programming.},\\n\\tbooktitle = {2016 {IEEE} 55th {Conference} on {Decision} and {Control} ({CDC})},\\n\\tauthor = {Motahar, Mohamad Shafiee and Veer, Sushant and Poulakakis, Ioannis},\\n\\tmonth = dec,\\n\\tyear = {2016},\\n\\tkeywords = {3D bipedal walker motion planning, 3D dynamically walking biped navigation, HZD, Legged locomotion, Limit-cycles, Navigation, Planning, Switched systems, Switches, Three-dimensional displays, collision avoidance, discrete time systems, discrete-time switched system, gait analysis, gait primitive, gait primitive extraction, higher-level planning algorithm, hybrid zero dynamic controller, legged locomotion, limit-cycle locomotion behaviors, obstacle avoidance, path planning, stability, stability limitations, sums-of-squares programming, switching signal, switching systems (control)},\\n\\tpages = {6368--6374},\\n}\\n\\n\",\"author_short\":[\"Motahar, M. S.\",\"Veer, S.\",\"Poulakakis, I.\"],\"key\":\"motahar_composing_2016\",\"id\":\"motahar_composing_2016\",\"bibbaseid\":\"motahar-veer-poulakakis-composinglimitcyclesformotionplanningof3dbipedalwalkers-2016\",\"role\":\"author\",\"urls\":{},\"keyword\":[\"3D bipedal walker motion planning\",\"3D dynamically walking biped navigation\",\"HZD\",\"Legged locomotion\",\"Limit-cycles\",\"Navigation\",\"Planning\",\"Switched systems\",\"Switches\",\"Three-dimensional displays\",\"collision avoidance\",\"discrete time systems\",\"discrete-time switched system\",\"gait analysis\",\"gait primitive\",\"gait primitive extraction\",\"higher-level planning algorithm\",\"hybrid zero dynamic controller\",\"legged locomotion\",\"limit-cycle locomotion behaviors\",\"obstacle avoidance\",\"path planning\",\"stability\",\"stability limitations\",\"sums-of-squares programming\",\"switching signal\",\"switching systems (control)\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"inproceedings\",\"type\":\"inproceedings\",\"title\":\"Discrete Control Barrier Functions for Safety-Critical Control of Discrete Systems with Application to Bipedal Robot Navigation\",\"isbn\":\"978-0-9923747-3-0\",\"url\":\"http://www.roboticsproceedings.org/rss13/p73.pdf\",\"doi\":\"10.15607/RSS.2017.XIII.073\",\"abstract\":\"In this paper, we extend the concept of control barrier functions, developed initially for continuous time systems, to the discrete-time domain. We demonstrate safety-critical control for nonlinear discrete-time systems with applications to 3D bipedal robot navigation. Particularly, we mathematically analyze two different formulations of control barrier functions, based on their continuous-time counterparts, and demonstrate how these can be applied to discrete-time systems. We show that the resulting formulation is a nonlinear program in contrast to the quadratic program for continuous-time systems and under certain conditions, the nonlinear program can be formulated as a quadratically constrained quadratic program. Furthermore, using the developed concept of discrete control barrier functions, we present a novel control method to address the problem of navigation of a high-dimensional bipedal robot through environments with moving obstacles that present time-varying safety-critical constraints.\",\"language\":\"en\",\"urldate\":\"2020-06-10\",\"booktitle\":\"Robotics: Science and Systems XIII\",\"publisher\":\"Robotics: Science and Systems Foundation\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Agrawal\"],\"firstnames\":[\"Ayush\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Sreenath\"],\"firstnames\":[\"Koushil\"],\"suffixes\":[]}],\"month\":\"July\",\"year\":\"2017\",\"bibtex\":\"@inproceedings{agrawal_discrete_2017,\\n\\ttitle = {Discrete {Control} {Barrier} {Functions} for {Safety}-{Critical} {Control} of {Discrete} {Systems} with {Application} to {Bipedal} {Robot} {Navigation}},\\n\\tisbn = {978-0-9923747-3-0},\\n\\turl = {http://www.roboticsproceedings.org/rss13/p73.pdf},\\n\\tdoi = {10.15607/RSS.2017.XIII.073},\\n\\tabstract = {In this paper, we extend the concept of control barrier functions, developed initially for continuous time systems, to the discrete-time domain. We demonstrate safety-critical control for nonlinear discrete-time systems with applications to 3D bipedal robot navigation. Particularly, we mathematically analyze two different formulations of control barrier functions, based on their continuous-time counterparts, and demonstrate how these can be applied to discrete-time systems. We show that the resulting formulation is a nonlinear program in contrast to the quadratic program for continuous-time systems and under certain conditions, the nonlinear program can be formulated as a quadratically constrained quadratic program. Furthermore, using the developed concept of discrete control barrier functions, we present a novel control method to address the problem of navigation of a high-dimensional bipedal robot through environments with moving obstacles that present time-varying safety-critical constraints.},\\n\\tlanguage = {en},\\n\\turldate = {2020-06-10},\\n\\tbooktitle = {Robotics: {Science} and {Systems} {XIII}},\\n\\tpublisher = {Robotics: Science and Systems Foundation},\\n\\tauthor = {Agrawal, Ayush and Sreenath, Koushil},\\n\\tmonth = jul,\\n\\tyear = {2017},\\n}\\n\\n\",\"author_short\":[\"Agrawal, A.\",\"Sreenath, K.\"],\"key\":\"agrawal_discrete_2017\",\"id\":\"agrawal_discrete_2017\",\"bibbaseid\":\"agrawal-sreenath-discretecontrolbarrierfunctionsforsafetycriticalcontrolofdiscretesystemswithapplicationtobipedalrobotnavigation-2017\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://www.roboticsproceedings.org/rss13/p73.pdf\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":2,\"html\":\"\"},{\"bibtype\":\"misc\",\"type\":\"misc\",\"title\":\"Path-following for linear systems with unstable zero dynamics\",\"shorttitle\":\"doi\",\"url\":\"https://reader.elsevier.com/reader/sd/pii/S0005109806002196?token=22AE7F0A9F0CADCFAE496B41BFC0C9359622CC05594126822D2F63027DD83F339905E4DEA4652A25699EFA5AE0ACAD4B\",\"language\":\"en\",\"urldate\":\"2020-06-09\",\"doi\":\"10.1016/j.automatica.2006.05.014\",\"note\":\"Library Catalog: reader.elsevier.com\",\"bibtex\":\"@misc{noauthor_path-following_nodate,\\n\\ttitle = {Path-following for linear systems with unstable zero dynamics},\\n\\tshorttitle = {doi},\\n\\turl = {https://reader.elsevier.com/reader/sd/pii/S0005109806002196?token=22AE7F0A9F0CADCFAE496B41BFC0C9359622CC05594126822D2F63027DD83F339905E4DEA4652A25699EFA5AE0ACAD4B},\\n\\tlanguage = {en},\\n\\turldate = {2020-06-09},\\n\\tdoi = {10.1016/j.automatica.2006.05.014},\\n\\tnote = {Library Catalog: reader.elsevier.com},\\n}\\n\\n\",\"key\":\"noauthor_path-following_nodate\",\"id\":\"noauthor_path-following_nodate\",\"bibbaseid\":\"anonymous-pathfollowingforlinearsystemswithunstablezerodynamics\",\"role\":\"\",\"urls\":{\"Paper\":\"https://reader.elsevier.com/reader/sd/pii/S0005109806002196?token=22AE7F0A9F0CADCFAE496B41BFC0C9359622CC05594126822D2F63027DD83F339905E4DEA4652A25699EFA5AE0ACAD4B\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Nonsmooth Barrier Functions With Applications to Multi-Robot Systems\",\"volume\":\"1\",\"issn\":\"2475-1456\",\"doi\":\"10.1109/LCSYS.2017.2710943\",\"abstract\":\"As multi-agent systems become more wide-spread and versatile, the ability to satisfy multiple system-level constraints grows increasingly important. In applications ranging from automated cruise control to safety in robot swarms, barrier functions have emerged as a tool to provably meet such constraints by guaranteeing forward invariance of desirable sets. However, satisfying multiple constraints typically implies formulating multiple barrier functions, which would be ameliorated if the barrier functions could be composed together as Boolean logic formulas. The use of max and min operators, which yields nonsmooth functions, represents one path to accomplish Boolean compositions of barrier functions, and this letter extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions. We validate our results by deploying Boolean compositions of nonsmooth barrier functions onto a team of mobile robots.\",\"number\":\"2\",\"journal\":\"IEEE Control Systems Letters\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Glotfelter\"],\"firstnames\":[\"Paul\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cortés\"],\"firstnames\":[\"Jorge\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Egerstedt\"],\"firstnames\":[\"Magnus\"],\"suffixes\":[]}],\"month\":\"October\",\"year\":\"2017\",\"note\":\"Conference Name: IEEE Control Systems Letters\",\"keywords\":\"Boolean compositions, Boolean functions, Boolean logic formulas, Collision avoidance, Differential equations, Lyapunov methods, Multi-agent systems, Robotics, Robots, Robustness, Tools, autonomous systems, differential inclusions, max operators, min operators, mobile robots, multi-robot systems, multiagent systems, multiple system-level constraints, multirobot systems, nonsmooth barrier functions\",\"pages\":\"310–315\",\"bibtex\":\"@article{glotfelter_nonsmooth_2017,\\n\\ttitle = {Nonsmooth {Barrier} {Functions} {With} {Applications} to {Multi}-{Robot} {Systems}},\\n\\tvolume = {1},\\n\\tissn = {2475-1456},\\n\\tdoi = {10.1109/LCSYS.2017.2710943},\\n\\tabstract = {As multi-agent systems become more wide-spread and versatile, the ability to satisfy multiple system-level constraints grows increasingly important. In applications ranging from automated cruise control to safety in robot swarms, barrier functions have emerged as a tool to provably meet such constraints by guaranteeing forward invariance of desirable sets. However, satisfying multiple constraints typically implies formulating multiple barrier functions, which would be ameliorated if the barrier functions could be composed together as Boolean logic formulas. The use of max and min operators, which yields nonsmooth functions, represents one path to accomplish Boolean compositions of barrier functions, and this letter extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions. We validate our results by deploying Boolean compositions of nonsmooth barrier functions onto a team of mobile robots.},\\n\\tnumber = {2},\\n\\tjournal = {IEEE Control Systems Letters},\\n\\tauthor = {Glotfelter, Paul and Cortés, Jorge and Egerstedt, Magnus},\\n\\tmonth = oct,\\n\\tyear = {2017},\\n\\tnote = {Conference Name: IEEE Control Systems Letters},\\n\\tkeywords = {Boolean compositions, Boolean functions, Boolean logic formulas, Collision avoidance, Differential equations, Lyapunov methods, Multi-agent systems, Robotics, Robots, Robustness, Tools, autonomous systems, differential inclusions, max operators, min operators, mobile robots, multi-robot systems, multiagent systems, multiple system-level constraints, multirobot systems, nonsmooth barrier functions},\\n\\tpages = {310--315},\\n}\\n\\n\",\"author_short\":[\"Glotfelter, P.\",\"Cortés, J.\",\"Egerstedt, M.\"],\"key\":\"glotfelter_nonsmooth_2017\",\"id\":\"glotfelter_nonsmooth_2017\",\"bibbaseid\":\"glotfelter-corts-egerstedt-nonsmoothbarrierfunctionswithapplicationstomultirobotsystems-2017\",\"role\":\"author\",\"urls\":{},\"keyword\":[\"Boolean compositions\",\"Boolean functions\",\"Boolean logic formulas\",\"Collision avoidance\",\"Differential equations\",\"Lyapunov methods\",\"Multi-agent systems\",\"Robotics\",\"Robots\",\"Robustness\",\"Tools\",\"autonomous systems\",\"differential inclusions\",\"max operators\",\"min operators\",\"mobile robots\",\"multi-robot systems\",\"multiagent systems\",\"multiple system-level constraints\",\"multirobot systems\",\"nonsmooth barrier functions\"],\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"A direct method for trajectory optimization of rigid bodies through contact\",\"volume\":\"33\",\"issn\":\"0278-3649, 1741-3176\",\"url\":\"http://journals.sagepub.com/doi/10.1177/0278364913506757\",\"doi\":\"10.1177/0278364913506757\",\"abstract\":\"Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform.\",\"language\":\"en\",\"number\":\"1\",\"urldate\":\"2020-06-08\",\"journal\":\"The International Journal of Robotics Research\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Posa\"],\"firstnames\":[\"Michael\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Cantu\"],\"firstnames\":[\"Cecilia\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Tedrake\"],\"firstnames\":[\"Russ\"],\"suffixes\":[]}],\"month\":\"January\",\"year\":\"2014\",\"pages\":\"69–81\",\"bibtex\":\"@article{posa_direct_2014,\\n\\ttitle = {A direct method for trajectory optimization of rigid bodies through contact},\\n\\tvolume = {33},\\n\\tissn = {0278-3649, 1741-3176},\\n\\turl = {http://journals.sagepub.com/doi/10.1177/0278364913506757},\\n\\tdoi = {10.1177/0278364913506757},\\n\\tabstract = {Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform.},\\n\\tlanguage = {en},\\n\\tnumber = {1},\\n\\turldate = {2020-06-08},\\n\\tjournal = {The International Journal of Robotics Research},\\n\\tauthor = {Posa, Michael and Cantu, Cecilia and Tedrake, Russ},\\n\\tmonth = jan,\\n\\tyear = {2014},\\n\\tpages = {69--81},\\n}\\n\\n\",\"author_short\":[\"Posa, M.\",\"Cantu, C.\",\"Tedrake, R.\"],\"key\":\"posa_direct_2014\",\"id\":\"posa_direct_2014\",\"bibbaseid\":\"posa-cantu-tedrake-adirectmethodfortrajectoryoptimizationofrigidbodiesthroughcontact-2014\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://journals.sagepub.com/doi/10.1177/0278364913506757\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Robust control barrier functions for constrained stabilization of nonlinear systems\",\"volume\":\"96\",\"issn\":\"00051098\",\"url\":\"https://linkinghub.elsevier.com/retrieve/pii/S0005109818303509\",\"doi\":\"10.1016/j.automatica.2018.07.004\",\"abstract\":\"Quadratic Programming (QP) has been used to combine Control Lyapunov and Control Barrier Functions (CLF and CBF) to design controllers for nonlinear systems with constraints. It has been successfully applied to robotic and automotive systems. The approach could be considered an extension of the CLF-based point-wise minimum norm controller. In this paper we modify the original QP problem in a way that guarantees that V˙ \\\\textless 0, if the barrier constraint is inactive, as well as local asymptotic stability under the standard (minimal) assumptions on the CLF and CBF. We also remove the assumption that the CBF has uniform relative degree one. The two design parameters of the new QP setup allow us to control how aggressive the resulting control law is when trying to satisfy the two control objectives. The paper presents the controller in a closed form making it unnecessary to solve the QP problem on line and facilitating the analysis. Next, we introduce the concept of Robust-CBF that, when combined with existing ISS-CLFs, produces controllers for constrained nonlinear systems with disturbances. In an example, a nonlinear system is used to illustrate the ease with which the proposed design method handles nonconvex constraints and disturbances and to illuminate some tradeoffs.\",\"language\":\"en\",\"urldate\":\"2020-06-08\",\"journal\":\"Automatica\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Jankovic\"],\"firstnames\":[\"Mrdjan\"],\"suffixes\":[]}],\"month\":\"October\",\"year\":\"2018\",\"pages\":\"359–367\",\"bibtex\":\"@article{jankovic_robust_2018,\\n\\ttitle = {Robust control barrier functions for constrained stabilization of nonlinear systems},\\n\\tvolume = {96},\\n\\tissn = {00051098},\\n\\turl = {https://linkinghub.elsevier.com/retrieve/pii/S0005109818303509},\\n\\tdoi = {10.1016/j.automatica.2018.07.004},\\n\\tabstract = {Quadratic Programming (QP) has been used to combine Control Lyapunov and Control Barrier Functions (CLF and CBF) to design controllers for nonlinear systems with constraints. It has been successfully applied to robotic and automotive systems. The approach could be considered an extension of the CLF-based point-wise minimum norm controller. In this paper we modify the original QP problem in a way that guarantees that V˙ {\\\\textless} 0, if the barrier constraint is inactive, as well as local asymptotic stability under the standard (minimal) assumptions on the CLF and CBF. We also remove the assumption that the CBF has uniform relative degree one. The two design parameters of the new QP setup allow us to control how aggressive the resulting control law is when trying to satisfy the two control objectives. The paper presents the controller in a closed form making it unnecessary to solve the QP problem on line and facilitating the analysis. Next, we introduce the concept of Robust-CBF that, when combined with existing ISS-CLFs, produces controllers for constrained nonlinear systems with disturbances. In an example, a nonlinear system is used to illustrate the ease with which the proposed design method handles nonconvex constraints and disturbances and to illuminate some tradeoffs.},\\n\\tlanguage = {en},\\n\\turldate = {2020-06-08},\\n\\tjournal = {Automatica},\\n\\tauthor = {Jankovic, Mrdjan},\\n\\tmonth = oct,\\n\\tyear = {2018},\\n\\tpages = {359--367},\\n}\\n\\n\",\"author_short\":[\"Jankovic, M.\"],\"key\":\"jankovic_robust_2018\",\"id\":\"jankovic_robust_2018\",\"bibbaseid\":\"jankovic-robustcontrolbarrierfunctionsforconstrainedstabilizationofnonlinearsystems-2018\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://linkinghub.elsevier.com/retrieve/pii/S0005109818303509\"},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Safety-Critical Rapid Aerial Exploration of Unknown Environments\",\"abstract\":\"This paper details a novel approach to collision avoidance for aerial vehicles that enables high-speed flight in uncertain environments. This framework is applied at the controller level and provides safety regardless of the planner that is used. The method is shown to be robust to state uncertainty and disturbances, and is computed entirely online utilizing the full nonlinear system dynamics. The effectiveness of this method is shown in a high-fidelity simulation of a quadrotor with onboard sensors rapidly and safely exploring a cave environment utilizing a simple planner.\",\"language\":\"en\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Singletary\"],\"firstnames\":[\"Andrew\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Gurriet\"],\"firstnames\":[\"Thomas\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Nilsson\"],\"firstnames\":[\"Petter\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ames\"],\"firstnames\":[\"Aaron\"],\"suffixes\":[]}],\"pages\":\"7\",\"bibtex\":\"@article{singletary_safety-critical_nodate,\\n\\ttitle = {Safety-{Critical} {Rapid} {Aerial} {Exploration} of {Unknown} {Environments}},\\n\\tabstract = {This paper details a novel approach to collision avoidance for aerial vehicles that enables high-speed flight in uncertain environments. This framework is applied at the controller level and provides safety regardless of the planner that is used. The method is shown to be robust to state uncertainty and disturbances, and is computed entirely online utilizing the full nonlinear system dynamics. The effectiveness of this method is shown in a high-fidelity simulation of a quadrotor with onboard sensors rapidly and safely exploring a cave environment utilizing a simple planner.},\\n\\tlanguage = {en},\\n\\tauthor = {Singletary, Andrew and Gurriet, Thomas and Nilsson, Petter and Ames, Aaron},\\n\\tpages = {7},\\n}\\n\",\"author_short\":[\"Singletary, A.\",\"Gurriet, T.\",\"Nilsson, P.\",\"Ames, A.\"],\"key\":\"singletary_safety-critical_nodate\",\"id\":\"singletary_safety-critical_nodate\",\"bibbaseid\":\"singletary-gurriet-nilsson-ames-safetycriticalrapidaerialexplorationofunknownenvironments\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{}},\"downloads\":0,\"html\":\"\"}],\n      metadata: {\"authorlinks\":{}},\n      ownerID: undefined\n    };\n  </script>\n\n  <script type=\"text/javascript\">\n  var site$;\n  if (typeof $ != 'undefined') {\n    console.log('existing jquery: storing and then restoring');\n    site$ = $;\n    $ = null;\n  }\n  </script>\n\n  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.2.4/jquery.min.js\">\n  </script>\n  <script type=\"text/javascript\">\n  if (site$) {\n    console.log('existing jquery: avoiding conflict and restoring');\n    bb$ = $.noConflict(true);\n    $ = site$;\n  } else {\n    bb$ = $;\n  }\n  </script>\n\n  <script src=\"//bibbase.org/js/bibbase.min.js\"\n          type=\"text/javascript\">\n  </script>\n\n  <script type=\"text/javascript\"\n          src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML\">\n  </script>\n  <script type=\"text/x-mathjax-config\">\n    MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]},\n                        skipTags: [\"body\"],\n                        processClass: \"bibbase_paper\"});\n  </script>\n\n  <style>\n  @media print {\n    .dontprint {\n        display: none !important;\n    }\n\n  .bibbase_group {\n    background-color: #E0E0E0;\n    font-style: italic;\n    font-size: larger;\n    text-shadow: 0px 0px 3px #FFFFFF;\n    border-radius: 4px 4px 4px 4px;\n    -moz-border-radius: 4px 4px 4px 4px;\n    -webkit-border-radius: 4px;\n    padding: 5px 40px 5px;\n    margin-top: 10px;\n    margin-bottom: 5px;\n    cursor: pointer;\n  }\n\n  .bibbase_paper {\n    margin-bottom: 5px;\n  }\n\n  }\n  </style>\n\n  \n  <div style=\"float: right; margin-right: 10px; margin-top: 10px; text-align: right; font-size: 12px\">\n    generated by\n    <a href=\"//bibbase.org\"\n       onclick=\"trackOutboundLink('bibbase', 'logo clicked', window.location.href, '//bibbase.org'); return false;\">\n      <img src=\"//bibbase.org/img/logo.svg\"\n           style=\"vertical-align: middle; margin-left: 3px; height: 16px;\"/\n           alt=\"bibbase.org\"\n           title=\"BibBase – The easiest way to maintain your publications page.\"\n        ></a>\n    \n  </div>\n  \n\n  <div id=\"bibbase_header\" class=\"dontprint\" style=\"\">\n\n    <ul class=\"nav nav-pills\" style=\"margin: 0px;\">\n\n      <li class=\"dropdown\" id=\"groupby_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\">\n          Group by\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li class=\"groupby year\"><a onclick=\"groupby('year')\">\n            Year</a>\n        </li>\n        <li class=\"groupby author\"><a onclick=\"groupby('author_short')\">\n            Author</a>\n        </li>\n        <li class=\"groupby type\"><a onclick=\"groupby('type')\">\n            Type</a>\n        </li>\n        <li class=\"groupby keyword\"><a onclick=\"groupby('keyword')\">\n            Keyword</a>\n        </li>\n        <li class=\"groupby downloads\"><a onclick=\"groupby('downloads')\">\n            Downloads</a>\n        </li>\n      </ul>\n      </li>\n\n\n      <li class=\"dropdown\" id=\"menu_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\" alt=\"controls\">\n          <i class=\"fa fa-reorder\" alt=\"controls\"></i>\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li>\n          <a onclick=\"toggleAll()\">\n            <i class=\"fa fa-chevron-down fa-fw\"></i> Expand/Collapse All\n          </a>\n        </li>\n        <li>\n          <a download=\"items\" href=\"data:text/bibtex;base64,@inproceedings{richards_robust_2005,
	address = {Portland, OR, USA},
	title = {Robust model predictive control with imperfect information},
	isbn = {978-0-7803-9098-0},
	url = {http://ieeexplore.ieee.org/document/1469944/},
	doi = {10.1109/ACC.2005.1469944},
	abstract = {This paper presents two extensions to robust Model Predictive Control (MPC) involving imperfect information. Previous work developed a form of MPC guaranteeing feasibility and constraint satisfaction given an unknown but bounded disturbance and perfect state information. In the ﬁrst extension, this controller is modiﬁed to account for an unknown but bounded state estimation error. As an example, a simple estimator is proposed and analyzed to provide the necessary error bounds. Furthermore, it is shown that delayed state information can be handled using the same method. These analyses depend on knowledge of bounds on the measurement and disturbance uncertainties. The second extension provides a method of estimating these bounds using available data, providing an adaptive form of the controller for cases where the error levels are poorly known a priori.},
	language = {en},
	urldate = {2021-02-01},
	booktitle = {Proceedings of the 2005, {American} {Control} {Conference}, 2005.},
	publisher = {IEEE},
	author = {Richards, A. and How, J.},
	year = {2005},
	pages = {268--273},
}



@inproceedings{carlo_dynamic_2018,
	title = {Dynamic {Locomotion} in the {MIT} {Cheetah} 3 {Through} {Convex} {Model}-{Predictive} {Control}},
	doi = {10.1109/IROS.2018.8594448},
	abstract = {This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20-30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.},
	booktitle = {2018 {IEEE}/{RSJ} {International} {Conference} on {Intelligent} {Robots} and {Systems} ({IROS})},
	author = {Carlo, J. Di and Wensing, P. M. and Katz, B. and Bledt, G. and Kim, S.},
	month = oct,
	year = {2018},
	note = {ISSN: 2153-0866},
	keywords = {Convex functions, Dynamics, Legged locomotion, MIT cheetah 3, Predictive control, Predictive models, Robot kinematics, convex model-predictive control, convex optimization, convex programming, dynamic locomotion, ground reaction force planning problems, legged locomotion, predictive control, robot dynamics, torque control, torque-controlled quadruped robot},
	pages = {1--9},
}



@article{da_learning_2020,
	title = {Learning a {Contact}-{Adaptive} {Controller} for {Robust}, {Efficient} {Legged} {Locomotion}},
	url = {http://arxiv.org/abs/2009.10019},
	abstract = {We present a hierarchical framework that combines model-based control and reinforcement learning (RL) to synthesize robust controllers for a quadruped (the Unitree Laikago). The system consists of a high-level controller that learns to choose from a set of primitives in response to changes in the environment and a low-level controller that utilizes an established control method to robustly execute the primitives. Our framework learns a controller that can adapt to challenging environmental changes on the ﬂy, including novel scenarios not seen during training. The learned controller is up to 85 percent more energy efﬁcient and is more robust compared to baseline methods. We also deploy the controller on a physical robot without any randomization or adaptation scheme.},
	language = {en},
	urldate = {2021-01-10},
	journal = {arXiv:2009.10019 [cs]},
	author = {Da, Xingye and Xie, Zhaoming and Hoeller, David and Boots, Byron and Anandkumar, Animashree and Zhu, Yuke and Babich, Buck and Garg, Animesh},
	month = nov,
	year = {2020},
	note = {arXiv: 2009.10019},
	keywords = {Computer Science - Machine Learning, Computer Science - Robotics},
}



@inproceedings{chellaboina_invariance_2000,
	address = {Chicago, IL, USA},
	title = {An invariance principle for nonlinear hybrid and impulsive dynamical systems},
	isbn = {978-0-7803-5519-4},
	url = {http://ieeexplore.ieee.org/document/879139/},
	doi = {10.1109/ACC.2000.879139},
	abstract = {In this paper we develop an invariance principle for dynamical systems possessing leftcontinuous ows. Speciÿcally, we show that left-continuity of the system trajectories in time for each ÿxed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi-inÿnite interval are su cient for establishing an invariance principle for hybrid and impulsive dynamical systems. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.},
	language = {en},
	urldate = {2020-12-31},
	booktitle = {Proceedings of the 2000 {American} {Control} {Conference}. {ACC} ({IEEE} {Cat}. {No}.{00CH36334})},
	publisher = {IEEE},
	author = {Chellaboina, V. and Bhat, S.P. and Haddad, W.M.},
	year = {2000},
	pages = {3116--3122 vol.5},
}



@article{nesic_framework_2004,
	title = {A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models},
	volume = {49},
	issn = {1558-2523},
	doi = {10.1109/TAC.2004.831175},
	abstract = {A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented. Both fixed and fast sampling are considered. In each case, sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete-time plant models also stabilizes the exact discrete-time plant model for sufficiently small integration and/or sampling periods. Previous results in the literature are extended to cover: 1) continuous-time plants modeled as differential inclusions; 2) general approximate discrete-time plant models; 3) dynamical discontinuous controllers modeled as difference inclusions; and 4) stability with respect to closed arbitrary (not necessarily compact) sets.},
	number = {7},
	journal = {IEEE Transactions on Automatic Control},
	author = {Nesic, D. and Teel, A. R.},
	month = jul,
	year = {2004},
	note = {Conference Name: IEEE Transactions on Automatic Control},
	keywords = {Australia Council, Control design, Feedback control, Hardware, Lyapunov method, Lyapunov methods, Military computing, Robustness, Sampling methods, Stability, Sufficient conditions, continuous time systems, continuous-time plants, control system synthesis, discrete time systems, discrete-time models, dynamical discontinuous controllers, fast sampling, fixed sampling, nonlinear control systems, nonlinear sampled-data systems stability, sampled data systems, sampled-data differential inclusions, stability},
	pages = {1103--1122},
}



@article{nesic_sufficient_1999,
	title = {Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations},
	volume = {38},
	issn = {0167-6911},
	url = {http://www.sciencedirect.com/science/article/pii/S0167691199000730},
	doi = {10.1016/S0167-6911(99)00073-0},
	abstract = {Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.},
	language = {en},
	number = {4},
	urldate = {2020-12-29},
	journal = {Systems \& Control Letters},
	author = {Nešić, D. and Teel, A. R. and Kokotović, P. V.},
	month = dec,
	year = {1999},
	keywords = {Discrete time, Nonlinear, Sampled data, Stabilization},
	pages = {259--270},
}



@article{bradley_at_2020,
	title = {At the {Interface} of {Algebra} and {Statistics}},
	url = {http://arxiv.org/abs/2004.05631},
	abstract = {This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the "fixed points" of a morphism with its adjoint encode interesting information.},
	language = {en},
	urldate = {2020-12-28},
	journal = {arXiv:2004.05631 [quant-ph, stat]},
	author = {Bradley, Tai-Danae},
	month = apr,
	year = {2020},
	note = {arXiv: 2004.05631},
	keywords = {Computer Science - Machine Learning, Mathematics - Category Theory, Quantum Physics, Statistics - Machine Learning},
}



@book{simic_towards_2000,
	title = {Towards a {Geometric} {Theory} of {Hybrid} {Systems}.},
	volume = {12},
	abstract = {We propose a framework for a geometric theory of hybrid systems. Given a deterministic, non-blocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non-smooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it is due to nonsmoothness of the hybrid flow. We introduce the notion of topological equivalence of hybrid systems and locally classify isolated Zeno states in dimension two.},
	author = {Simic, Slobodan and Johansson, Karl and Sastry, Shankar and Lygeros, John},
	month = jan,
	year = {2000},
	note = {Journal Abbreviation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Pages: 436
Publication Title: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms},
}



@article{linan_global_2020,
	title = {Global controllability tests for geometric hybrid control systems},
	url = {http://arxiv.org/abs/1905.02490},
	abstract = {This paper introduces a novel geometric framework to deﬁne and study hybrid systems. We exploit the geometry and topology of the set of jump points, where the instantaneous change of dynamics takes place, in order to gain controllability for the system. This approach allows us to describe new global controllability tests for hybrid control systems. We illustrate these results with several examples where none of the continuous control systems are controllable, but the associated hybrid system is controllable because of the characteristics of the jump set.},
	language = {en},
	urldate = {2020-12-28},
	journal = {arXiv:1905.02490 [math]},
	author = {Liñán, M. Barbero and Cortés, J. and de Diego, D. Martín and Martínez, S. and Lecanda, M. C. Muñoz},
	month = jun,
	year = {2020},
	note = {arXiv: 1905.02490},
	keywords = {93C30, 93B05, 93B27, Mathematics - Differential Geometry, Mathematics - Optimization and Control},
}



@article{guanfeng_liu_unified_2002,
	title = {A unified geometric approach to modeling and control of constrained mechanical systems},
	volume = {18},
	issn = {2374-958X},
	doi = {10.1109/TRA.2002.802207},
	abstract = {Dynamic control of constrained mechanical systems, such as robotic manipulators under end-effector constraints, parallel manipulators, and multifingered robotic hands under closure constraints have been classic problems in robotics research. In this paper, we provide a unified geometric framework for modeling, analysis, and control of constrained mechanical systems. Starting with the constraint, we define two canonical subspaces, namely the subspace of constraint forces and the tangent space of the constraint manifold for holonomic constraint. Using the kinetic energy metric, we define the remaining subspaces and show explicitly the relations among these subspaces. We project the Euler-Lagrange equation of a constrained mechanical system into two orthogonal components and give geometric and physical interpretations of the projected equations. Based on the projected equations, a unified and asymptotically stable hybrid position/force-control algorithm is proposed, along with experimental results for several practical examples. In the case of nonholonomic constraints, we show that the equations can be projected to the distribution/codistribution associated with the constraints and the control law reduces to hybrid velocity/force control.},
	number = {4},
	journal = {IEEE Transactions on Robotics and Automation},
	author = {Guanfeng Liu and Zexiang Li},
	month = aug,
	year = {2002},
	note = {1000},
	keywords = {Control system analysis, Control systems, Equations, Euler-Lagrange equation, Force control, Manipulator dynamics, Mechanical systems, Orbital robotics, Parallel robots, Solid modeling, Subspace constraints, asymptotic stability, canonical subspaces, closure constraints, constrained mechanical systems, constraint forces subspace, constraint manifold tangent space, constraint theory, control, control system analysis, dexterous manipulators, distribution/codistribution, dynamic control, end-effector constraints, force control, holonomic constraint, hybrid velocity/force control, industrial manipulators, kinetic energy metric, manipulator dynamics, modeling, multifingered robotic hands, nonholonomic constraints, orthogonal components, parallel manipulators, position control, robotic manipulators, unified asymptotically stable hybrid position/force-control algorithm, unified geometric approach, velocity control},
	pages = {574--587},
}



@incollection{biran_floer_2006,
	address = {Dordrecht},
	title = {{FLOER} {HOMOLOGY}, {DYNAMICS} {AND} {GROUPS}},
	volume = {217},
	isbn = {978-1-4020-4272-0},
	url = {http://link.springer.com/10.1007/1-4020-4266-3_09},
	abstract = {We discuss some recent results on algebraic properties of the group of Hamiltonian diﬀeomorphisms of a symplectic manifold. We focus on two topics which lie at the interface between Floer theory and dynamics: 1) Restrictions on Hamiltonian actions of ﬁnitely generated groups, including a Hamiltonian version of the Zimmer program dealing with actions of lattices; 2) Quasi-morphisms on the group of Hamiltonian diﬀeomorphisms. The unifying theme is the study of distortion of cyclic and one-parameter subgroups with respect to various metrics on the group of Hamiltonian diﬀeomorphisms.},
	language = {en},
	urldate = {2020-11-13},
	booktitle = {Morse {Theoretic} {Methods} in {Nonlinear} {Analysis} and in {Symplectic} {Topology}},
	publisher = {Kluwer Academic Publishers},
	author = {Polterovich, Leonid},
	editor = {Biran, Paul and Cornea, Octav and Lalonde, François},
	year = {2006},
	doi = {10.1007/1-4020-4266-3_09},
	note = {Series Title: NATO Science Series II: Mathematics, Physics and Chemistry},
	pages = {417--438},
}



@article{sullivan_homology_nodate,
	title = {{HOMOLOGY} {THEORY} {AND} {DYNAMICAL} {SYSTEMS}},
	language = {en},
	author = {Sullivan, D},
	pages = {24},
}



@article{burridge_sequential_1999,
	title = {Sequential {Composition} of {Dynamically} {Dexterous} {Robot} {Behaviors}},
	volume = {18},
	issn = {0278-3649, 1741-3176},
	url = {http://journals.sagepub.com/doi/10.1177/02783649922066385},
	doi = {10.1177/02783649922066385},
	abstract = {We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a ﬂat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a speciﬁed location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.},
	language = {en},
	number = {6},
	urldate = {2020-10-20},
	journal = {The International Journal of Robotics Research},
	author = {Burridge, R. R. and Rizzi, A. A. and Koditschek, D. E.},
	month = jun,
	year = {1999},
	pages = {534--555},
}



@article{burridge_sequential_1999-1,
	title = {Sequential {Composition} of {Dynamically} {Dexterous} {Robot} {Behaviors}},
	volume = {18},
	issn = {0278-3649, 1741-3176},
	url = {http://journals.sagepub.com/doi/10.1177/02783649922066385},
	doi = {10.1177/02783649922066385},
	abstract = {We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a ﬂat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a speciﬁed location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.},
	language = {en},
	number = {6},
	urldate = {2020-07-10},
	journal = {The International Journal of Robotics Research},
	author = {Burridge, R. R. and Rizzi, A. A. and Koditschek, D. E.},
	month = jun,
	year = {1999},
	note = {5},
	pages = {534--555},
}



@article{taylor_adaptive_nodate,
	title = {Adaptive {Safety} with {Control} {Barrier} {Functions}},
	abstract = {Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunovbased methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the system’s state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this uniﬁed framework to achieve stability and safety in an Adaptive Cruise Control (ACC) simulation.},
	language = {en},
	author = {Taylor, Andrew and Ames, Aaron D},
	pages = {7},
}



@article{reher_inverse_nodate,
	title = {An {Inverse} {Dynamics} {Approach} to {Control} {Lyapunov} {Functions}},
	abstract = {With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots. The primary focus of this paper is on the development of an alternative approach to the implementation of controllers utilizing control Lyapunov function based quadratic programs. This approach utilizes many of the desirable aspects from successful inverse dynamics based controllers in the literature, while also incorporating a variant of control Lyapunov functions that renders better convergence in the context of tracking outputs. The principal beneﬁts of this formulation include a greater ability to add costs which regulate the resulting behavior of the robot. In addition, the model error-prone inertia matrix is used only once, in a non-inverted form. The result is a successful demonstration of the controller for walking in simulation, and applied on hardware in real-time for dynamic crouching.},
	language = {en},
	author = {Reher, Jenna and Kann, Claudia and Ames, Aaron D},
	pages = {8},
}



@article{chen_density_nodate,
	title = {Density {Functions} for {Guaranteed} {Safety} on {Robotic} {Systems}},
	abstract = {The recent study on density functions as the dual of value functions for optimal control gives a new method for synthesizing safe controllers. A density function describes the state distribution in the state space, and its evolution follows the Liouville Partial Differential Equation (PDE). The duality between the density function and the value function in optimal control can be utilized to solve constrained optimal control problems with a primal-dual algorithm. This paper focuses on the application of the method on robotic systems and proposes an implementation of the primal-dual algorithm that is less computationally demanding than the method used in the literature. To be speciﬁc, we use kernel density estimation to estimate the density function, which scales better than the ODE approach in the literature and only requires a simulator instead of a dynamic model. The Hamilton Jacobi Bellman (HJB) PDE is solved with the ﬁnite element method in an implicit form, which accelerates the value iteration process. We show an application of the safe control synthesis with density functions on a segway control problem demonstrated experimentally.},
	language = {en},
	author = {Chen, Yuxiao and Singletary, Andrew and Ames, Aaron D},
	pages = {6},
}



@article{pandey_converse_nodate,
	title = {On a {Converse} {Theorem} for {Finite}-{Time} {Lyapunov} {Functions} to {Estimate} {Domains} of {Attraction}},
	abstract = {The main result of the paper is a new converse theorem for ﬁnite-time Lyapunov functions. We show the existence of a ﬁnite-time Lyapunov function for an autonomous continuoustime nonlinear dynamical system if the origin of the system is asymptotically stable. Our proof extends the recent results in ﬁnite-time Lyapunov function theory by providing an alternative converse proof for the existence of ﬁnite-time Lyapunov functions. In particular, we show that given asymptotic stability of the origin, the linearized dynamics satisfy global ﬁnitetime Lyapunov function conditions hence proving the converse theorem. Using our results, we present a consolidated theory for using and constructing Lyapunov functions to certify system stability properties. We also propose a constructive algorithm to efﬁciently compute non-conservative estimates of the domain of attraction for nonlinear dynamical systems.},
	language = {en},
	author = {Pandey, Ayush and Ames, Aaron D},
	pages = {7},
}



@article{doeser_invariant_nodate,
	title = {Invariant {Sets} for {Integrators} and {Quadrotor} {Obstacle} {Avoidance}},
	abstract = {Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, ﬁnding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difﬁcult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nthorder integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n ≤ 4. Using differential ﬂatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of ﬁnding analytical expressions for control-invariant sets.},
	language = {en},
	author = {Doeser, Ludvig and Nilsson, Petter and Ames, Aaron D and Murray, Richard M},
	pages = {8},
}



@article{nilsson_lyapunov-like_nodate,
	title = {Lyapunov-{Like} {Conditions} for {Tight} {Exit} {Probability} {Bounds} through {Comparison} {Theorems} for {SDEs}},
	abstract = {Computing upper bounds on exit probabilities—the probability that a system reaches certain “bad” sets—may assist decision-making in control of stochastic systems. Existing analytical bounds for systems described by stochastic differential equations are quite loose, especially for low-probability events, which limits their applicability in practical situations. In this paper we analyze why existing bounds are loose, and conclude that it is a fundamental issue with the underlying techniques based on martingale inequalities. As an alternative, we give comparison results for stochastic differential equations that via a Lyapunov-like function allow exit probabilities of an ndimensional system to be upper-bounded by an exit probability of a one-dimensional Ornstein-Uhlenbeck process. Even though no closed-form expression is known for the latter, it depends on three or four parameters and can be a priori tabulated for applications. We extend these ideas to the controlled setting and state a stochastic analogue of control barrier functions. The bounds are illustrated on numerical examples and are shown to be much tighter than those based on martingale inequalities.},
	language = {en},
	author = {Nilsson, Petter and Ames, Aaron D},
	pages = {7},
}



@article{hamed_distributed_nodate,
	title = {Distributed {Feedback} {Controllers} for {Stable} {Cooperative} {Locomotion} of {Quadrupedal} {Robots}: {A} {Virtual} {Constraint} {Approach}},
	abstract = {This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. The paper then generates modiﬁed and local virtual constraints for each agent that allow stable collaborative locomotion. Optimal distributed feedback controllers, based on nonlinear control and quadratic programming, are developed to impose the local virtual constraints. To demonstrate the power of the analytical foundation, an extensive numerical simulation for cooperative locomotion of two quadrupedal robots with robotic manipulators is presented. The numerical complex hybrid model has 64 continuous-time domains, 192 discretetime transitions, 96 state variables, and 36 control inputs.},
	language = {en},
	author = {Hamed, Kaveh Akbari},
	pages = {8},
}



@article{chen_optimal_nodate,
	title = {Optimal {Safe} {Controller} {Synthesis}: {A} {Density} {Function} {Approach}},
	abstract = {This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value function. The density function follows the Liouville equation and is the dual of the value function, which satisﬁes Bellman’s optimality principle. Thanks to density functions, constraints over the distribution of states, such as safety constraints, can be posed straightforwardly in an optimal control problem. The constrained optimal control problem is then solved with a primal-dual algorithm. This formulation is extended to the case with external disturbances, and we show that the robust constrained optimal control can be solved with a modiﬁed primal-dual algorithm. We apply this formulation to the problem of ﬁnding the optimal safe controller that minimizes the cumulative intervention. An adaptive cruise control (ACC) example is used to demonstrate the efﬁcacy of the proposed, wherein we compare the result of the density function approach with the conventional control barrier function (CBF) method.},
	language = {en},
	author = {Chen, Yuxiao and Ahmadi, Mohamadreza and Ames, Aaron D},
	pages = {6},
}



@article{romero_continuous-time_nodate,
	title = {Continuous-{Time} {Optimization} of {Time}-{Varying} {Cost} {Functions} {Via} {Finite}-{Time} {Stability} with {Pre}-{Defined} {Convergence} {Time}},
	abstract = {In this paper, we propose a new family of continuous-time optimization algorithms for time-varying, locally strongly convex cost functions, based on discontinuous second-order gradient optimization ﬂows with provable ﬁnite-time convergence to local optima. To analyze our ﬂows, we ﬁrst extend a well-know Lyapunov inequality condition for ﬁnite-time stability, to the case of arbitrary time-varying differential inclusions, particularly of the Filippov type. We then prove the convergence of our proposed ﬂows in ﬁnite time. We illustrate the performance of our proposed ﬂows on a quadratic cost function to track a decaying sinusoid.},
	language = {en},
	author = {Romero, Orlando and Benosman, Mouhacine},
	pages = {6},
}



@article{lopez_robust_2020,
	title = {Robust {Adaptive} {Control} {Barrier} {Functions}: {An} {Adaptive} \& {Data}-{Driven} {Approach} to {Safety} ({Extended} {Version})},
	copyright = {5},
	shorttitle = {Robust {Adaptive} {Control} {Barrier} {Functions}},
	url = {http://arxiv.org/abs/2003.10028},
	abstract = {A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive control algorithm for systems nominally contracting in closed-loop. This uniﬁcation is more general than other safety controllers as closed-loop contraction does not require the system be invertible or in a particular form. Additionally, the approach is less expensive than nonlinear model predictive control as it does not require a full desired trajectory, but rather only a desired terminal state. The approach is illustrated on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.},
	language = {en},
	urldate = {2020-07-02},
	journal = {arXiv:2003.10028 [cs, eess]},
	author = {Lopez, Brett T. and Slotine, Jean-Jacques E. and How, Jonathan P.},
	month = may,
	year = {2020},
	note = {arXiv: 2003.10028},
	keywords = {Electrical Engineering and Systems Science - Systems and Control},
}



@article{siravuru_nonlinear_nodate,
	title = {Nonlinear {Control} {Using} {Coordinate}-{Free} and {Euler} {Formulations}: {An} {Empirical} {Evaluation} on a {3D} {Pendulum}},
	abstract = {Pendulum dynamics are widely utilized in robotics control literature to test and evaluate novel control design techniques. They exhibit many interesting features commonly seen in real-world nonlinear systems and yet they are simple enough for quick prototyping, further analysis, and benchmarking. In this work, we study the impact of a 3D pendulum’s orientation parametrization on stabilization performance. Mainly, we show that using a global or coordinate-free formulation for dynamics and control is not only singularity-free but also more input-eﬃcient. We validate this empirically by running over 700 stabilization simulations across the full conﬁguration space of a 3D pendulum and compare the performance of a geometric and a Euler-parametrized controller. We show that the geometric controller is able to leverage the inherent manifold curvature and ﬂow along geodesics for eﬃcient stabilization.},
	language = {en},
	author = {Siravuru, Avinash and Sreenath, Koushil},
	pages = {6},
}



@article{grandia_nonlinear_2020,
	title = {Nonlinear {Model} {Predictive} {Control} of {Robotic} {Systems} with {Control} {Lyapunov} {Functions}},
	url = {http://arxiv.org/abs/2006.01229},
	abstract = {The theoretical uniﬁcation of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the ﬁrst real-time realization of a uniﬁed NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efﬁciently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difﬁcult cost function and parameter tuning required by NMPC. Therefore the uniﬁed controller improves the performance of each isolated controller and simpliﬁes the overall design process.},
	language = {en},
	urldate = {2020-06-25},
	journal = {arXiv:2006.01229 [cs, eess]},
	author = {Grandia, Ruben and Taylor, Andrew J. and Singletary, Andrew and Hutter, Marco and Ames, Aaron D.},
	month = jun,
	year = {2020},
	note = {arXiv: 2006.01229},
	keywords = {Computer Science - Robotics, Electrical Engineering and Systems Science - Systems and Control},
}



@article{rosa_jr_topological_2020,
	title = {A {Topological} {Approach} to {Gait} {Generation} for {Biped} {Robots}},
	url = {http://arxiv.org/abs/2006.03785},
	abstract = {This paper describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2D and 3D biped walkers subject to conﬁguration inequality constraints, physical holonomic constraints (e.g., closed chains), and virtual holonomic constraints (user-deﬁned constraints enforced through feedback control). Our method constructs implicitly-deﬁned manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium conﬁgurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2D and 3D biped walkers.},
	language = {en},
	urldate = {2020-06-25},
	journal = {arXiv:2006.03785 [cs]},
	author = {Rosa Jr., Nelson and Lynch, Kevin M.},
	month = jun,
	year = {2020},
	note = {arXiv: 2006.03785},
	keywords = {Computer Science - Robotics},
}



@article{lekien_lagrangian_2007,
	title = {Lagrangian coherent structures in n-dimensional systems},
	volume = {48},
	issn = {0022-2488, 1089-7658},
	url = {http://aip.scitation.org/doi/10.1063/1.2740025},
	doi = {10.1063/1.2740025},
	language = {en},
	number = {6},
	urldate = {2020-06-25},
	journal = {Journal of Mathematical Physics},
	author = {Lekien, Francois and Shadden, Shawn C. and Marsden, Jerrold E.},
	month = jun,
	year = {2007},
	pages = {065404},
}



@misc{artstein_stabilization_nodate,
	title = {{STABILIZATION} {WITH} {RELAXED} {CONTROLS}},
	shorttitle = {{PII}},
	url = {https://reader.elsevier.com/reader/sd/pii/0362546X83900494?token=B88DBE74ECF120DBA01EA046831622DD7E545B033FA36243E3552AA41910AC40C4AC00AEF64C05628DED2123DF4CD220},
	language = {en},
	urldate = {2020-06-22},
	author = {Artstein},
	doi = {10.1016/0362-546X(83)90049-4},
	note = {ISSN: 10.1016/0362-546X(83)90049-4
Library Catalog: reader.elsevier.com},
}



@article{sontag_characterizations_1995,
	title = {On characterizations of the input-to-state stability property},
	volume = {24},
	issn = {01676911},
	url = {https://linkinghub.elsevier.com/retrieve/pii/0167691194000506},
	doi = {10.1016/0167-6911(94)00050-6},
	abstract = {We show that the well-known Lyapunov suﬃcient condition for “input-to-state stability” is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.},
	language = {en},
	number = {5},
	urldate = {2020-06-22},
	journal = {Systems \& Control Letters},
	author = {Sontag, Eduardo D. and Wang, Yuan},
	month = apr,
	year = {1995},
	pages = {351--359},
}



@inproceedings{sussmann_general_1993,
	title = {A general result on the stabilization of linear systems using bounded controls},
	doi = {10.1109/CDC.1993.325264},
	abstract = {We present two constructions of controllers that globally stabilize linear systems subject to control saturation. The only conditions imposed are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition holds. We use essentially arbitrary saturations /spl sigma/, subject only to the requirement that: (i) /spl sigma/ is locally Lipschitz, (ii) s/spl sigma/(s){\textgreater}0 whenever s/spl ne/0, (iii) /spl sigma/ is differentiable at 0 and /spl sigma/'(0){\textgreater}0, and (iv) lim inf/sub {\textbar}s{\textbar}/spl rarr//spl infin//{\textbar}/spl sigma/(s){\textbar}{\textgreater}0.{\textless}{\textgreater}},
	booktitle = {Proceedings of 32nd {IEEE} {Conference} on {Decision} and {Control}},
	author = {Sussmann, H. and Sontag, E. and Yang, Y.},
	month = dec,
	year = {1993},
	keywords = {Actuators, Control systems, Control theory, Eigenvalues and eigenfunctions, Linear systems, Mathematics, Negative feedback, Open loop systems, Power engineering and energy, Power supplies, bounded controls, control saturation, control system analysis, eigenvalues, eigenvalues and eigenfunctions, global stability, linear systems, linear time invariant continuous time systems, stability, stabilization},
	pages = {1802--1807 vol.2},
}



@article{sontag_nonlinear_1981,
	title = {Nonlinear regulation: {The} piecewise linear approach},
	volume = {26},
	issn = {1558-2523},
	shorttitle = {Nonlinear regulation},
	doi = {10.1109/TAC.1981.1102596},
	abstract = {This paper approaches nonlinear control problems through the use of (discrete-time) piecewise linear systems. These are systems whose next-state and output maps are both described by PL maps, i.e., by maps which are affine on each of the components of a finite polyhedral partition. Various results on state and output feedback, observers, and inverses, standard for linear systems, are proved for PL systems. Many of these results are then used in the study of more general (both discrete- and continuous-time) systems, using suitable approximations.},
	number = {2},
	journal = {IEEE Transactions on Automatic Control},
	author = {Sontag, E.},
	month = apr,
	year = {1981},
	note = {Conference Name: IEEE Transactions on Automatic Control},
	keywords = {Arithmetic, Control systems, Digital control, Linear programming, Linear systems, Logic, Microprocessors, Nonlinear control systems, Piecewise linear approximation, Piecewise linear techniques, Piecewise-linear approximation, Regulators, nonlinear systems, State feedback, nonlinear systems},
	pages = {346--358},
}



@incollection{morel_input_2008,
	address = {Berlin, Heidelberg},
	title = {Input to {State} {Stability}: {Basic} {Concepts} and {Results}},
	volume = {1932},
	isbn = {978-3-540-77644-4 978-3-540-77653-6},
	shorttitle = {Input to {State} {Stability}},
	url = {http://link.springer.com/10.1007/978-3-540-77653-6_3},
	language = {en},
	urldate = {2020-06-22},
	booktitle = {Nonlinear and {Optimal} {Control} {Theory}},
	publisher = {Springer Berlin Heidelberg},
	author = {Sontag, Eduardo D.},
	editor = {Morel, J. -M. and Takens, F. and Teissier, B. and Nistri, Paolo and Stefani, Gianna},
	collaborator = {Agrachev, Andrei A. and Morse, A. Stephen and Sontag, Eduardo D. and Sussmann, Héctor J. and Utkin, Vadim I.},
	year = {2008},
	doi = {10.1007/978-3-540-77653-6_3},
	note = {Series Title: Lecture Notes in Mathematics},
	pages = {163--220},
}



@article{sontag_universal_1989,
	title = {A ‘universal’ construction of {Artstein}'s theorem on nonlinear stabilization},
	volume = {13},
	issn = {01676911},
	url = {https://linkinghub.elsevier.com/retrieve/pii/0167691189900285},
	doi = {10.1016/0167-6911(89)90028-5},
	abstract = {This note presents an explicit proof of the theorem due to Artstein - which states that the existence of a smooth control-Lyapunov function implies smooth stabilizabifity. Moreover, the result is extended to the real-analytic and rational cases as well. The proof uses a "universal' formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation.},
	language = {en},
	number = {2},
	urldate = {2020-06-22},
	journal = {Systems \& Control Letters},
	author = {Sontag, Eduardo D.},
	month = aug,
	year = {1989},
	pages = {117--123},
}



@article{morris_hybrid_2009,
	title = {Hybrid {Invariant} {Manifolds} in {Systems} {With} {Impulse} {Effects} {With} {Application} to {Periodic} {Locomotion} in {Bipedal} {Robots}},
	volume = {54},
	issn = {1558-2523},
	doi = {10.1109/TAC.2009.2024563},
	abstract = {Motivated by the problem of controlling walking in a biped with series compliant actuation, this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects. The first main result shows that when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold, there exist local coordinate transforms under which the Jacobian linearization of the Poincare return map has a block upper triangular structure. One diagonal block is the linearization of the system as restricted to the hybrid invariant manifold, also called the hybrid zero dynamics. The other is the product of two sensitivity matrices related to the transverse dynamics-one pertaining to the impact map and the other pertaining to the closed-loop vector field. When either of these sensitivity matrices is sufficiently close to zero, the stability of the return map is determined solely by the stability of the hybrid zero dynamics. The second main result of the paper details the construction of a hybrid invariant manifold, such as that required by the first main theorem. Forward invariance follows from the methods of Byrnes and Isidori, and impact invariance is achieved by a novel construction of impact-updated control parameters. In addition to providing impact invariance, the construction allows entries of the impact sensitivity matrix of the transverse dynamics to be made arbitrarily small. A simulation example is provided where stable walking is achieved in a 5-link biped with series compliant actuation.},
	number = {8},
	journal = {IEEE Transactions on Automatic Control},
	author = {Morris, Benjamin and Grizzle, Jessy W.},
	month = aug,
	year = {2009},
	note = {Conference Name: IEEE Transactions on Automatic Control},
	keywords = {Bipedal robots, Control systems, Differential equations, Feedback, Jacobian linearization, Jacobian matrices, Legged locomotion, Nonlinear systems, Orbital robotics, Orbits, Poincare invariance, Poincare return map, Robot kinematics, Stability, bipedal robot, closed loop systems, closed-loop vector field, forward invariance, hybrid invariant manifold, hybrid systems, hybrid zero dynamics, impact invariance, impact map, impact-updated control parameter, impulse effects, legged locomotion, linearisation techniques, local coordinate transforms, periodic control, periodic locomotion, periodic orbit, sensitivity analysis, sensitivity matrix, stability, stabilization, stable walking, transverse dynamics, underactuated systems, walking control, zero assignment, zero dynamics},
	pages = {1751--1764},
}



@misc{noauthor_frobenius_2020,
	title = {Frobenius theorem (differential topology)},
	copyright = {Creative Commons Attribution-ShareAlike License},
	url = {https://en.wikipedia.org/w/index.php?title=Frobenius_theorem_(differential_topology)&oldid=938445316},
	abstract = {In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an underdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds.  The theorem is foundational in differential topology and calculus on manifolds.},
	language = {en},
	urldate = {2020-06-16},
	journal = {Wikipedia},
	month = jan,
	year = {2020},
	note = {Page Version ID: 938445316},
}



@inproceedings{papachristodoulou_construction_2002,
	title = {On the construction of {Lyapunov} functions using the sum of squares decomposition},
	volume = {3},
	copyright = {5},
	doi = {10.1109/CDC.2002.1184414},
	abstract = {A relaxation of Lyapunov's direct method has been proposed elsewhere that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In the paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certain non-polynomial nonlinearities in the vector field to be handled exactly and the constructed Lyapunov functions to contain non-polynomial terms. It also allows robustness analysis to be performed. Some examples are given to illustrate how this is done.},
	booktitle = {Proceedings of the 41st {IEEE} {Conference} on {Decision} and {Control}, 2002.},
	author = {Papachristodoulou, A. and Prajna, S.},
	month = dec,
	year = {2002},
	note = {ISSN: 0191-2216},
	keywords = {Biological system modeling, Control systems, Lyapunov functions, Lyapunov method, Lyapunov methods, Nonlinear control systems, Nonlinear systems, Polynomials, Robust stability, Robustness, Sufficient conditions, Uncertainty, control system analysis, equality constraints, inequality constraints, integral constraints, nonlinear control systems, nonlinear dynamical systems, nonlinear systems, nonpolynomial nonlinearities, polynomials, robust control, robustness analysis, stability of equilibria, sum of squares decomposition, vectors},
	pages = {3482--3487 vol.3},
}



@inproceedings{motahar_composing_2016,
	title = {Composing limit cycles for motion planning of {3D} bipedal walkers},
	doi = {10.1109/CDC.2016.7799249},
	abstract = {This paper presents a framework for navigation of 3D dynamically walking bipeds. The framework is based on extracting gait primitives in the form of limit-cycle locomotion behaviors, which are then composed by a higher-level planning algorithm with the purpose of navigating the biped to a goal location while avoiding obstacles. By formulating motion planning as a discrete-time switched system with multiple equilibria - each corresponding to a gait primitive - we provide analytical conditions that constrain the frequency of the switching signal so that the biped is guaranteed to stably execute a suggested plan. Effectively, these conditions distill the stability limitations of the system dynamics in a form that can be readily incorporated to the planning algorithm. We demonstrate the feasibility of the method in the context of a 3D bipedal model, walking dynamically under the influence of a Hybrid Zero Dynamics (HZD) controller. It is shown that the dimensional reduction afforded by HZD greatly facilitates the application of the method by allowing certificates of stability for gait primitives using sums-of-squares programming.},
	booktitle = {2016 {IEEE} 55th {Conference} on {Decision} and {Control} ({CDC})},
	author = {Motahar, Mohamad Shafiee and Veer, Sushant and Poulakakis, Ioannis},
	month = dec,
	year = {2016},
	keywords = {3D bipedal walker motion planning, 3D dynamically walking biped navigation, HZD, Legged locomotion, Limit-cycles, Navigation, Planning, Switched systems, Switches, Three-dimensional displays, collision avoidance, discrete time systems, discrete-time switched system, gait analysis, gait primitive, gait primitive extraction, higher-level planning algorithm, hybrid zero dynamic controller, legged locomotion, limit-cycle locomotion behaviors, obstacle avoidance, path planning, stability, stability limitations, sums-of-squares programming, switching signal, switching systems (control)},
	pages = {6368--6374},
}



@inproceedings{agrawal_discrete_2017,
	title = {Discrete {Control} {Barrier} {Functions} for {Safety}-{Critical} {Control} of {Discrete} {Systems} with {Application} to {Bipedal} {Robot} {Navigation}},
	isbn = {978-0-9923747-3-0},
	url = {http://www.roboticsproceedings.org/rss13/p73.pdf},
	doi = {10.15607/RSS.2017.XIII.073},
	abstract = {In this paper, we extend the concept of control barrier functions, developed initially for continuous time systems, to the discrete-time domain. We demonstrate safety-critical control for nonlinear discrete-time systems with applications to 3D bipedal robot navigation. Particularly, we mathematically analyze two different formulations of control barrier functions, based on their continuous-time counterparts, and demonstrate how these can be applied to discrete-time systems. We show that the resulting formulation is a nonlinear program in contrast to the quadratic program for continuous-time systems and under certain conditions, the nonlinear program can be formulated as a quadratically constrained quadratic program. Furthermore, using the developed concept of discrete control barrier functions, we present a novel control method to address the problem of navigation of a high-dimensional bipedal robot through environments with moving obstacles that present time-varying safety-critical constraints.},
	language = {en},
	urldate = {2020-06-10},
	booktitle = {Robotics: {Science} and {Systems} {XIII}},
	publisher = {Robotics: Science and Systems Foundation},
	author = {Agrawal, Ayush and Sreenath, Koushil},
	month = jul,
	year = {2017},
}



@misc{noauthor_path-following_nodate,
	title = {Path-following for linear systems with unstable zero dynamics},
	shorttitle = {doi},
	url = {https://reader.elsevier.com/reader/sd/pii/S0005109806002196?token=22AE7F0A9F0CADCFAE496B41BFC0C9359622CC05594126822D2F63027DD83F339905E4DEA4652A25699EFA5AE0ACAD4B},
	language = {en},
	urldate = {2020-06-09},
	doi = {10.1016/j.automatica.2006.05.014},
	note = {Library Catalog: reader.elsevier.com},
}



@article{glotfelter_nonsmooth_2017,
	title = {Nonsmooth {Barrier} {Functions} {With} {Applications} to {Multi}-{Robot} {Systems}},
	volume = {1},
	issn = {2475-1456},
	doi = {10.1109/LCSYS.2017.2710943},
	abstract = {As multi-agent systems become more wide-spread and versatile, the ability to satisfy multiple system-level constraints grows increasingly important. In applications ranging from automated cruise control to safety in robot swarms, barrier functions have emerged as a tool to provably meet such constraints by guaranteeing forward invariance of desirable sets. However, satisfying multiple constraints typically implies formulating multiple barrier functions, which would be ameliorated if the barrier functions could be composed together as Boolean logic formulas. The use of max and min operators, which yields nonsmooth functions, represents one path to accomplish Boolean compositions of barrier functions, and this letter extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions. We validate our results by deploying Boolean compositions of nonsmooth barrier functions onto a team of mobile robots.},
	number = {2},
	journal = {IEEE Control Systems Letters},
	author = {Glotfelter, Paul and Cortés, Jorge and Egerstedt, Magnus},
	month = oct,
	year = {2017},
	note = {Conference Name: IEEE Control Systems Letters},
	keywords = {Boolean compositions, Boolean functions, Boolean logic formulas, Collision avoidance, Differential equations, Lyapunov methods, Multi-agent systems, Robotics, Robots, Robustness, Tools, autonomous systems, differential inclusions, max operators, min operators, mobile robots, multi-robot systems, multiagent systems, multiple system-level constraints, multirobot systems, nonsmooth barrier functions},
	pages = {310--315},
}



@article{posa_direct_2014,
	title = {A direct method for trajectory optimization of rigid bodies through contact},
	volume = {33},
	issn = {0278-3649, 1741-3176},
	url = {http://journals.sagepub.com/doi/10.1177/0278364913506757},
	doi = {10.1177/0278364913506757},
	abstract = {Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a speciﬁed sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisﬁes the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a ﬁnger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform.},
	language = {en},
	number = {1},
	urldate = {2020-06-08},
	journal = {The International Journal of Robotics Research},
	author = {Posa, Michael and Cantu, Cecilia and Tedrake, Russ},
	month = jan,
	year = {2014},
	pages = {69--81},
}



@article{jankovic_robust_2018,
	title = {Robust control barrier functions for constrained stabilization of nonlinear systems},
	volume = {96},
	issn = {00051098},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0005109818303509},
	doi = {10.1016/j.automatica.2018.07.004},
	abstract = {Quadratic Programming (QP) has been used to combine Control Lyapunov and Control Barrier Functions (CLF and CBF) to design controllers for nonlinear systems with constraints. It has been successfully applied to robotic and automotive systems. The approach could be considered an extension of the CLF-based point-wise minimum norm controller. In this paper we modify the original QP problem in a way that guarantees that V˙ {\textless} 0, if the barrier constraint is inactive, as well as local asymptotic stability under the standard (minimal) assumptions on the CLF and CBF. We also remove the assumption that the CBF has uniform relative degree one. The two design parameters of the new QP setup allow us to control how aggressive the resulting control law is when trying to satisfy the two control objectives. The paper presents the controller in a closed form making it unnecessary to solve the QP problem on line and facilitating the analysis. Next, we introduce the concept of Robust-CBF that, when combined with existing ISS-CLFs, produces controllers for constrained nonlinear systems with disturbances. In an example, a nonlinear system is used to illustrate the ease with which the proposed design method handles nonconvex constraints and disturbances and to illuminate some tradeoffs.},
	language = {en},
	urldate = {2020-06-08},
	journal = {Automatica},
	author = {Jankovic, Mrdjan},
	month = oct,
	year = {2018},
	pages = {359--367},
}



@article{singletary_safety-critical_nodate,
	title = {Safety-{Critical} {Rapid} {Aerial} {Exploration} of {Unknown} {Environments}},
	abstract = {This paper details a novel approach to collision avoidance for aerial vehicles that enables high-speed ﬂight in uncertain environments. This framework is applied at the controller level and provides safety regardless of the planner that is used. The method is shown to be robust to state uncertainty and disturbances, and is computed entirely online utilizing the full nonlinear system dynamics. The effectiveness of this method is shown in a high-ﬁdelity simulation of a quadrotor with onboard sensors rapidly and safely exploring a cave environment utilizing a simple planner.},
	language = {en},
	author = {Singletary, Andrew and Gurriet, Thomas and Nilsson, Petter and Ames, Aaron},
	pages = {7},
}
\">\n            <i class=\"fa fa-download fa-fw\"></i> Download BibTeX\n          </a>\n        </li>\n        <li>\n          <a href=\"//bibbase.org/rss?bib=https://api.zotero.org/users/5612529/collections/2NUUABGE/items?key=aiprMlXOSKe71AbbxNPHHfe7&amp;format=bibtex&amp;limit=100\">\n            <i class=\"fa fa-rss fa-fw\"></i> RSS Feed\n          </a>\n          </li>\n      </ul>\n      </li>\n\n      \n\n\n      \n    </ul>\n\n\n    <div class=\"alert alert-success bibbase_msg\" id=\"bibbase_msg_embed\"\n         style=\"display: none;\">\n\n      Excellent! Next you can\n      <a href=\"/network/register?next=/network/newSiteFromTemplate%3Fbiburl=https://api.zotero.org/users/5612529/collections/2NUUABGE/items?key=aiprMlXOSKe71AbbxNPHHfe7&amp;format=bibtex&amp;limit=100\"\n      >create a new website with this list</a>, or\n      embed it in an existing web page by copying &amp; pasting\n      any of the following snippets.\n\n      <div style=\"text-align: left; margin-top: 1em;\">\n        <strong>JavaScript</strong>\n        <span class=\"comment recommended\">(easiest)</span>\n        <div class=\"well well-small\">\n          <code>\n            &lt;script src=\"https://bibbase.org/show?bib=https%3A%2F%2Fapi.zotero.org%2Fusers%2F5612529%2Fcollections%2F2NUUABGE%2Fitems%3Fkey%3DaiprMlXOSKe71AbbxNPHHfe7%26format%3Dbibtex%26limit%3D100&amp;jsonp=1&amp;jsonp=1\"&gt;&lt;/script&gt;\n          </code>\n        </div>\n\n        <strong>PHP</strong>\n        <div class=\"well well-small\">\n          <code>\n            &lt;?php\n            $contents = file_get_contents(\"https://bibbase.org/show?bib=https%3A%2F%2Fapi.zotero.org%2Fusers%2F5612529%2Fcollections%2F2NUUABGE%2Fitems%3Fkey%3DaiprMlXOSKe71AbbxNPHHfe7%26format%3Dbibtex%26limit%3D100&amp;jsonp=1\");\n            print_r($contents);\n            ?&gt;\n          </code>\n        </div>\n\n        <strong>iFrame</strong>\n        <span class=\"comment\">(not recommended)</span>\n        <div class=\"well well-small\">\n          <code>\n            &lt;iframe src=\"https://bibbase.org/show?bib=https%3A%2F%2Fapi.zotero.org%2Fusers%2F5612529%2Fcollections%2F2NUUABGE%2Fitems%3Fkey%3DaiprMlXOSKe71AbbxNPHHfe7%26format%3Dbibtex%26limit%3D100&amp;jsonp=1\"&gt;&lt;/iframe&gt;\n          </code>\n        </div>\n\n        <p>\n          For more details see the <a href=\"//bibbase.org/help\">documention</a>.\n        </p>\n      </div>\n    </div>\n\n    <div class=\"alert alert-success bibbase_msg\" id=\"bibbase_msg_preview\"\n         style=\"display: none;\">\n\n      This is a preview! To use this list on your own web site\n      or create a new web site from it,\n      <a href=\"/network/register?next=/network/newAccountWithFile%3FfileId=\"\n      >create a free account</a>. The file will be added\n      and you will be able to edit it in the File Manager.\n      We will show you instructions once you've created your account.\n    </div>\n\n    <div class=\"alert alert-warning bibbase_msg\" id=\"bibbase_msg_mendeley1\"\n         style=\"display: none;\">\n\n      <p>To the site owner:</p>\n\n      <p><strong>Action required!</strong> Mendeley is changing its\n        API. In order to keep using Mendeley with BibBase past April\n        14th, you need to:\n        <ol>\n          <li>renew the authorization for BibBase on Mendeley, and</li>\n          <li>update the BibBase URL\n            in your page the same way you did when you initially set up\n            this page.\n          </li>\n        </ol>\n      </p>\n\n      <p>\n        <a href=\"http://bibbase.org/cgi-bin/mendeley2/get.py\">\n          <i class=\"fa fa-angle-double-right\"></i>\n          Fix it now</a>\n      </p>\n    </div>\n\n  </div>\n\n\n  <div id=\"bibbase_body\">\n    \n  \n  <div class=\"bibbase_group_whole\" id=\"group_2020\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2020')\"\n      onkeypress=\"toggleGroup('group_2020')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2020</span>\n      <span class=\"bibbase_group_count\">\n        \n        (7)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"da-xie-hoeller-boots-anandkumar-zhu-babich-garg-learningacontactadaptivecontrollerforrobustefficientleggedlocomotion-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/2009.10019\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'da-xie-hoeller-boots-anandkumar-zhu-babich-garg-learningacontactadaptivecontrollerforrobustefficientleggedlocomotion-2020', 'http://arxiv.org/abs/2009.10019', event);\">\n    Learning a Contact-Adaptive Controller for Robust, Efficient Legged Locomotion.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Da, X.; Xie, Z.; Hoeller, D.; Boots, B.; Anandkumar, A.; Zhu, Y.; Babich, B.;  and Garg, A.\n</span>\n\n  \n\n</span>\n\n  <i>arXiv:2009.10019 [cs]</i>. November 2020.\n  <span class=\"note\">arXiv: 2009.10019</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/2009.10019\"\n     onclick=\"log_download('da-xie-hoeller-boots-anandkumar-zhu-babich-garg-learningacontactadaptivecontrollerforrobustefficientleggedlocomotion-2020', 'http://arxiv.org/abs/2009.10019', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Learning a Contact-Adaptive Controller for Robust, Efficient Legged Locomotion [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/da-xie-hoeller-boots-anandkumar-zhu-babich-garg-learningacontactadaptivecontrollerforrobustefficientleggedlocomotion-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('da-xie-hoeller-boots-anandkumar-zhu-babich-garg-learningacontactadaptivecontrollerforrobustefficientleggedlocomotion-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{da_learning_2020,\n\ttitle = {Learning a {Contact}-{Adaptive} {Controller} for {Robust}, {Efficient} {Legged} {Locomotion}},\n\turl = {http://arxiv.org/abs/2009.10019},\n\tabstract = {We present a hierarchical framework that combines model-based control and reinforcement learning (RL) to synthesize robust controllers for a quadruped (the Unitree Laikago). The system consists of a high-level controller that learns to choose from a set of primitives in response to changes in the environment and a low-level controller that utilizes an established control method to robustly execute the primitives. Our framework learns a controller that can adapt to challenging environmental changes on the fly, including novel scenarios not seen during training. The learned controller is up to 85 percent more energy efficient and is more robust compared to baseline methods. We also deploy the controller on a physical robot without any randomization or adaptation scheme.},\n\tlanguage = {en},\n\turldate = {2021-01-10},\n\tjournal = {arXiv:2009.10019 [cs]},\n\tauthor = {Da, Xingye and Xie, Zhaoming and Hoeller, David and Boots, Byron and Anandkumar, Animashree and Zhu, Yuke and Babich, Buck and Garg, Animesh},\n\tmonth = nov,\n\tyear = {2020},\n\tnote = {arXiv: 2009.10019},\n\tkeywords = {Computer Science - Machine Learning, Computer Science - Robotics},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We present a hierarchical framework that combines model-based control and reinforcement learning (RL) to synthesize robust controllers for a quadruped (the Unitree Laikago). The system consists of a high-level controller that learns to choose from a set of primitives in response to changes in the environment and a low-level controller that utilizes an established control method to robustly execute the primitives. Our framework learns a controller that can adapt to challenging environmental changes on the fly, including novel scenarios not seen during training. The learned controller is up to 85 percent more energy efficient and is more robust compared to baseline methods. We also deploy the controller on a physical robot without any randomization or adaptation scheme.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"bradley-attheinterfaceofalgebraandstatistics-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/2004.05631\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'bradley-attheinterfaceofalgebraandstatistics-2020', 'http://arxiv.org/abs/2004.05631', event);\">\n    At the Interface of Algebra and Statistics.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Bradley, T.\n</span>\n\n  \n\n</span>\n\n  <i>arXiv:2004.05631 [quant-ph, stat]</i>. April 2020.\n  <span class=\"note\">arXiv: 2004.05631</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/2004.05631\"\n     onclick=\"log_download('bradley-attheinterfaceofalgebraandstatistics-2020', 'http://arxiv.org/abs/2004.05631', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"At the Interface of Algebra and Statistics [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/bradley-attheinterfaceofalgebraandstatistics-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('bradley-attheinterfaceofalgebraandstatistics-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{bradley_at_2020,\n\ttitle = {At the {Interface} of {Algebra} and {Statistics}},\n\turl = {http://arxiv.org/abs/2004.05631},\n\tabstract = {This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture &quot;concepts&quot; inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the &quot;fixed points&quot; of a morphism with its adjoint encode interesting information.},\n\tlanguage = {en},\n\turldate = {2020-12-28},\n\tjournal = {arXiv:2004.05631 [quant-ph, stat]},\n\tauthor = {Bradley, Tai-Danae},\n\tmonth = apr,\n\tyear = {2020},\n\tnote = {arXiv: 2004.05631},\n\tkeywords = {Computer Science - Machine Learning, Mathematics - Category Theory, Quantum Physics, Statistics - Machine Learning},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture \"concepts\" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the \"fixed points\" of a morphism with its adjoint encode interesting information.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"lin-corts-dediego-martnez-lecanda-globalcontrollabilitytestsforgeometrichybridcontrolsystems-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/1905.02490\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'lin-corts-dediego-martnez-lecanda-globalcontrollabilitytestsforgeometrichybridcontrolsystems-2020', 'http://arxiv.org/abs/1905.02490', event);\">\n    Global controllability tests for geometric hybrid control systems.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Liñán, M. B.; Cortés, J.; de Diego, D. M.; Martínez, S.;  and Lecanda, M. C. M.\n</span>\n\n  \n\n</span>\n\n  <i>arXiv:1905.02490 [math]</i>. June 2020.\n  <span class=\"note\">arXiv: 1905.02490</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/1905.02490\"\n     onclick=\"log_download('lin-corts-dediego-martnez-lecanda-globalcontrollabilitytestsforgeometrichybridcontrolsystems-2020', 'http://arxiv.org/abs/1905.02490', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Global controllability tests for geometric hybrid control systems [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/lin-corts-dediego-martnez-lecanda-globalcontrollabilitytestsforgeometrichybridcontrolsystems-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('lin-corts-dediego-martnez-lecanda-globalcontrollabilitytestsforgeometrichybridcontrolsystems-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{linan_global_2020,\n\ttitle = {Global controllability tests for geometric hybrid control systems},\n\turl = {http://arxiv.org/abs/1905.02490},\n\tabstract = {This paper introduces a novel geometric framework to define and study hybrid systems. We exploit the geometry and topology of the set of jump points, where the instantaneous change of dynamics takes place, in order to gain controllability for the system. This approach allows us to describe new global controllability tests for hybrid control systems. We illustrate these results with several examples where none of the continuous control systems are controllable, but the associated hybrid system is controllable because of the characteristics of the jump set.},\n\tlanguage = {en},\n\turldate = {2020-12-28},\n\tjournal = {arXiv:1905.02490 [math]},\n\tauthor = {Liñán, M. Barbero and Cortés, J. and de Diego, D. Martín and Martínez, S. and Lecanda, M. C. Muñoz},\n\tmonth = jun,\n\tyear = {2020},\n\tnote = {arXiv: 1905.02490},\n\tkeywords = {93C30, 93B05, 93B27, Mathematics - Differential Geometry, Mathematics - Optimization and Control},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper introduces a novel geometric framework to define and study hybrid systems. We exploit the geometry and topology of the set of jump points, where the instantaneous change of dynamics takes place, in order to gain controllability for the system. This approach allows us to describe new global controllability tests for hybrid control systems. We illustrate these results with several examples where none of the continuous control systems are controllable, but the associated hybrid system is controllable because of the characteristics of the jump set.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"lopez-slotine-how-robustadaptivecontrolbarrierfunctionsanadaptivedatadrivenapproachtosafetyextendedversion-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/2003.10028\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'lopez-slotine-how-robustadaptivecontrolbarrierfunctionsanadaptivedatadrivenapproachtosafetyextendedversion-2020', 'http://arxiv.org/abs/2003.10028', event);\">\n    Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version).\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Lopez, B. T.; Slotine, J. E.;  and How, J. P.\n</span>\n\n  \n\n</span>\n\n  <i>arXiv:2003.10028 [cs, eess]</i>. May 2020.\n  <span class=\"note\">arXiv: 2003.10028</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/2003.10028\"\n     onclick=\"log_download('lopez-slotine-how-robustadaptivecontrolbarrierfunctionsanadaptivedatadrivenapproachtosafetyextendedversion-2020', 'http://arxiv.org/abs/2003.10028', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Robust Adaptive Control Barrier Functions: An Adaptive &amp; Data-Driven Approach to Safety (Extended Version) [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/lopez-slotine-how-robustadaptivecontrolbarrierfunctionsanadaptivedatadrivenapproachtosafetyextendedversion-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('lopez-slotine-how-robustadaptivecontrolbarrierfunctionsanadaptivedatadrivenapproachtosafetyextendedversion-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{lopez_robust_2020,\n\ttitle = {Robust {Adaptive} {Control} {Barrier} {Functions}: {An} {Adaptive} \\&amp; {Data}-{Driven} {Approach} to {Safety} ({Extended} {Version})},\n\tcopyright = {5},\n\tshorttitle = {Robust {Adaptive} {Control} {Barrier} {Functions}},\n\turl = {http://arxiv.org/abs/2003.10028},\n\tabstract = {A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive control algorithm for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as closed-loop contraction does not require the system be invertible or in a particular form. Additionally, the approach is less expensive than nonlinear model predictive control as it does not require a full desired trajectory, but rather only a desired terminal state. The approach is illustrated on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.},\n\tlanguage = {en},\n\turldate = {2020-07-02},\n\tjournal = {arXiv:2003.10028 [cs, eess]},\n\tauthor = {Lopez, Brett T. and Slotine, Jean-Jacques E. and How, Jonathan P.},\n\tmonth = may,\n\tyear = {2020},\n\tnote = {arXiv: 2003.10028},\n\tkeywords = {Electrical Engineering and Systems Science - Systems and Control},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive control algorithm for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as closed-loop contraction does not require the system be invertible or in a particular form. Additionally, the approach is less expensive than nonlinear model predictive control as it does not require a full desired trajectory, but rather only a desired terminal state. The approach is illustrated on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"grandia-taylor-singletary-hutter-ames-nonlinearmodelpredictivecontrolofroboticsystemswithcontrollyapunovfunctions-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/2006.01229\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'grandia-taylor-singletary-hutter-ames-nonlinearmodelpredictivecontrolofroboticsystemswithcontrollyapunovfunctions-2020', 'http://arxiv.org/abs/2006.01229', event);\">\n    Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Grandia, R.; Taylor, A. J.; Singletary, A.; Hutter, M.;  and <a class=\"bibbase author link\" href=\"http://www.bipedalrobotics.com/publications.html\">Ames, A. D.</a>\n</span>\n\n  \n\n</span>\n\n  <i>arXiv:2006.01229 [cs, eess]</i>. June 2020.\n  <span class=\"note\">arXiv: 2006.01229</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/2006.01229\"\n     onclick=\"log_download('grandia-taylor-singletary-hutter-ames-nonlinearmodelpredictivecontrolofroboticsystemswithcontrollyapunovfunctions-2020', 'http://arxiv.org/abs/2006.01229', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/grandia-taylor-singletary-hutter-ames-nonlinearmodelpredictivecontrolofroboticsystemswithcontrollyapunovfunctions-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>15 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('grandia-taylor-singletary-hutter-ames-nonlinearmodelpredictivecontrolofroboticsystemswithcontrollyapunovfunctions-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{grandia_nonlinear_2020,\n\ttitle = {Nonlinear {Model} {Predictive} {Control} of {Robotic} {Systems} with {Control} {Lyapunov} {Functions}},\n\turl = {http://arxiv.org/abs/2006.01229},\n\tabstract = {The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process.},\n\tlanguage = {en},\n\turldate = {2020-06-25},\n\tjournal = {arXiv:2006.01229 [cs, eess]},\n\tauthor = {Grandia, Ruben and Taylor, Andrew J. and Singletary, Andrew and Hutter, Marco and Ames, Aaron D.},\n\tmonth = jun,\n\tyear = {2020},\n\tnote = {arXiv: 2006.01229},\n\tkeywords = {Computer Science - Robotics, Electrical Engineering and Systems Science - Systems and Control},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"rosajr-lynch-atopologicalapproachtogaitgenerationforbipedrobots-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://arxiv.org/abs/2006.03785\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'rosajr-lynch-atopologicalapproachtogaitgenerationforbipedrobots-2020', 'http://arxiv.org/abs/2006.03785', event);\">\n    A Topological Approach to Gait Generation for Biped Robots.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Rosa Jr., N.;  and Lynch, K. M.\n</span>\n\n  \n\n</span>\n\n  <i>arXiv:2006.03785 [cs]</i>. June 2020.\n  <span class=\"note\">arXiv: 2006.03785</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://arxiv.org/abs/2006.03785\"\n     onclick=\"log_download('rosajr-lynch-atopologicalapproachtogaitgenerationforbipedrobots-2020', 'http://arxiv.org/abs/2006.03785', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A Topological Approach to Gait Generation for Biped Robots [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/rosajr-lynch-atopologicalapproachtogaitgenerationforbipedrobots-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('rosajr-lynch-atopologicalapproachtogaitgenerationforbipedrobots-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{rosa_jr_topological_2020,\n\ttitle = {A {Topological} {Approach} to {Gait} {Generation} for {Biped} {Robots}},\n\turl = {http://arxiv.org/abs/2006.03785},\n\tabstract = {This paper describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2D and 3D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g., closed chains), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly-defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2D and 3D biped walkers.},\n\tlanguage = {en},\n\turldate = {2020-06-25},\n\tjournal = {arXiv:2006.03785 [cs]},\n\tauthor = {Rosa Jr., Nelson and Lynch, Kevin M.},\n\tmonth = jun,\n\tyear = {2020},\n\tnote = {arXiv: 2006.03785},\n\tkeywords = {Computer Science - Robotics},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2D and 3D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g., closed chains), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly-defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2D and 3D biped walkers.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"anonymous-frobeniustheoremdifferentialtopology-2020\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://en.wikipedia.org/w/index.php?title=Frobenius_theorem_(differential_topology)&amp;oldid=938445316\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'anonymous-frobeniustheoremdifferentialtopology-2020', 'https://en.wikipedia.org/w/index.php?title=Frobenius_theorem_(differential_topology)&amp;oldid=938445316', event);\">\n    Frobenius theorem (differential topology).\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  \n</span>\n\n  \n\n</span>\n\n  January 2020.\n  <span class=\"note\">Page Version ID: 938445316</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://en.wikipedia.org/w/index.php?title=Frobenius_theorem_(differential_topology)&amp;oldid=938445316\"\n     onclick=\"log_download('anonymous-frobeniustheoremdifferentialtopology-2020', 'https://en.wikipedia.org/w/index.php?title=Frobenius_theorem_(differential_topology)&amp;oldid=938445316', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Frobenius theorem (differential topology) [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/anonymous-frobeniustheoremdifferentialtopology-2020\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('anonymous-frobeniustheoremdifferentialtopology-2020')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{noauthor_frobenius_2020,\n\ttitle = {Frobenius theorem (differential topology)},\n\tcopyright = {Creative Commons Attribution-ShareAlike License},\n\turl = {https://en.wikipedia.org/w/index.php?title=Frobenius_theorem_(differential_topology)&amp;oldid=938445316},\n\tabstract = {In mathematics, Frobenius&#x27; theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an underdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds.  The theorem is foundational in differential topology and calculus on manifolds.},\n\tlanguage = {en},\n\turldate = {2020-06-16},\n\tjournal = {Wikipedia},\n\tmonth = jan,\n\tyear = {2020},\n\tnote = {Page Version ID: 938445316},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an underdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds. The theorem is foundational in differential topology and calculus on manifolds.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2018\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2018')\"\n      onkeypress=\"toggleGroup('group_2018')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2018</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"carlo-wensing-katz-bledt-kim-dynamiclocomotioninthemitcheetah3throughconvexmodelpredictivecontrol-2018\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Carlo, J. D.; Wensing, P. M.; Katz, B.; Bledt, G.;  and Kim, S.\n</span>\n\n  \n\n</span>\n\n  In <i>2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)</i>, pages 1–9, October 2018. \n  <span class=\"note\">ISSN: 2153-0866</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n  <a href=\"http://doi.org/10.1109/IROS.2018.8594448\"\n     onclick=\"log_download('carlo-wensing-katz-bledt-kim-dynamiclocomotioninthemitcheetah3throughconvexmodelpredictivecontrol-2018', 'http://doi.org/10.1109/IROS.2018.8594448', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/carlo-wensing-katz-bledt-kim-dynamiclocomotioninthemitcheetah3throughconvexmodelpredictivecontrol-2018\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('carlo-wensing-katz-bledt-kim-dynamiclocomotioninthemitcheetah3throughconvexmodelpredictivecontrol-2018')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{carlo_dynamic_2018,\n\ttitle = {Dynamic {Locomotion} in the {MIT} {Cheetah} 3 {Through} {Convex} {Model}-{Predictive} {Control}},\n\tdoi = {10.1109/IROS.2018.8594448},\n\tabstract = {This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20-30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.},\n\tbooktitle = {2018 {IEEE}/{RSJ} {International} {Conference} on {Intelligent} {Robots} and {Systems} ({IROS})},\n\tauthor = {Carlo, J. Di and Wensing, P. M. and Katz, B. and Bledt, G. and Kim, S.},\n\tmonth = oct,\n\tyear = {2018},\n\tnote = {ISSN: 2153-0866},\n\tkeywords = {Convex functions, Dynamics, Legged locomotion, MIT cheetah 3, Predictive control, Predictive models, Robot kinematics, convex model-predictive control, convex optimization, convex programming, dynamic locomotion, ground reaction force planning problems, legged locomotion, predictive control, robot dynamics, torque control, torque-controlled quadruped robot},\n\tpages = {1--9},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20-30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"jankovic-robustcontrolbarrierfunctionsforconstrainedstabilizationofnonlinearsystems-2018\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://linkinghub.elsevier.com/retrieve/pii/S0005109818303509\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'jankovic-robustcontrolbarrierfunctionsforconstrainedstabilizationofnonlinearsystems-2018', 'https://linkinghub.elsevier.com/retrieve/pii/S0005109818303509', event);\">\n    Robust control barrier functions for constrained stabilization of nonlinear systems.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Jankovic, M.\n</span>\n\n  \n\n</span>\n\n  <i>Automatica</i>, 96: 359–367. October 2018.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://linkinghub.elsevier.com/retrieve/pii/S0005109818303509\"\n     onclick=\"log_download('jankovic-robustcontrolbarrierfunctionsforconstrainedstabilizationofnonlinearsystems-2018', 'https://linkinghub.elsevier.com/retrieve/pii/S0005109818303509', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Robust control barrier functions for constrained stabilization of nonlinear systems [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/j.automatica.2018.07.004\"\n     onclick=\"log_download('jankovic-robustcontrolbarrierfunctionsforconstrainedstabilizationofnonlinearsystems-2018', 'http://doi.org/10.1016/j.automatica.2018.07.004', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/jankovic-robustcontrolbarrierfunctionsforconstrainedstabilizationofnonlinearsystems-2018\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('jankovic-robustcontrolbarrierfunctionsforconstrainedstabilizationofnonlinearsystems-2018')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{jankovic_robust_2018,\n\ttitle = {Robust control barrier functions for constrained stabilization of nonlinear systems},\n\tvolume = {96},\n\tissn = {00051098},\n\turl = {https://linkinghub.elsevier.com/retrieve/pii/S0005109818303509},\n\tdoi = {10.1016/j.automatica.2018.07.004},\n\tabstract = {Quadratic Programming (QP) has been used to combine Control Lyapunov and Control Barrier Functions (CLF and CBF) to design controllers for nonlinear systems with constraints. It has been successfully applied to robotic and automotive systems. The approach could be considered an extension of the CLF-based point-wise minimum norm controller. In this paper we modify the original QP problem in a way that guarantees that V˙ {\\textless} 0, if the barrier constraint is inactive, as well as local asymptotic stability under the standard (minimal) assumptions on the CLF and CBF. We also remove the assumption that the CBF has uniform relative degree one. The two design parameters of the new QP setup allow us to control how aggressive the resulting control law is when trying to satisfy the two control objectives. The paper presents the controller in a closed form making it unnecessary to solve the QP problem on line and facilitating the analysis. Next, we introduce the concept of Robust-CBF that, when combined with existing ISS-CLFs, produces controllers for constrained nonlinear systems with disturbances. In an example, a nonlinear system is used to illustrate the ease with which the proposed design method handles nonconvex constraints and disturbances and to illuminate some tradeoffs.},\n\tlanguage = {en},\n\turldate = {2020-06-08},\n\tjournal = {Automatica},\n\tauthor = {Jankovic, Mrdjan},\n\tmonth = oct,\n\tyear = {2018},\n\tpages = {359--367},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Quadratic Programming (QP) has been used to combine Control Lyapunov and Control Barrier Functions (CLF and CBF) to design controllers for nonlinear systems with constraints. It has been successfully applied to robotic and automotive systems. The approach could be considered an extension of the CLF-based point-wise minimum norm controller. In this paper we modify the original QP problem in a way that guarantees that V˙ \\textless 0, if the barrier constraint is inactive, as well as local asymptotic stability under the standard (minimal) assumptions on the CLF and CBF. We also remove the assumption that the CBF has uniform relative degree one. The two design parameters of the new QP setup allow us to control how aggressive the resulting control law is when trying to satisfy the two control objectives. The paper presents the controller in a closed form making it unnecessary to solve the QP problem on line and facilitating the analysis. Next, we introduce the concept of Robust-CBF that, when combined with existing ISS-CLFs, produces controllers for constrained nonlinear systems with disturbances. In an example, a nonlinear system is used to illustrate the ease with which the proposed design method handles nonconvex constraints and disturbances and to illuminate some tradeoffs.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2017\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2017')\"\n      onkeypress=\"toggleGroup('group_2017')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2017</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"agrawal-sreenath-discretecontrolbarrierfunctionsforsafetycriticalcontrolofdiscretesystemswithapplicationtobipedalrobotnavigation-2017\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://www.roboticsproceedings.org/rss13/p73.pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'agrawal-sreenath-discretecontrolbarrierfunctionsforsafetycriticalcontrolofdiscretesystemswithapplicationtobipedalrobotnavigation-2017', 'http://www.roboticsproceedings.org/rss13/p73.pdf', event);\">\n    Discrete Control Barrier Functions for Safety-Critical Control of Discrete Systems with Application to Bipedal Robot Navigation.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Agrawal, A.;  and Sreenath, K.\n</span>\n\n  \n\n</span>\n\n  In <i>Robotics: Science and Systems XIII</i>, July 2017. Robotics: Science and Systems Foundation\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://www.roboticsproceedings.org/rss13/p73.pdf\"\n     onclick=\"log_download('agrawal-sreenath-discretecontrolbarrierfunctionsforsafetycriticalcontrolofdiscretesystemswithapplicationtobipedalrobotnavigation-2017', 'http://www.roboticsproceedings.org/rss13/p73.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Discrete Control Barrier Functions for Safety-Critical Control of Discrete Systems with Application to Bipedal Robot Navigation [pdf]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.15607/RSS.2017.XIII.073\"\n     onclick=\"log_download('agrawal-sreenath-discretecontrolbarrierfunctionsforsafetycriticalcontrolofdiscretesystemswithapplicationtobipedalrobotnavigation-2017', 'http://doi.org/10.15607/RSS.2017.XIII.073', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/agrawal-sreenath-discretecontrolbarrierfunctionsforsafetycriticalcontrolofdiscretesystemswithapplicationtobipedalrobotnavigation-2017\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('agrawal-sreenath-discretecontrolbarrierfunctionsforsafetycriticalcontrolofdiscretesystemswithapplicationtobipedalrobotnavigation-2017')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{agrawal_discrete_2017,\n\ttitle = {Discrete {Control} {Barrier} {Functions} for {Safety}-{Critical} {Control} of {Discrete} {Systems} with {Application} to {Bipedal} {Robot} {Navigation}},\n\tisbn = {978-0-9923747-3-0},\n\turl = {http://www.roboticsproceedings.org/rss13/p73.pdf},\n\tdoi = {10.15607/RSS.2017.XIII.073},\n\tabstract = {In this paper, we extend the concept of control barrier functions, developed initially for continuous time systems, to the discrete-time domain. We demonstrate safety-critical control for nonlinear discrete-time systems with applications to 3D bipedal robot navigation. Particularly, we mathematically analyze two different formulations of control barrier functions, based on their continuous-time counterparts, and demonstrate how these can be applied to discrete-time systems. We show that the resulting formulation is a nonlinear program in contrast to the quadratic program for continuous-time systems and under certain conditions, the nonlinear program can be formulated as a quadratically constrained quadratic program. Furthermore, using the developed concept of discrete control barrier functions, we present a novel control method to address the problem of navigation of a high-dimensional bipedal robot through environments with moving obstacles that present time-varying safety-critical constraints.},\n\tlanguage = {en},\n\turldate = {2020-06-10},\n\tbooktitle = {Robotics: {Science} and {Systems} {XIII}},\n\tpublisher = {Robotics: Science and Systems Foundation},\n\tauthor = {Agrawal, Ayush and Sreenath, Koushil},\n\tmonth = jul,\n\tyear = {2017},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we extend the concept of control barrier functions, developed initially for continuous time systems, to the discrete-time domain. We demonstrate safety-critical control for nonlinear discrete-time systems with applications to 3D bipedal robot navigation. Particularly, we mathematically analyze two different formulations of control barrier functions, based on their continuous-time counterparts, and demonstrate how these can be applied to discrete-time systems. We show that the resulting formulation is a nonlinear program in contrast to the quadratic program for continuous-time systems and under certain conditions, the nonlinear program can be formulated as a quadratically constrained quadratic program. Furthermore, using the developed concept of discrete control barrier functions, we present a novel control method to address the problem of navigation of a high-dimensional bipedal robot through environments with moving obstacles that present time-varying safety-critical constraints.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"glotfelter-corts-egerstedt-nonsmoothbarrierfunctionswithapplicationstomultirobotsystems-2017\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Nonsmooth Barrier Functions With Applications to Multi-Robot Systems.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Glotfelter, P.; Cortés, J.;  and Egerstedt, M.\n</span>\n\n  \n\n</span>\n\n  <i>IEEE Control Systems Letters</i>, 1(2): 310–315. October 2017.\n  <span class=\"note\">Conference Name: IEEE Control Systems Letters</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n  <a href=\"http://doi.org/10.1109/LCSYS.2017.2710943\"\n     onclick=\"log_download('glotfelter-corts-egerstedt-nonsmoothbarrierfunctionswithapplicationstomultirobotsystems-2017', 'http://doi.org/10.1109/LCSYS.2017.2710943', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/glotfelter-corts-egerstedt-nonsmoothbarrierfunctionswithapplicationstomultirobotsystems-2017\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('glotfelter-corts-egerstedt-nonsmoothbarrierfunctionswithapplicationstomultirobotsystems-2017')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{glotfelter_nonsmooth_2017,\n\ttitle = {Nonsmooth {Barrier} {Functions} {With} {Applications} to {Multi}-{Robot} {Systems}},\n\tvolume = {1},\n\tissn = {2475-1456},\n\tdoi = {10.1109/LCSYS.2017.2710943},\n\tabstract = {As multi-agent systems become more wide-spread and versatile, the ability to satisfy multiple system-level constraints grows increasingly important. In applications ranging from automated cruise control to safety in robot swarms, barrier functions have emerged as a tool to provably meet such constraints by guaranteeing forward invariance of desirable sets. However, satisfying multiple constraints typically implies formulating multiple barrier functions, which would be ameliorated if the barrier functions could be composed together as Boolean logic formulas. The use of max and min operators, which yields nonsmooth functions, represents one path to accomplish Boolean compositions of barrier functions, and this letter extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions. We validate our results by deploying Boolean compositions of nonsmooth barrier functions onto a team of mobile robots.},\n\tnumber = {2},\n\tjournal = {IEEE Control Systems Letters},\n\tauthor = {Glotfelter, Paul and Cortés, Jorge and Egerstedt, Magnus},\n\tmonth = oct,\n\tyear = {2017},\n\tnote = {Conference Name: IEEE Control Systems Letters},\n\tkeywords = {Boolean compositions, Boolean functions, Boolean logic formulas, Collision avoidance, Differential equations, Lyapunov methods, Multi-agent systems, Robotics, Robots, Robustness, Tools, autonomous systems, differential inclusions, max operators, min operators, mobile robots, multi-robot systems, multiagent systems, multiple system-level constraints, multirobot systems, nonsmooth barrier functions},\n\tpages = {310--315},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  As multi-agent systems become more wide-spread and versatile, the ability to satisfy multiple system-level constraints grows increasingly important. In applications ranging from automated cruise control to safety in robot swarms, barrier functions have emerged as a tool to provably meet such constraints by guaranteeing forward invariance of desirable sets. However, satisfying multiple constraints typically implies formulating multiple barrier functions, which would be ameliorated if the barrier functions could be composed together as Boolean logic formulas. The use of max and min operators, which yields nonsmooth functions, represents one path to accomplish Boolean compositions of barrier functions, and this letter extends previously established concepts for barrier functions to a class of nonsmooth barrier functions that operate on systems described by differential inclusions. We validate our results by deploying Boolean compositions of nonsmooth barrier functions onto a team of mobile robots.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2016\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2016')\"\n      onkeypress=\"toggleGroup('group_2016')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2016</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"motahar-veer-poulakakis-composinglimitcyclesformotionplanningof3dbipedalwalkers-2016\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Composing limit cycles for motion planning of 3D bipedal walkers.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Motahar, M. S.; Veer, S.;  and Poulakakis, I.\n</span>\n\n  \n\n</span>\n\n  In <i>2016 IEEE 55th Conference on Decision and Control (CDC)</i>, pages 6368–6374, December 2016. \n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n  <a href=\"http://doi.org/10.1109/CDC.2016.7799249\"\n     onclick=\"log_download('motahar-veer-poulakakis-composinglimitcyclesformotionplanningof3dbipedalwalkers-2016', 'http://doi.org/10.1109/CDC.2016.7799249', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/motahar-veer-poulakakis-composinglimitcyclesformotionplanningof3dbipedalwalkers-2016\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('motahar-veer-poulakakis-composinglimitcyclesformotionplanningof3dbipedalwalkers-2016')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{motahar_composing_2016,\n\ttitle = {Composing limit cycles for motion planning of {3D} bipedal walkers},\n\tdoi = {10.1109/CDC.2016.7799249},\n\tabstract = {This paper presents a framework for navigation of 3D dynamically walking bipeds. The framework is based on extracting gait primitives in the form of limit-cycle locomotion behaviors, which are then composed by a higher-level planning algorithm with the purpose of navigating the biped to a goal location while avoiding obstacles. By formulating motion planning as a discrete-time switched system with multiple equilibria - each corresponding to a gait primitive - we provide analytical conditions that constrain the frequency of the switching signal so that the biped is guaranteed to stably execute a suggested plan. Effectively, these conditions distill the stability limitations of the system dynamics in a form that can be readily incorporated to the planning algorithm. We demonstrate the feasibility of the method in the context of a 3D bipedal model, walking dynamically under the influence of a Hybrid Zero Dynamics (HZD) controller. It is shown that the dimensional reduction afforded by HZD greatly facilitates the application of the method by allowing certificates of stability for gait primitives using sums-of-squares programming.},\n\tbooktitle = {2016 {IEEE} 55th {Conference} on {Decision} and {Control} ({CDC})},\n\tauthor = {Motahar, Mohamad Shafiee and Veer, Sushant and Poulakakis, Ioannis},\n\tmonth = dec,\n\tyear = {2016},\n\tkeywords = {3D bipedal walker motion planning, 3D dynamically walking biped navigation, HZD, Legged locomotion, Limit-cycles, Navigation, Planning, Switched systems, Switches, Three-dimensional displays, collision avoidance, discrete time systems, discrete-time switched system, gait analysis, gait primitive, gait primitive extraction, higher-level planning algorithm, hybrid zero dynamic controller, legged locomotion, limit-cycle locomotion behaviors, obstacle avoidance, path planning, stability, stability limitations, sums-of-squares programming, switching signal, switching systems (control)},\n\tpages = {6368--6374},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper presents a framework for navigation of 3D dynamically walking bipeds. The framework is based on extracting gait primitives in the form of limit-cycle locomotion behaviors, which are then composed by a higher-level planning algorithm with the purpose of navigating the biped to a goal location while avoiding obstacles. By formulating motion planning as a discrete-time switched system with multiple equilibria - each corresponding to a gait primitive - we provide analytical conditions that constrain the frequency of the switching signal so that the biped is guaranteed to stably execute a suggested plan. Effectively, these conditions distill the stability limitations of the system dynamics in a form that can be readily incorporated to the planning algorithm. We demonstrate the feasibility of the method in the context of a 3D bipedal model, walking dynamically under the influence of a Hybrid Zero Dynamics (HZD) controller. It is shown that the dimensional reduction afforded by HZD greatly facilitates the application of the method by allowing certificates of stability for gait primitives using sums-of-squares programming.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2014\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2014')\"\n      onkeypress=\"toggleGroup('group_2014')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2014</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"posa-cantu-tedrake-adirectmethodfortrajectoryoptimizationofrigidbodiesthroughcontact-2014\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://journals.sagepub.com/doi/10.1177/0278364913506757\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'posa-cantu-tedrake-adirectmethodfortrajectoryoptimizationofrigidbodiesthroughcontact-2014', 'http://journals.sagepub.com/doi/10.1177/0278364913506757', event);\">\n    A direct method for trajectory optimization of rigid bodies through contact.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Posa, M.; Cantu, C.;  and Tedrake, R.\n</span>\n\n  \n\n</span>\n\n  <i>The International Journal of Robotics Research</i>, 33(1): 69–81. January 2014.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://journals.sagepub.com/doi/10.1177/0278364913506757\"\n     onclick=\"log_download('posa-cantu-tedrake-adirectmethodfortrajectoryoptimizationofrigidbodiesthroughcontact-2014', 'http://journals.sagepub.com/doi/10.1177/0278364913506757', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A direct method for trajectory optimization of rigid bodies through contact [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1177/0278364913506757\"\n     onclick=\"log_download('posa-cantu-tedrake-adirectmethodfortrajectoryoptimizationofrigidbodiesthroughcontact-2014', 'http://doi.org/10.1177/0278364913506757', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/posa-cantu-tedrake-adirectmethodfortrajectoryoptimizationofrigidbodiesthroughcontact-2014\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('posa-cantu-tedrake-adirectmethodfortrajectoryoptimizationofrigidbodiesthroughcontact-2014')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{posa_direct_2014,\n\ttitle = {A direct method for trajectory optimization of rigid bodies through contact},\n\tvolume = {33},\n\tissn = {0278-3649, 1741-3176},\n\turl = {http://journals.sagepub.com/doi/10.1177/0278364913506757},\n\tdoi = {10.1177/0278364913506757},\n\tabstract = {Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform.},\n\tlanguage = {en},\n\tnumber = {1},\n\turldate = {2020-06-08},\n\tjournal = {The International Journal of Robotics Research},\n\tauthor = {Posa, Michael and Cantu, Cecilia and Tedrake, Russ},\n\tmonth = jan,\n\tyear = {2014},\n\tpages = {69--81},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2009\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2009')\"\n      onkeypress=\"toggleGroup('group_2009')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2009</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"morris-grizzle-hybridinvariantmanifoldsinsystemswithimpulseeffectswithapplicationtoperiodiclocomotioninbipedalrobots-2009\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Hybrid Invariant Manifolds in Systems With Impulse Effects With Application to Periodic Locomotion in Bipedal Robots.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Morris, B.;  and Grizzle, J. W.\n</span>\n\n  \n\n</span>\n\n  <i>IEEE Transactions on Automatic Control</i>, 54(8): 1751–1764. August 2009.\n  <span class=\"note\">Conference Name: IEEE Transactions on Automatic Control</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n  <a href=\"http://doi.org/10.1109/TAC.2009.2024563\"\n     onclick=\"log_download('morris-grizzle-hybridinvariantmanifoldsinsystemswithimpulseeffectswithapplicationtoperiodiclocomotioninbipedalrobots-2009', 'http://doi.org/10.1109/TAC.2009.2024563', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/morris-grizzle-hybridinvariantmanifoldsinsystemswithimpulseeffectswithapplicationtoperiodiclocomotioninbipedalrobots-2009\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('morris-grizzle-hybridinvariantmanifoldsinsystemswithimpulseeffectswithapplicationtoperiodiclocomotioninbipedalrobots-2009')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{morris_hybrid_2009,\n\ttitle = {Hybrid {Invariant} {Manifolds} in {Systems} {With} {Impulse} {Effects} {With} {Application} to {Periodic} {Locomotion} in {Bipedal} {Robots}},\n\tvolume = {54},\n\tissn = {1558-2523},\n\tdoi = {10.1109/TAC.2009.2024563},\n\tabstract = {Motivated by the problem of controlling walking in a biped with series compliant actuation, this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects. The first main result shows that when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold, there exist local coordinate transforms under which the Jacobian linearization of the Poincare return map has a block upper triangular structure. One diagonal block is the linearization of the system as restricted to the hybrid invariant manifold, also called the hybrid zero dynamics. The other is the product of two sensitivity matrices related to the transverse dynamics-one pertaining to the impact map and the other pertaining to the closed-loop vector field. When either of these sensitivity matrices is sufficiently close to zero, the stability of the return map is determined solely by the stability of the hybrid zero dynamics. The second main result of the paper details the construction of a hybrid invariant manifold, such as that required by the first main theorem. Forward invariance follows from the methods of Byrnes and Isidori, and impact invariance is achieved by a novel construction of impact-updated control parameters. In addition to providing impact invariance, the construction allows entries of the impact sensitivity matrix of the transverse dynamics to be made arbitrarily small. A simulation example is provided where stable walking is achieved in a 5-link biped with series compliant actuation.},\n\tnumber = {8},\n\tjournal = {IEEE Transactions on Automatic Control},\n\tauthor = {Morris, Benjamin and Grizzle, Jessy W.},\n\tmonth = aug,\n\tyear = {2009},\n\tnote = {Conference Name: IEEE Transactions on Automatic Control},\n\tkeywords = {Bipedal robots, Control systems, Differential equations, Feedback, Jacobian linearization, Jacobian matrices, Legged locomotion, Nonlinear systems, Orbital robotics, Orbits, Poincare invariance, Poincare return map, Robot kinematics, Stability, bipedal robot, closed loop systems, closed-loop vector field, forward invariance, hybrid invariant manifold, hybrid systems, hybrid zero dynamics, impact invariance, impact map, impact-updated control parameter, impulse effects, legged locomotion, linearisation techniques, local coordinate transforms, periodic control, periodic locomotion, periodic orbit, sensitivity analysis, sensitivity matrix, stability, stabilization, stable walking, transverse dynamics, underactuated systems, walking control, zero assignment, zero dynamics},\n\tpages = {1751--1764},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Motivated by the problem of controlling walking in a biped with series compliant actuation, this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects. The first main result shows that when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold, there exist local coordinate transforms under which the Jacobian linearization of the Poincare return map has a block upper triangular structure. One diagonal block is the linearization of the system as restricted to the hybrid invariant manifold, also called the hybrid zero dynamics. The other is the product of two sensitivity matrices related to the transverse dynamics-one pertaining to the impact map and the other pertaining to the closed-loop vector field. When either of these sensitivity matrices is sufficiently close to zero, the stability of the return map is determined solely by the stability of the hybrid zero dynamics. The second main result of the paper details the construction of a hybrid invariant manifold, such as that required by the first main theorem. Forward invariance follows from the methods of Byrnes and Isidori, and impact invariance is achieved by a novel construction of impact-updated control parameters. In addition to providing impact invariance, the construction allows entries of the impact sensitivity matrix of the transverse dynamics to be made arbitrarily small. A simulation example is provided where stable walking is achieved in a 5-link biped with series compliant actuation.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2008\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2008')\"\n      onkeypress=\"toggleGroup('group_2008')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2008</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"sontag-inputtostatestabilitybasicconceptsandresults-2008\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.springer.com/10.1007/978-3-540-77653-6_3\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'sontag-inputtostatestabilitybasicconceptsandresults-2008', 'http://link.springer.com/10.1007/978-3-540-77653-6_3', event);\">\n    Input to State Stability: Basic Concepts and Results.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Sontag, E. D.\n</span>\n\n  \n\n</span>\n\n  In Morel, J. -.; Takens, F.; Teissier, B.; Nistri, P.;  and Stefani, G., editor(s), <i>Nonlinear and Optimal Control Theory</i>, volume 1932, pages 163–220. Springer Berlin Heidelberg, Berlin, Heidelberg,  2008.\n  <span class=\"note\">Series Title: Lecture Notes in Mathematics</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.springer.com/10.1007/978-3-540-77653-6_3\"\n     onclick=\"log_download('sontag-inputtostatestabilitybasicconceptsandresults-2008', 'http://link.springer.com/10.1007/978-3-540-77653-6_3', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Input to State Stability: Basic Concepts and Results [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/978-3-540-77653-6_3\"\n     onclick=\"log_download('sontag-inputtostatestabilitybasicconceptsandresults-2008', 'http://doi.org/10.1007/978-3-540-77653-6_3', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/sontag-inputtostatestabilitybasicconceptsandresults-2008\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>1 download</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('sontag-inputtostatestabilitybasicconceptsandresults-2008')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@incollection{morel_input_2008,\n\taddress = {Berlin, Heidelberg},\n\ttitle = {Input to {State} {Stability}: {Basic} {Concepts} and {Results}},\n\tvolume = {1932},\n\tisbn = {978-3-540-77644-4 978-3-540-77653-6},\n\tshorttitle = {Input to {State} {Stability}},\n\turl = {http://link.springer.com/10.1007/978-3-540-77653-6_3},\n\tlanguage = {en},\n\turldate = {2020-06-22},\n\tbooktitle = {Nonlinear and {Optimal} {Control} {Theory}},\n\tpublisher = {Springer Berlin Heidelberg},\n\tauthor = {Sontag, Eduardo D.},\n\teditor = {Morel, J. -M. and Takens, F. and Teissier, B. and Nistri, Paolo and Stefani, Gianna},\n\tcollaborator = {Agrachev, Andrei A. and Morse, A. Stephen and Sontag, Eduardo D. and Sussmann, Héctor J. and Utkin, Vadim I.},\n\tyear = {2008},\n\tdoi = {10.1007/978-3-540-77653-6_3},\n\tnote = {Series Title: Lecture Notes in Mathematics},\n\tpages = {163--220},\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2007\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2007')\"\n      onkeypress=\"toggleGroup('group_2007')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2007</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"lekien-shadden-marsden-lagrangiancoherentstructuresinndimensionalsystems-2007\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://aip.scitation.org/doi/10.1063/1.2740025\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'lekien-shadden-marsden-lagrangiancoherentstructuresinndimensionalsystems-2007', 'http://aip.scitation.org/doi/10.1063/1.2740025', event);\">\n    Lagrangian coherent structures in n-dimensional systems.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Lekien, F.; Shadden, S. C.;  and Marsden, J. E.\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Mathematical Physics</i>, 48(6): 065404. June 2007.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://aip.scitation.org/doi/10.1063/1.2740025\"\n     onclick=\"log_download('lekien-shadden-marsden-lagrangiancoherentstructuresinndimensionalsystems-2007', 'http://aip.scitation.org/doi/10.1063/1.2740025', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Lagrangian coherent structures in n-dimensional systems [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1063/1.2740025\"\n     onclick=\"log_download('lekien-shadden-marsden-lagrangiancoherentstructuresinndimensionalsystems-2007', 'http://doi.org/10.1063/1.2740025', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/lekien-shadden-marsden-lagrangiancoherentstructuresinndimensionalsystems-2007\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('lekien-shadden-marsden-lagrangiancoherentstructuresinndimensionalsystems-2007')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{lekien_lagrangian_2007,\n\ttitle = {Lagrangian coherent structures in n-dimensional systems},\n\tvolume = {48},\n\tissn = {0022-2488, 1089-7658},\n\turl = {http://aip.scitation.org/doi/10.1063/1.2740025},\n\tdoi = {10.1063/1.2740025},\n\tlanguage = {en},\n\tnumber = {6},\n\turldate = {2020-06-25},\n\tjournal = {Journal of Mathematical Physics},\n\tauthor = {Lekien, Francois and Shadden, Shawn C. and Marsden, Jerrold E.},\n\tmonth = jun,\n\tyear = {2007},\n\tpages = {065404},\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2006\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2006')\"\n      onkeypress=\"toggleGroup('group_2006')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2006</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"polterovich-floerhomologydynamicsandgroups-2006\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://link.springer.com/10.1007/1-4020-4266-3_09\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'polterovich-floerhomologydynamicsandgroups-2006', 'http://link.springer.com/10.1007/1-4020-4266-3_09', event);\">\n    FLOER HOMOLOGY, DYNAMICS AND GROUPS.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Polterovich, L.\n</span>\n\n  \n\n</span>\n\n  In Biran, P.; Cornea, O.;  and Lalonde, F., editor(s), <i>Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology</i>, volume 217, pages 417–438. Kluwer Academic Publishers, Dordrecht,  2006.\n  <span class=\"note\">Series Title: NATO Science Series II: Mathematics, Physics and Chemistry</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://link.springer.com/10.1007/1-4020-4266-3_09\"\n     onclick=\"log_download('polterovich-floerhomologydynamicsandgroups-2006', 'http://link.springer.com/10.1007/1-4020-4266-3_09', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"FLOER HOMOLOGY, DYNAMICS AND GROUPS [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/1-4020-4266-3_09\"\n     onclick=\"log_download('polterovich-floerhomologydynamicsandgroups-2006', 'http://doi.org/10.1007/1-4020-4266-3_09', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/polterovich-floerhomologydynamicsandgroups-2006\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('polterovich-floerhomologydynamicsandgroups-2006')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@incollection{biran_floer_2006,\n\taddress = {Dordrecht},\n\ttitle = {{FLOER} {HOMOLOGY}, {DYNAMICS} {AND} {GROUPS}},\n\tvolume = {217},\n\tisbn = {978-1-4020-4272-0},\n\turl = {http://link.springer.com/10.1007/1-4020-4266-3_09},\n\tabstract = {We discuss some recent results on algebraic properties of the group of Hamiltonian diffeomorphisms of a symplectic manifold. We focus on two topics which lie at the interface between Floer theory and dynamics: 1) Restrictions on Hamiltonian actions of finitely generated groups, including a Hamiltonian version of the Zimmer program dealing with actions of lattices; 2) Quasi-morphisms on the group of Hamiltonian diffeomorphisms. The unifying theme is the study of distortion of cyclic and one-parameter subgroups with respect to various metrics on the group of Hamiltonian diffeomorphisms.},\n\tlanguage = {en},\n\turldate = {2020-11-13},\n\tbooktitle = {Morse {Theoretic} {Methods} in {Nonlinear} {Analysis} and in {Symplectic} {Topology}},\n\tpublisher = {Kluwer Academic Publishers},\n\tauthor = {Polterovich, Leonid},\n\teditor = {Biran, Paul and Cornea, Octav and Lalonde, François},\n\tyear = {2006},\n\tdoi = {10.1007/1-4020-4266-3_09},\n\tnote = {Series Title: NATO Science Series II: Mathematics, Physics and Chemistry},\n\tpages = {417--438},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We discuss some recent results on algebraic properties of the group of Hamiltonian diffeomorphisms of a symplectic manifold. We focus on two topics which lie at the interface between Floer theory and dynamics: 1) Restrictions on Hamiltonian actions of finitely generated groups, including a Hamiltonian version of the Zimmer program dealing with actions of lattices; 2) Quasi-morphisms on the group of Hamiltonian diffeomorphisms. The unifying theme is the study of distortion of cyclic and one-parameter subgroups with respect to various metrics on the group of Hamiltonian diffeomorphisms.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2005\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2005')\"\n      onkeypress=\"toggleGroup('group_2005')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2005</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"richards-how-robustmodelpredictivecontrolwithimperfectinformation-2005\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://ieeexplore.ieee.org/document/1469944/\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'richards-how-robustmodelpredictivecontrolwithimperfectinformation-2005', 'http://ieeexplore.ieee.org/document/1469944/', event);\">\n    Robust model predictive control with imperfect information.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Richards, A.;  and How, J.\n</span>\n\n  \n\n</span>\n\n  In <i>Proceedings of the 2005, American Control Conference, 2005.</i>, pages 268–273, Portland, OR, USA,  2005. IEEE\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://ieeexplore.ieee.org/document/1469944/\"\n     onclick=\"log_download('richards-how-robustmodelpredictivecontrolwithimperfectinformation-2005', 'http://ieeexplore.ieee.org/document/1469944/', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Robust model predictive control with imperfect information [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1109/ACC.2005.1469944\"\n     onclick=\"log_download('richards-how-robustmodelpredictivecontrolwithimperfectinformation-2005', 'http://doi.org/10.1109/ACC.2005.1469944', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/richards-how-robustmodelpredictivecontrolwithimperfectinformation-2005\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('richards-how-robustmodelpredictivecontrolwithimperfectinformation-2005')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{richards_robust_2005,\n\taddress = {Portland, OR, USA},\n\ttitle = {Robust model predictive control with imperfect information},\n\tisbn = {978-0-7803-9098-0},\n\turl = {http://ieeexplore.ieee.org/document/1469944/},\n\tdoi = {10.1109/ACC.2005.1469944},\n\tabstract = {This paper presents two extensions to robust Model Predictive Control (MPC) involving imperfect information. Previous work developed a form of MPC guaranteeing feasibility and constraint satisfaction given an unknown but bounded disturbance and perfect state information. In the first extension, this controller is modified to account for an unknown but bounded state estimation error. As an example, a simple estimator is proposed and analyzed to provide the necessary error bounds. Furthermore, it is shown that delayed state information can be handled using the same method. These analyses depend on knowledge of bounds on the measurement and disturbance uncertainties. The second extension provides a method of estimating these bounds using available data, providing an adaptive form of the controller for cases where the error levels are poorly known a priori.},\n\tlanguage = {en},\n\turldate = {2021-02-01},\n\tbooktitle = {Proceedings of the 2005, {American} {Control} {Conference}, 2005.},\n\tpublisher = {IEEE},\n\tauthor = {Richards, A. and How, J.},\n\tyear = {2005},\n\tpages = {268--273},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper presents two extensions to robust Model Predictive Control (MPC) involving imperfect information. Previous work developed a form of MPC guaranteeing feasibility and constraint satisfaction given an unknown but bounded disturbance and perfect state information. In the first extension, this controller is modified to account for an unknown but bounded state estimation error. As an example, a simple estimator is proposed and analyzed to provide the necessary error bounds. Furthermore, it is shown that delayed state information can be handled using the same method. These analyses depend on knowledge of bounds on the measurement and disturbance uncertainties. The second extension provides a method of estimating these bounds using available data, providing an adaptive form of the controller for cases where the error levels are poorly known a priori.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2004\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2004')\"\n      onkeypress=\"toggleGroup('group_2004')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2004</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"nesic-teel-aframeworkforstabilizationofnonlinearsampleddatasystemsbasedontheirapproximatediscretetimemodels-2004\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Nesic, D.;  and Teel, A. R.\n</span>\n\n  \n\n</span>\n\n  <i>IEEE Transactions on Automatic Control</i>, 49(7): 1103–1122. July 2004.\n  <span class=\"note\">Conference Name: IEEE Transactions on Automatic Control</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n  <a href=\"http://doi.org/10.1109/TAC.2004.831175\"\n     onclick=\"log_download('nesic-teel-aframeworkforstabilizationofnonlinearsampleddatasystemsbasedontheirapproximatediscretetimemodels-2004', 'http://doi.org/10.1109/TAC.2004.831175', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/nesic-teel-aframeworkforstabilizationofnonlinearsampleddatasystemsbasedontheirapproximatediscretetimemodels-2004\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('nesic-teel-aframeworkforstabilizationofnonlinearsampleddatasystemsbasedontheirapproximatediscretetimemodels-2004')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{nesic_framework_2004,\n\ttitle = {A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models},\n\tvolume = {49},\n\tissn = {1558-2523},\n\tdoi = {10.1109/TAC.2004.831175},\n\tabstract = {A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented. Both fixed and fast sampling are considered. In each case, sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete-time plant models also stabilizes the exact discrete-time plant model for sufficiently small integration and/or sampling periods. Previous results in the literature are extended to cover: 1) continuous-time plants modeled as differential inclusions; 2) general approximate discrete-time plant models; 3) dynamical discontinuous controllers modeled as difference inclusions; and 4) stability with respect to closed arbitrary (not necessarily compact) sets.},\n\tnumber = {7},\n\tjournal = {IEEE Transactions on Automatic Control},\n\tauthor = {Nesic, D. and Teel, A. R.},\n\tmonth = jul,\n\tyear = {2004},\n\tnote = {Conference Name: IEEE Transactions on Automatic Control},\n\tkeywords = {Australia Council, Control design, Feedback control, Hardware, Lyapunov method, Lyapunov methods, Military computing, Robustness, Sampling methods, Stability, Sufficient conditions, continuous time systems, continuous-time plants, control system synthesis, discrete time systems, discrete-time models, dynamical discontinuous controllers, fast sampling, fixed sampling, nonlinear control systems, nonlinear sampled-data systems stability, sampled data systems, sampled-data differential inclusions, stability},\n\tpages = {1103--1122},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented. Both fixed and fast sampling are considered. In each case, sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete-time plant models also stabilizes the exact discrete-time plant model for sufficiently small integration and/or sampling periods. Previous results in the literature are extended to cover: 1) continuous-time plants modeled as differential inclusions; 2) general approximate discrete-time plant models; 3) dynamical discontinuous controllers modeled as difference inclusions; and 4) stability with respect to closed arbitrary (not necessarily compact) sets.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2002\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2002')\"\n      onkeypress=\"toggleGroup('group_2002')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2002</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"liu-li-aunifiedgeometricapproachtomodelingandcontrolofconstrainedmechanicalsystems-2002\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  A unified geometric approach to modeling and control of constrained mechanical systems.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Liu, G.;  and Li, Z.\n</span>\n\n  \n\n</span>\n\n  <i>IEEE Transactions on Robotics and Automation</i>, 18(4): 574–587. August 2002.\n  <span class=\"note\">1000</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n  <a href=\"http://doi.org/10.1109/TRA.2002.802207\"\n     onclick=\"log_download('liu-li-aunifiedgeometricapproachtomodelingandcontrolofconstrainedmechanicalsystems-2002', 'http://doi.org/10.1109/TRA.2002.802207', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/liu-li-aunifiedgeometricapproachtomodelingandcontrolofconstrainedmechanicalsystems-2002\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('liu-li-aunifiedgeometricapproachtomodelingandcontrolofconstrainedmechanicalsystems-2002')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{guanfeng_liu_unified_2002,\n\ttitle = {A unified geometric approach to modeling and control of constrained mechanical systems},\n\tvolume = {18},\n\tissn = {2374-958X},\n\tdoi = {10.1109/TRA.2002.802207},\n\tabstract = {Dynamic control of constrained mechanical systems, such as robotic manipulators under end-effector constraints, parallel manipulators, and multifingered robotic hands under closure constraints have been classic problems in robotics research. In this paper, we provide a unified geometric framework for modeling, analysis, and control of constrained mechanical systems. Starting with the constraint, we define two canonical subspaces, namely the subspace of constraint forces and the tangent space of the constraint manifold for holonomic constraint. Using the kinetic energy metric, we define the remaining subspaces and show explicitly the relations among these subspaces. We project the Euler-Lagrange equation of a constrained mechanical system into two orthogonal components and give geometric and physical interpretations of the projected equations. Based on the projected equations, a unified and asymptotically stable hybrid position/force-control algorithm is proposed, along with experimental results for several practical examples. In the case of nonholonomic constraints, we show that the equations can be projected to the distribution/codistribution associated with the constraints and the control law reduces to hybrid velocity/force control.},\n\tnumber = {4},\n\tjournal = {IEEE Transactions on Robotics and Automation},\n\tauthor = {Guanfeng Liu and Zexiang Li},\n\tmonth = aug,\n\tyear = {2002},\n\tnote = {1000},\n\tkeywords = {Control system analysis, Control systems, Equations, Euler-Lagrange equation, Force control, Manipulator dynamics, Mechanical systems, Orbital robotics, Parallel robots, Solid modeling, Subspace constraints, asymptotic stability, canonical subspaces, closure constraints, constrained mechanical systems, constraint forces subspace, constraint manifold tangent space, constraint theory, control, control system analysis, dexterous manipulators, distribution/codistribution, dynamic control, end-effector constraints, force control, holonomic constraint, hybrid velocity/force control, industrial manipulators, kinetic energy metric, manipulator dynamics, modeling, multifingered robotic hands, nonholonomic constraints, orthogonal components, parallel manipulators, position control, robotic manipulators, unified asymptotically stable hybrid position/force-control algorithm, unified geometric approach, velocity control},\n\tpages = {574--587},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Dynamic control of constrained mechanical systems, such as robotic manipulators under end-effector constraints, parallel manipulators, and multifingered robotic hands under closure constraints have been classic problems in robotics research. In this paper, we provide a unified geometric framework for modeling, analysis, and control of constrained mechanical systems. Starting with the constraint, we define two canonical subspaces, namely the subspace of constraint forces and the tangent space of the constraint manifold for holonomic constraint. Using the kinetic energy metric, we define the remaining subspaces and show explicitly the relations among these subspaces. We project the Euler-Lagrange equation of a constrained mechanical system into two orthogonal components and give geometric and physical interpretations of the projected equations. Based on the projected equations, a unified and asymptotically stable hybrid position/force-control algorithm is proposed, along with experimental results for several practical examples. In the case of nonholonomic constraints, we show that the equations can be projected to the distribution/codistribution associated with the constraints and the control law reduces to hybrid velocity/force control.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"papachristodoulou-prajna-ontheconstructionoflyapunovfunctionsusingthesumofsquaresdecomposition-2002\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  On the construction of Lyapunov functions using the sum of squares decomposition.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Papachristodoulou, A.;  and Prajna, S.\n</span>\n\n  \n\n</span>\n\n  In <i>Proceedings of the 41st IEEE Conference on Decision and Control, 2002.</i>, volume 3, pages 3482–3487 vol.3, December 2002. \n  <span class=\"note\">ISSN: 0191-2216</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n  <a href=\"http://doi.org/10.1109/CDC.2002.1184414\"\n     onclick=\"log_download('papachristodoulou-prajna-ontheconstructionoflyapunovfunctionsusingthesumofsquaresdecomposition-2002', 'http://doi.org/10.1109/CDC.2002.1184414', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/papachristodoulou-prajna-ontheconstructionoflyapunovfunctionsusingthesumofsquaresdecomposition-2002\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('papachristodoulou-prajna-ontheconstructionoflyapunovfunctionsusingthesumofsquaresdecomposition-2002')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{papachristodoulou_construction_2002,\n\ttitle = {On the construction of {Lyapunov} functions using the sum of squares decomposition},\n\tvolume = {3},\n\tcopyright = {5},\n\tdoi = {10.1109/CDC.2002.1184414},\n\tabstract = {A relaxation of Lyapunov&#x27;s direct method has been proposed elsewhere that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In the paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certain non-polynomial nonlinearities in the vector field to be handled exactly and the constructed Lyapunov functions to contain non-polynomial terms. It also allows robustness analysis to be performed. Some examples are given to illustrate how this is done.},\n\tbooktitle = {Proceedings of the 41st {IEEE} {Conference} on {Decision} and {Control}, 2002.},\n\tauthor = {Papachristodoulou, A. and Prajna, S.},\n\tmonth = dec,\n\tyear = {2002},\n\tnote = {ISSN: 0191-2216},\n\tkeywords = {Biological system modeling, Control systems, Lyapunov functions, Lyapunov method, Lyapunov methods, Nonlinear control systems, Nonlinear systems, Polynomials, Robust stability, Robustness, Sufficient conditions, Uncertainty, control system analysis, equality constraints, inequality constraints, integral constraints, nonlinear control systems, nonlinear dynamical systems, nonlinear systems, nonpolynomial nonlinearities, polynomials, robust control, robustness analysis, stability of equilibria, sum of squares decomposition, vectors},\n\tpages = {3482--3487 vol.3},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  A relaxation of Lyapunov's direct method has been proposed elsewhere that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In the paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certain non-polynomial nonlinearities in the vector field to be handled exactly and the constructed Lyapunov functions to contain non-polynomial terms. It also allows robustness analysis to be performed. Some examples are given to illustrate how this is done.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2000\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2000')\"\n      onkeypress=\"toggleGroup('group_2000')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2000</span>\n      <span class=\"bibbase_group_count\">\n        \n        (2)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"chellaboina-bhat-haddad-aninvarianceprinciplefornonlinearhybridandimpulsivedynamicalsystems-2000\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://ieeexplore.ieee.org/document/879139/\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'chellaboina-bhat-haddad-aninvarianceprinciplefornonlinearhybridandimpulsivedynamicalsystems-2000', 'http://ieeexplore.ieee.org/document/879139/', event);\">\n    An invariance principle for nonlinear hybrid and impulsive dynamical systems.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Chellaboina, V.; Bhat, S.;  and Haddad, W.\n</span>\n\n  \n\n</span>\n\n  In <i>Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334)</i>, pages 3116–3122 vol.5, Chicago, IL, USA,  2000. IEEE\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://ieeexplore.ieee.org/document/879139/\"\n     onclick=\"log_download('chellaboina-bhat-haddad-aninvarianceprinciplefornonlinearhybridandimpulsivedynamicalsystems-2000', 'http://ieeexplore.ieee.org/document/879139/', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"An invariance principle for nonlinear hybrid and impulsive dynamical systems [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1109/ACC.2000.879139\"\n     onclick=\"log_download('chellaboina-bhat-haddad-aninvarianceprinciplefornonlinearhybridandimpulsivedynamicalsystems-2000', 'http://doi.org/10.1109/ACC.2000.879139', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/chellaboina-bhat-haddad-aninvarianceprinciplefornonlinearhybridandimpulsivedynamicalsystems-2000\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('chellaboina-bhat-haddad-aninvarianceprinciplefornonlinearhybridandimpulsivedynamicalsystems-2000')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{chellaboina_invariance_2000,\n\taddress = {Chicago, IL, USA},\n\ttitle = {An invariance principle for nonlinear hybrid and impulsive dynamical systems},\n\tisbn = {978-0-7803-5519-4},\n\turl = {http://ieeexplore.ieee.org/document/879139/},\n\tdoi = {10.1109/ACC.2000.879139},\n\tabstract = {In this paper we develop an invariance principle for dynamical systems possessing leftcontinuous ows. Speciÿcally, we show that left-continuity of the system trajectories in time for each ÿxed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi-inÿnite interval are su cient for establishing an invariance principle for hybrid and impulsive dynamical systems. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.},\n\tlanguage = {en},\n\turldate = {2020-12-31},\n\tbooktitle = {Proceedings of the 2000 {American} {Control} {Conference}. {ACC} ({IEEE} {Cat}. {No}.{00CH36334})},\n\tpublisher = {IEEE},\n\tauthor = {Chellaboina, V. and Bhat, S.P. and Haddad, W.M.},\n\tyear = {2000},\n\tpages = {3116--3122 vol.5},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper we develop an invariance principle for dynamical systems possessing leftcontinuous ows. Speciÿcally, we show that left-continuity of the system trajectories in time for each ÿxed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi-inÿnite interval are su cient for establishing an invariance principle for hybrid and impulsive dynamical systems. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"simic-johansson-sastry-lygeros-towardsageometrictheoryofhybridsystems-2000\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Towards a Geometric Theory of Hybrid Systems.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Simic, S.; Johansson, K.; Sastry, S.;  and Lygeros, J.\n</span>\n\n  \n\n</span>\n\n  Volume 12 January 2000.\n  <span class=\"note\">Journal Abbreviation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms Pages: 436 Publication Title: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/simic-johansson-sastry-lygeros-towardsageometrictheoryofhybridsystems-2000\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('simic-johansson-sastry-lygeros-towardsageometrictheoryofhybridsystems-2000')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@book{simic_towards_2000,\n\ttitle = {Towards a {Geometric} {Theory} of {Hybrid} {Systems}.},\n\tvolume = {12},\n\tabstract = {We propose a framework for a geometric theory of hybrid systems. Given a deterministic, non-blocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non-smooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it is due to nonsmoothness of the hybrid flow. We introduce the notion of topological equivalence of hybrid systems and locally classify isolated Zeno states in dimension two.},\n\tauthor = {Simic, Slobodan and Johansson, Karl and Sastry, Shankar and Lygeros, John},\n\tmonth = jan,\n\tyear = {2000},\n\tnote = {Journal Abbreviation: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms\nPages: 436\nPublication Title: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We propose a framework for a geometric theory of hybrid systems. Given a deterministic, non-blocking hybrid system, we introduce the notion of its hybrifold with the associated hybrid flow on it. This enables us to study hybrid systems from a global geometric perspective as (generally non-smooth) dynamical systems. This point of view is adopted in studying the Zeno phenomenon. We show that it is due to nonsmoothness of the hybrid flow. We introduce the notion of topological equivalence of hybrid systems and locally classify isolated Zeno states in dimension two.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1999\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1999')\"\n      onkeypress=\"toggleGroup('group_1999')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1999</span>\n      <span class=\"bibbase_group_count\">\n        \n        (3)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"nei-teel-kokotovi-sufficientconditionsforstabilizationofsampleddatanonlinearsystemsviadiscretetimeapproximations-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S0167691199000730\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'nei-teel-kokotovi-sufficientconditionsforstabilizationofsampleddatanonlinearsystemsviadiscretetimeapproximations-1999', 'http://www.sciencedirect.com/science/article/pii/S0167691199000730', event);\">\n    Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Nešić, D.; Teel, A. R.;  and Kokotović, P. V.\n</span>\n\n  \n\n</span>\n\n  <i>Systems & Control Letters</i>, 38(4): 259–270. December 1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S0167691199000730\"\n     onclick=\"log_download('nei-teel-kokotovi-sufficientconditionsforstabilizationofsampleddatanonlinearsystemsviadiscretetimeapproximations-1999', 'http://www.sciencedirect.com/science/article/pii/S0167691199000730', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/S0167-6911(99)00073-0\"\n     onclick=\"log_download('nei-teel-kokotovi-sufficientconditionsforstabilizationofsampleddatanonlinearsystemsviadiscretetimeapproximations-1999', 'http://doi.org/10.1016/S0167-6911(99)00073-0', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/nei-teel-kokotovi-sufficientconditionsforstabilizationofsampleddatanonlinearsystemsviadiscretetimeapproximations-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('nei-teel-kokotovi-sufficientconditionsforstabilizationofsampleddatanonlinearsystemsviadiscretetimeapproximations-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{nesic_sufficient_1999,\n\ttitle = {Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations},\n\tvolume = {38},\n\tissn = {0167-6911},\n\turl = {http://www.sciencedirect.com/science/article/pii/S0167691199000730},\n\tdoi = {10.1016/S0167-6911(99)00073-0},\n\tabstract = {Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.},\n\tlanguage = {en},\n\tnumber = {4},\n\turldate = {2020-12-29},\n\tjournal = {Systems \\&amp; Control Letters},\n\tauthor = {Nešić, D. and Teel, A. R. and Kokotović, P. V.},\n\tmonth = dec,\n\tyear = {1999},\n\tkeywords = {Discrete time, Nonlinear, Sampled data, Stabilization},\n\tpages = {259--270},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://journals.sagepub.com/doi/10.1177/02783649922066385\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999', 'http://journals.sagepub.com/doi/10.1177/02783649922066385', event);\">\n    Sequential Composition of Dynamically Dexterous Robot Behaviors.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Burridge, R. R.; Rizzi, A. A.;  and Koditschek, D. E.\n</span>\n\n  \n\n</span>\n\n  <i>The International Journal of Robotics Research</i>, 18(6): 534–555. June 1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://journals.sagepub.com/doi/10.1177/02783649922066385\"\n     onclick=\"log_download('burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999', 'http://journals.sagepub.com/doi/10.1177/02783649922066385', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Sequential Composition of Dynamically Dexterous Robot Behaviors [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1177/02783649922066385\"\n     onclick=\"log_download('burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999', 'http://doi.org/10.1177/02783649922066385', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{burridge_sequential_1999,\n\ttitle = {Sequential {Composition} of {Dynamically} {Dexterous} {Robot} {Behaviors}},\n\tvolume = {18},\n\tissn = {0278-3649, 1741-3176},\n\turl = {http://journals.sagepub.com/doi/10.1177/02783649922066385},\n\tdoi = {10.1177/02783649922066385},\n\tabstract = {We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.},\n\tlanguage = {en},\n\tnumber = {6},\n\turldate = {2020-10-20},\n\tjournal = {The International Journal of Robotics Research},\n\tauthor = {Burridge, R. R. and Rizzi, A. A. and Koditschek, D. E.},\n\tmonth = jun,\n\tyear = {1999},\n\tpages = {534--555},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://journals.sagepub.com/doi/10.1177/02783649922066385\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999', 'http://journals.sagepub.com/doi/10.1177/02783649922066385', event);\">\n    Sequential Composition of Dynamically Dexterous Robot Behaviors.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Burridge, R. R.; Rizzi, A. A.;  and Koditschek, D. E.\n</span>\n\n  \n\n</span>\n\n  <i>The International Journal of Robotics Research</i>, 18(6): 534–555. June 1999.\n  <span class=\"note\">5</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://journals.sagepub.com/doi/10.1177/02783649922066385\"\n     onclick=\"log_download('burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999', 'http://journals.sagepub.com/doi/10.1177/02783649922066385', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Sequential Composition of Dynamically Dexterous Robot Behaviors [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1177/02783649922066385\"\n     onclick=\"log_download('burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999', 'http://doi.org/10.1177/02783649922066385', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('burridge-rizzi-koditschek-sequentialcompositionofdynamicallydexterousrobotbehaviors-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{burridge_sequential_1999-1,\n\ttitle = {Sequential {Composition} of {Dynamically} {Dexterous} {Robot} {Behaviors}},\n\tvolume = {18},\n\tissn = {0278-3649, 1741-3176},\n\turl = {http://journals.sagepub.com/doi/10.1177/02783649922066385},\n\tdoi = {10.1177/02783649922066385},\n\tabstract = {We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.},\n\tlanguage = {en},\n\tnumber = {6},\n\turldate = {2020-07-10},\n\tjournal = {The International Journal of Robotics Research},\n\tauthor = {Burridge, R. R. and Rizzi, A. A. and Koditschek, D. E.},\n\tmonth = jun,\n\tyear = {1999},\n\tnote = {5},\n\tpages = {534--555},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We report on our efforts to develop a sequential robot controllercomposition technique in the context of dexterous “batting” maneuvers. A robot with a flat paddle is required to strike repeatedly at a thrown ball until the ball is brought to rest on the paddle at a specified location. The robot’s reachable workspace is blocked by an obstacle that disconnects the free space formed when the ball and paddle remain in contact, forcing the machine to “let go” for a time to bring the ball to the desired state. The controller compositions we create guarantee that a ball introduced in the “safe workspace” remains there and is ultimately brought to the goal. We report on experimental results from an implementation of these formal composition methods, and present descriptive statistics characterizing the experiments.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1995\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1995')\"\n      onkeypress=\"toggleGroup('group_1995')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1995</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"sontag-wang-oncharacterizationsoftheinputtostatestabilityproperty-1995\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://linkinghub.elsevier.com/retrieve/pii/0167691194000506\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'sontag-wang-oncharacterizationsoftheinputtostatestabilityproperty-1995', 'https://linkinghub.elsevier.com/retrieve/pii/0167691194000506', event);\">\n    On characterizations of the input-to-state stability property.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Sontag, E. D.;  and Wang, Y.\n</span>\n\n  \n\n</span>\n\n  <i>Systems & Control Letters</i>, 24(5): 351–359. April 1995.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://linkinghub.elsevier.com/retrieve/pii/0167691194000506\"\n     onclick=\"log_download('sontag-wang-oncharacterizationsoftheinputtostatestabilityproperty-1995', 'https://linkinghub.elsevier.com/retrieve/pii/0167691194000506', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"On characterizations of the input-to-state stability property [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/0167-6911(94)00050-6\"\n     onclick=\"log_download('sontag-wang-oncharacterizationsoftheinputtostatestabilityproperty-1995', 'http://doi.org/10.1016/0167-6911(94)00050-6', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/sontag-wang-oncharacterizationsoftheinputtostatestabilityproperty-1995\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('sontag-wang-oncharacterizationsoftheinputtostatestabilityproperty-1995')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{sontag_characterizations_1995,\n\ttitle = {On characterizations of the input-to-state stability property},\n\tvolume = {24},\n\tissn = {01676911},\n\turl = {https://linkinghub.elsevier.com/retrieve/pii/0167691194000506},\n\tdoi = {10.1016/0167-6911(94)00050-6},\n\tabstract = {We show that the well-known Lyapunov sufficient condition for “input-to-state stability” is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.},\n\tlanguage = {en},\n\tnumber = {5},\n\turldate = {2020-06-22},\n\tjournal = {Systems \\&amp; Control Letters},\n\tauthor = {Sontag, Eduardo D. and Wang, Yuan},\n\tmonth = apr,\n\tyear = {1995},\n\tpages = {351--359},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We show that the well-known Lyapunov sufficient condition for “input-to-state stability” is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1993\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1993')\"\n      onkeypress=\"toggleGroup('group_1993')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1993</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"sussmann-sontag-yang-ageneralresultonthestabilizationoflinearsystemsusingboundedcontrols-1993\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  A general result on the stabilization of linear systems using bounded controls.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Sussmann, H.; Sontag, E.;  and Yang, Y.\n</span>\n\n  \n\n</span>\n\n  In <i>Proceedings of 32nd IEEE Conference on Decision and Control</i>, pages 1802–1807 vol.2, December 1993. \n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n  <a href=\"http://doi.org/10.1109/CDC.1993.325264\"\n     onclick=\"log_download('sussmann-sontag-yang-ageneralresultonthestabilizationoflinearsystemsusingboundedcontrols-1993', 'http://doi.org/10.1109/CDC.1993.325264', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/sussmann-sontag-yang-ageneralresultonthestabilizationoflinearsystemsusingboundedcontrols-1993\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('sussmann-sontag-yang-ageneralresultonthestabilizationoflinearsystemsusingboundedcontrols-1993')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@inproceedings{sussmann_general_1993,\n\ttitle = {A general result on the stabilization of linear systems using bounded controls},\n\tdoi = {10.1109/CDC.1993.325264},\n\tabstract = {We present two constructions of controllers that globally stabilize linear systems subject to control saturation. The only conditions imposed are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition holds. We use essentially arbitrary saturations /spl sigma/, subject only to the requirement that: (i) /spl sigma/ is locally Lipschitz, (ii) s/spl sigma/(s){\\textgreater}0 whenever s/spl ne/0, (iii) /spl sigma/ is differentiable at 0 and /spl sigma/&#x27;(0){\\textgreater}0, and (iv) lim inf/sub {\\textbar}s{\\textbar}/spl rarr//spl infin//{\\textbar}/spl sigma/(s){\\textbar}{\\textgreater}0.{\\textless}{\\textgreater}},\n\tbooktitle = {Proceedings of 32nd {IEEE} {Conference} on {Decision} and {Control}},\n\tauthor = {Sussmann, H. and Sontag, E. and Yang, Y.},\n\tmonth = dec,\n\tyear = {1993},\n\tkeywords = {Actuators, Control systems, Control theory, Eigenvalues and eigenfunctions, Linear systems, Mathematics, Negative feedback, Open loop systems, Power engineering and energy, Power supplies, bounded controls, control saturation, control system analysis, eigenvalues, eigenvalues and eigenfunctions, global stability, linear systems, linear time invariant continuous time systems, stability, stabilization},\n\tpages = {1802--1807 vol.2},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We present two constructions of controllers that globally stabilize linear systems subject to control saturation. The only conditions imposed are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition holds. We use essentially arbitrary saturations /spl sigma/, subject only to the requirement that: (i) /spl sigma/ is locally Lipschitz, (ii) s/spl sigma/(s)\\textgreater0 whenever s/spl ne/0, (iii) /spl sigma/ is differentiable at 0 and /spl sigma/'(0)\\textgreater0, and (iv) lim inf/sub \\textbars\\textbar/spl rarr//spl infin//\\textbar/spl sigma/(s)\\textbar\\textgreater0.\\textless\\textgreater\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1989\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1989')\"\n      onkeypress=\"toggleGroup('group_1989')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1989</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"sontag-auniversalconstructionofartsteinstheoremonnonlinearstabilization-1989\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://linkinghub.elsevier.com/retrieve/pii/0167691189900285\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'sontag-auniversalconstructionofartsteinstheoremonnonlinearstabilization-1989', 'https://linkinghub.elsevier.com/retrieve/pii/0167691189900285', event);\">\n    A ‘universal’ construction of Artstein's theorem on nonlinear stabilization.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Sontag, E. D.\n</span>\n\n  \n\n</span>\n\n  <i>Systems & Control Letters</i>, 13(2): 117–123. August 1989.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://linkinghub.elsevier.com/retrieve/pii/0167691189900285\"\n     onclick=\"log_download('sontag-auniversalconstructionofartsteinstheoremonnonlinearstabilization-1989', 'https://linkinghub.elsevier.com/retrieve/pii/0167691189900285', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"A ‘universal’ construction of Artstein&#x27;s theorem on nonlinear stabilization [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/0167-6911(89)90028-5\"\n     onclick=\"log_download('sontag-auniversalconstructionofartsteinstheoremonnonlinearstabilization-1989', 'http://doi.org/10.1016/0167-6911(89)90028-5', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/sontag-auniversalconstructionofartsteinstheoremonnonlinearstabilization-1989\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('sontag-auniversalconstructionofartsteinstheoremonnonlinearstabilization-1989')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{sontag_universal_1989,\n\ttitle = {A ‘universal’ construction of {Artstein}&#x27;s theorem on nonlinear stabilization},\n\tvolume = {13},\n\tissn = {01676911},\n\turl = {https://linkinghub.elsevier.com/retrieve/pii/0167691189900285},\n\tdoi = {10.1016/0167-6911(89)90028-5},\n\tabstract = {This note presents an explicit proof of the theorem due to Artstein - which states that the existence of a smooth control-Lyapunov function implies smooth stabilizabifity. Moreover, the result is extended to the real-analytic and rational cases as well. The proof uses a &quot;universal&#x27; formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation.},\n\tlanguage = {en},\n\tnumber = {2},\n\turldate = {2020-06-22},\n\tjournal = {Systems \\&amp; Control Letters},\n\tauthor = {Sontag, Eduardo D.},\n\tmonth = aug,\n\tyear = {1989},\n\tpages = {117--123},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This note presents an explicit proof of the theorem due to Artstein - which states that the existence of a smooth control-Lyapunov function implies smooth stabilizabifity. Moreover, the result is extended to the real-analytic and rational cases as well. The proof uses a \"universal' formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1981\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1981')\"\n      onkeypress=\"toggleGroup('group_1981')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1981</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"sontag-nonlinearregulationthepiecewiselinearapproach-1981\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Nonlinear regulation: The piecewise linear approach.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Sontag, E.\n</span>\n\n  \n\n</span>\n\n  <i>IEEE Transactions on Automatic Control</i>, 26(2): 346–358. April 1981.\n  <span class=\"note\">Conference Name: IEEE Transactions on Automatic Control</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n  <a href=\"http://doi.org/10.1109/TAC.1981.1102596\"\n     onclick=\"log_download('sontag-nonlinearregulationthepiecewiselinearapproach-1981', 'http://doi.org/10.1109/TAC.1981.1102596', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/sontag-nonlinearregulationthepiecewiselinearapproach-1981\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('sontag-nonlinearregulationthepiecewiselinearapproach-1981')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{sontag_nonlinear_1981,\n\ttitle = {Nonlinear regulation: {The} piecewise linear approach},\n\tvolume = {26},\n\tissn = {1558-2523},\n\tshorttitle = {Nonlinear regulation},\n\tdoi = {10.1109/TAC.1981.1102596},\n\tabstract = {This paper approaches nonlinear control problems through the use of (discrete-time) piecewise linear systems. These are systems whose next-state and output maps are both described by PL maps, i.e., by maps which are affine on each of the components of a finite polyhedral partition. Various results on state and output feedback, observers, and inverses, standard for linear systems, are proved for PL systems. Many of these results are then used in the study of more general (both discrete- and continuous-time) systems, using suitable approximations.},\n\tnumber = {2},\n\tjournal = {IEEE Transactions on Automatic Control},\n\tauthor = {Sontag, E.},\n\tmonth = apr,\n\tyear = {1981},\n\tnote = {Conference Name: IEEE Transactions on Automatic Control},\n\tkeywords = {Arithmetic, Control systems, Digital control, Linear programming, Linear systems, Logic, Microprocessors, Nonlinear control systems, Piecewise linear approximation, Piecewise linear techniques, Piecewise-linear approximation, Regulators, nonlinear systems, State feedback, nonlinear systems},\n\tpages = {346--358},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper approaches nonlinear control problems through the use of (discrete-time) piecewise linear systems. These are systems whose next-state and output maps are both described by PL maps, i.e., by maps which are affine on each of the components of a finite polyhedral partition. Various results on state and output feedback, observers, and inverses, standard for linear systems, are proved for PL systems. Many of these results are then used in the study of more general (both discrete- and continuous-time) systems, using suitable approximations.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_undefined\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_undefined')\"\n      onkeypress=\"toggleGroup('group_undefined')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>undefined</span>\n      <span class=\"bibbase_group_count\">\n        \n        (14)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"sullivan-homologytheoryanddynamicalsystems\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  HOMOLOGY THEORY AND DYNAMICAL SYSTEMS.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Sullivan, D\n</span>\n\n  \n\n</span>\n\n  ,24.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/sullivan-homologytheoryanddynamicalsystems\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('sullivan-homologytheoryanddynamicalsystems')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{sullivan_homology_nodate,\n\ttitle = {{HOMOLOGY} {THEORY} {AND} {DYNAMICAL} {SYSTEMS}},\n\tlanguage = {en},\n\tauthor = {Sullivan, D},\n\tpages = {24},\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"taylor-ames-adaptivesafetywithcontrolbarrierfunctions\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Adaptive Safety with Control Barrier Functions.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Taylor, A.;  and Ames, A. D\n</span>\n\n  \n\n</span>\n\n  ,7.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/taylor-ames-adaptivesafetywithcontrolbarrierfunctions\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('taylor-ames-adaptivesafetywithcontrolbarrierfunctions')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{taylor_adaptive_nodate,\n\ttitle = {Adaptive {Safety} with {Control} {Barrier} {Functions}},\n\tabstract = {Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunovbased methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the system’s state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an Adaptive Cruise Control (ACC) simulation.},\n\tlanguage = {en},\n\tauthor = {Taylor, Andrew and Ames, Aaron D},\n\tpages = {7},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Adaptive Control Lyapunov Functions (aCLFs) were introduced 20 years ago, and provided a Lyapunovbased methodology for stabilizing systems with parameter uncertainty. The goal of this paper is to revisit this classic formulation in the context of safety-critical control. This will motivate a variant of aCLFs in the context of safety: adaptive Control Barrier Functions (aCBFs). Our proposed approach adaptively achieves safety by keeping the system’s state within a safe set even in the presence of parametric model uncertainty. We unify aCLFs and aCBFs into a single control methodology for systems with uncertain parameters in the context of a Quadratic Program (QP) based framework. We validate the ability of this unified framework to achieve stability and safety in an Adaptive Cruise Control (ACC) simulation.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"reher-kann-ames-aninversedynamicsapproachtocontrollyapunovfunctions\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  An Inverse Dynamics Approach to Control Lyapunov Functions.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Reher, J.; Kann, C.;  and Ames, A. D\n</span>\n\n  \n\n</span>\n\n  ,8.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/reher-kann-ames-aninversedynamicsapproachtocontrollyapunovfunctions\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('reher-kann-ames-aninversedynamicsapproachtocontrollyapunovfunctions')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{reher_inverse_nodate,\n\ttitle = {An {Inverse} {Dynamics} {Approach} to {Control} {Lyapunov} {Functions}},\n\tabstract = {With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots. The primary focus of this paper is on the development of an alternative approach to the implementation of controllers utilizing control Lyapunov function based quadratic programs. This approach utilizes many of the desirable aspects from successful inverse dynamics based controllers in the literature, while also incorporating a variant of control Lyapunov functions that renders better convergence in the context of tracking outputs. The principal benefits of this formulation include a greater ability to add costs which regulate the resulting behavior of the robot. In addition, the model error-prone inertia matrix is used only once, in a non-inverted form. The result is a successful demonstration of the controller for walking in simulation, and applied on hardware in real-time for dynamic crouching.},\n\tlanguage = {en},\n\tauthor = {Reher, Jenna and Kann, Claudia and Ames, Aaron D},\n\tpages = {8},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots. The primary focus of this paper is on the development of an alternative approach to the implementation of controllers utilizing control Lyapunov function based quadratic programs. This approach utilizes many of the desirable aspects from successful inverse dynamics based controllers in the literature, while also incorporating a variant of control Lyapunov functions that renders better convergence in the context of tracking outputs. The principal benefits of this formulation include a greater ability to add costs which regulate the resulting behavior of the robot. In addition, the model error-prone inertia matrix is used only once, in a non-inverted form. The result is a successful demonstration of the controller for walking in simulation, and applied on hardware in real-time for dynamic crouching.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"chen-singletary-ames-densityfunctionsforguaranteedsafetyonroboticsystems\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Density Functions for Guaranteed Safety on Robotic Systems.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Chen, Y.; Singletary, A.;  and Ames, A. D\n</span>\n\n  \n\n</span>\n\n  ,6.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/chen-singletary-ames-densityfunctionsforguaranteedsafetyonroboticsystems\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('chen-singletary-ames-densityfunctionsforguaranteedsafetyonroboticsystems')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{chen_density_nodate,\n\ttitle = {Density {Functions} for {Guaranteed} {Safety} on {Robotic} {Systems}},\n\tabstract = {The recent study on density functions as the dual of value functions for optimal control gives a new method for synthesizing safe controllers. A density function describes the state distribution in the state space, and its evolution follows the Liouville Partial Differential Equation (PDE). The duality between the density function and the value function in optimal control can be utilized to solve constrained optimal control problems with a primal-dual algorithm. This paper focuses on the application of the method on robotic systems and proposes an implementation of the primal-dual algorithm that is less computationally demanding than the method used in the literature. To be specific, we use kernel density estimation to estimate the density function, which scales better than the ODE approach in the literature and only requires a simulator instead of a dynamic model. The Hamilton Jacobi Bellman (HJB) PDE is solved with the finite element method in an implicit form, which accelerates the value iteration process. We show an application of the safe control synthesis with density functions on a segway control problem demonstrated experimentally.},\n\tlanguage = {en},\n\tauthor = {Chen, Yuxiao and Singletary, Andrew and Ames, Aaron D},\n\tpages = {6},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The recent study on density functions as the dual of value functions for optimal control gives a new method for synthesizing safe controllers. A density function describes the state distribution in the state space, and its evolution follows the Liouville Partial Differential Equation (PDE). The duality between the density function and the value function in optimal control can be utilized to solve constrained optimal control problems with a primal-dual algorithm. This paper focuses on the application of the method on robotic systems and proposes an implementation of the primal-dual algorithm that is less computationally demanding than the method used in the literature. To be specific, we use kernel density estimation to estimate the density function, which scales better than the ODE approach in the literature and only requires a simulator instead of a dynamic model. The Hamilton Jacobi Bellman (HJB) PDE is solved with the finite element method in an implicit form, which accelerates the value iteration process. We show an application of the safe control synthesis with density functions on a segway control problem demonstrated experimentally.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"pandey-ames-onaconversetheoremforfinitetimelyapunovfunctionstoestimatedomainsofattraction\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  On a Converse Theorem for Finite-Time Lyapunov Functions to Estimate Domains of Attraction.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Pandey, A.;  and Ames, A. D\n</span>\n\n  \n\n</span>\n\n  ,7.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/pandey-ames-onaconversetheoremforfinitetimelyapunovfunctionstoestimatedomainsofattraction\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('pandey-ames-onaconversetheoremforfinitetimelyapunovfunctionstoestimatedomainsofattraction')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{pandey_converse_nodate,\n\ttitle = {On a {Converse} {Theorem} for {Finite}-{Time} {Lyapunov} {Functions} to {Estimate} {Domains} of {Attraction}},\n\tabstract = {The main result of the paper is a new converse theorem for finite-time Lyapunov functions. We show the existence of a finite-time Lyapunov function for an autonomous continuoustime nonlinear dynamical system if the origin of the system is asymptotically stable. Our proof extends the recent results in finite-time Lyapunov function theory by providing an alternative converse proof for the existence of finite-time Lyapunov functions. In particular, we show that given asymptotic stability of the origin, the linearized dynamics satisfy global finitetime Lyapunov function conditions hence proving the converse theorem. Using our results, we present a consolidated theory for using and constructing Lyapunov functions to certify system stability properties. We also propose a constructive algorithm to efficiently compute non-conservative estimates of the domain of attraction for nonlinear dynamical systems.},\n\tlanguage = {en},\n\tauthor = {Pandey, Ayush and Ames, Aaron D},\n\tpages = {7},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  The main result of the paper is a new converse theorem for finite-time Lyapunov functions. We show the existence of a finite-time Lyapunov function for an autonomous continuoustime nonlinear dynamical system if the origin of the system is asymptotically stable. Our proof extends the recent results in finite-time Lyapunov function theory by providing an alternative converse proof for the existence of finite-time Lyapunov functions. In particular, we show that given asymptotic stability of the origin, the linearized dynamics satisfy global finitetime Lyapunov function conditions hence proving the converse theorem. Using our results, we present a consolidated theory for using and constructing Lyapunov functions to certify system stability properties. We also propose a constructive algorithm to efficiently compute non-conservative estimates of the domain of attraction for nonlinear dynamical systems.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"doeser-nilsson-ames-murray-invariantsetsforintegratorsandquadrotorobstacleavoidance\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Invariant Sets for Integrators and Quadrotor Obstacle Avoidance.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Doeser, L.; Nilsson, P.; Ames, A. D;  and Murray, R. M\n</span>\n\n  \n\n</span>\n\n  ,8.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/doeser-nilsson-ames-murray-invariantsetsforintegratorsandquadrotorobstacleavoidance\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('doeser-nilsson-ames-murray-invariantsetsforintegratorsandquadrotorobstacleavoidance')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{doeser_invariant_nodate,\n\ttitle = {Invariant {Sets} for {Integrators} and {Quadrotor} {Obstacle} {Avoidance}},\n\tabstract = {Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nthorder integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n ≤ 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.},\n\tlanguage = {en},\n\tauthor = {Doeser, Ludvig and Nilsson, Petter and Ames, Aaron D and Murray, Richard M},\n\tpages = {8},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nthorder integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n ≤ 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"nilsson-ames-lyapunovlikeconditionsfortightexitprobabilityboundsthroughcomparisontheoremsforsdes\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Lyapunov-Like Conditions for Tight Exit Probability Bounds through Comparison Theorems for SDEs.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Nilsson, P.;  and Ames, A. D\n</span>\n\n  \n\n</span>\n\n  ,7.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/nilsson-ames-lyapunovlikeconditionsfortightexitprobabilityboundsthroughcomparisontheoremsforsdes\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('nilsson-ames-lyapunovlikeconditionsfortightexitprobabilityboundsthroughcomparisontheoremsforsdes')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{nilsson_lyapunov-like_nodate,\n\ttitle = {Lyapunov-{Like} {Conditions} for {Tight} {Exit} {Probability} {Bounds} through {Comparison} {Theorems} for {SDEs}},\n\tabstract = {Computing upper bounds on exit probabilities—the probability that a system reaches certain “bad” sets—may assist decision-making in control of stochastic systems. Existing analytical bounds for systems described by stochastic differential equations are quite loose, especially for low-probability events, which limits their applicability in practical situations. In this paper we analyze why existing bounds are loose, and conclude that it is a fundamental issue with the underlying techniques based on martingale inequalities. As an alternative, we give comparison results for stochastic differential equations that via a Lyapunov-like function allow exit probabilities of an ndimensional system to be upper-bounded by an exit probability of a one-dimensional Ornstein-Uhlenbeck process. Even though no closed-form expression is known for the latter, it depends on three or four parameters and can be a priori tabulated for applications. We extend these ideas to the controlled setting and state a stochastic analogue of control barrier functions. The bounds are illustrated on numerical examples and are shown to be much tighter than those based on martingale inequalities.},\n\tlanguage = {en},\n\tauthor = {Nilsson, Petter and Ames, Aaron D},\n\tpages = {7},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Computing upper bounds on exit probabilities—the probability that a system reaches certain “bad” sets—may assist decision-making in control of stochastic systems. Existing analytical bounds for systems described by stochastic differential equations are quite loose, especially for low-probability events, which limits their applicability in practical situations. In this paper we analyze why existing bounds are loose, and conclude that it is a fundamental issue with the underlying techniques based on martingale inequalities. As an alternative, we give comparison results for stochastic differential equations that via a Lyapunov-like function allow exit probabilities of an ndimensional system to be upper-bounded by an exit probability of a one-dimensional Ornstein-Uhlenbeck process. Even though no closed-form expression is known for the latter, it depends on three or four parameters and can be a priori tabulated for applications. We extend these ideas to the controlled setting and state a stochastic analogue of control barrier functions. The bounds are illustrated on numerical examples and are shown to be much tighter than those based on martingale inequalities.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"hamed-distributedfeedbackcontrollersforstablecooperativelocomotionofquadrupedalrobotsavirtualconstraintapproach\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Distributed Feedback Controllers for Stable Cooperative Locomotion of Quadrupedal Robots: A Virtual Constraint Approach.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Hamed, K. A.\n</span>\n\n  \n\n</span>\n\n  ,8.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/hamed-distributedfeedbackcontrollersforstablecooperativelocomotionofquadrupedalrobotsavirtualconstraintapproach\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('hamed-distributedfeedbackcontrollersforstablecooperativelocomotionofquadrupedalrobotsavirtualconstraintapproach')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{hamed_distributed_nodate,\n\ttitle = {Distributed {Feedback} {Controllers} for {Stable} {Cooperative} {Locomotion} of {Quadrupedal} {Robots}: {A} {Virtual} {Constraint} {Approach}},\n\tabstract = {This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. The paper then generates modified and local virtual constraints for each agent that allow stable collaborative locomotion. Optimal distributed feedback controllers, based on nonlinear control and quadratic programming, are developed to impose the local virtual constraints. To demonstrate the power of the analytical foundation, an extensive numerical simulation for cooperative locomotion of two quadrupedal robots with robotic manipulators is presented. The numerical complex hybrid model has 64 continuous-time domains, 192 discretetime transitions, 96 state variables, and 36 control inputs.},\n\tlanguage = {en},\n\tauthor = {Hamed, Kaveh Akbari},\n\tpages = {8},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. The paper then generates modified and local virtual constraints for each agent that allow stable collaborative locomotion. Optimal distributed feedback controllers, based on nonlinear control and quadratic programming, are developed to impose the local virtual constraints. To demonstrate the power of the analytical foundation, an extensive numerical simulation for cooperative locomotion of two quadrupedal robots with robotic manipulators is presented. The numerical complex hybrid model has 64 continuous-time domains, 192 discretetime transitions, 96 state variables, and 36 control inputs.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"chen-ahmadi-ames-optimalsafecontrollersynthesisadensityfunctionapproach\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Optimal Safe Controller Synthesis: A Density Function Approach.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Chen, Y.; Ahmadi, M.;  and Ames, A. D\n</span>\n\n  \n\n</span>\n\n  ,6.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/chen-ahmadi-ames-optimalsafecontrollersynthesisadensityfunctionapproach\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('chen-ahmadi-ames-optimalsafecontrollersynthesisadensityfunctionapproach')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{chen_optimal_nodate,\n\ttitle = {Optimal {Safe} {Controller} {Synthesis}: {A} {Density} {Function} {Approach}},\n\tabstract = {This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value function. The density function follows the Liouville equation and is the dual of the value function, which satisfies Bellman’s optimality principle. Thanks to density functions, constraints over the distribution of states, such as safety constraints, can be posed straightforwardly in an optimal control problem. The constrained optimal control problem is then solved with a primal-dual algorithm. This formulation is extended to the case with external disturbances, and we show that the robust constrained optimal control can be solved with a modified primal-dual algorithm. We apply this formulation to the problem of finding the optimal safe controller that minimizes the cumulative intervention. An adaptive cruise control (ACC) example is used to demonstrate the efficacy of the proposed, wherein we compare the result of the density function approach with the conventional control barrier function (CBF) method.},\n\tlanguage = {en},\n\tauthor = {Chen, Yuxiao and Ahmadi, Mohamadreza and Ames, Aaron D},\n\tpages = {6},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value function. The density function follows the Liouville equation and is the dual of the value function, which satisfies Bellman’s optimality principle. Thanks to density functions, constraints over the distribution of states, such as safety constraints, can be posed straightforwardly in an optimal control problem. The constrained optimal control problem is then solved with a primal-dual algorithm. This formulation is extended to the case with external disturbances, and we show that the robust constrained optimal control can be solved with a modified primal-dual algorithm. We apply this formulation to the problem of finding the optimal safe controller that minimizes the cumulative intervention. An adaptive cruise control (ACC) example is used to demonstrate the efficacy of the proposed, wherein we compare the result of the density function approach with the conventional control barrier function (CBF) method.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"romero-benosman-continuoustimeoptimizationoftimevaryingcostfunctionsviafinitetimestabilitywithpredefinedconvergencetime\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Continuous-Time Optimization of Time-Varying Cost Functions Via Finite-Time Stability with Pre-Defined Convergence Time.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Romero, O.;  and Benosman, M.\n</span>\n\n  \n\n</span>\n\n  ,6.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/romero-benosman-continuoustimeoptimizationoftimevaryingcostfunctionsviafinitetimestabilitywithpredefinedconvergencetime\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('romero-benosman-continuoustimeoptimizationoftimevaryingcostfunctionsviafinitetimestabilitywithpredefinedconvergencetime')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{romero_continuous-time_nodate,\n\ttitle = {Continuous-{Time} {Optimization} of {Time}-{Varying} {Cost} {Functions} {Via} {Finite}-{Time} {Stability} with {Pre}-{Defined} {Convergence} {Time}},\n\tabstract = {In this paper, we propose a new family of continuous-time optimization algorithms for time-varying, locally strongly convex cost functions, based on discontinuous second-order gradient optimization flows with provable finite-time convergence to local optima. To analyze our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of arbitrary time-varying differential inclusions, particularly of the Filippov type. We then prove the convergence of our proposed flows in finite time. We illustrate the performance of our proposed flows on a quadratic cost function to track a decaying sinusoid.},\n\tlanguage = {en},\n\tauthor = {Romero, Orlando and Benosman, Mouhacine},\n\tpages = {6},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In this paper, we propose a new family of continuous-time optimization algorithms for time-varying, locally strongly convex cost functions, based on discontinuous second-order gradient optimization flows with provable finite-time convergence to local optima. To analyze our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of arbitrary time-varying differential inclusions, particularly of the Filippov type. We then prove the convergence of our proposed flows in finite time. We illustrate the performance of our proposed flows on a quadratic cost function to track a decaying sinusoid.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"siravuru-sreenath-nonlinearcontrolusingcoordinatefreeandeulerformulationsanempiricalevaluationona3dpendulum\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Nonlinear Control Using Coordinate-Free and Euler Formulations: An Empirical Evaluation on a 3D Pendulum.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Siravuru, A.;  and Sreenath, K.\n</span>\n\n  \n\n</span>\n\n  ,6.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/siravuru-sreenath-nonlinearcontrolusingcoordinatefreeandeulerformulationsanempiricalevaluationona3dpendulum\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('siravuru-sreenath-nonlinearcontrolusingcoordinatefreeandeulerformulationsanempiricalevaluationona3dpendulum')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{siravuru_nonlinear_nodate,\n\ttitle = {Nonlinear {Control} {Using} {Coordinate}-{Free} and {Euler} {Formulations}: {An} {Empirical} {Evaluation} on a {3D} {Pendulum}},\n\tabstract = {Pendulum dynamics are widely utilized in robotics control literature to test and evaluate novel control design techniques. They exhibit many interesting features commonly seen in real-world nonlinear systems and yet they are simple enough for quick prototyping, further analysis, and benchmarking. In this work, we study the impact of a 3D pendulum’s orientation parametrization on stabilization performance. Mainly, we show that using a global or coordinate-free formulation for dynamics and control is not only singularity-free but also more input-efficient. We validate this empirically by running over 700 stabilization simulations across the full configuration space of a 3D pendulum and compare the performance of a geometric and a Euler-parametrized controller. We show that the geometric controller is able to leverage the inherent manifold curvature and flow along geodesics for efficient stabilization.},\n\tlanguage = {en},\n\tauthor = {Siravuru, Avinash and Sreenath, Koushil},\n\tpages = {6},\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Pendulum dynamics are widely utilized in robotics control literature to test and evaluate novel control design techniques. They exhibit many interesting features commonly seen in real-world nonlinear systems and yet they are simple enough for quick prototyping, further analysis, and benchmarking. In this work, we study the impact of a 3D pendulum’s orientation parametrization on stabilization performance. Mainly, we show that using a global or coordinate-free formulation for dynamics and control is not only singularity-free but also more input-efficient. We validate this empirically by running over 700 stabilization simulations across the full configuration space of a 3D pendulum and compare the performance of a geometric and a Euler-parametrized controller. We show that the geometric controller is able to leverage the inherent manifold curvature and flow along geodesics for efficient stabilization.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"artstein-stabilizationwithrelaxedcontrols\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://reader.elsevier.com/reader/sd/pii/0362546X83900494?token=B88DBE74ECF120DBA01EA046831622DD7E545B033FA36243E3552AA41910AC40C4AC00AEF64C05628DED2123DF4CD220\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'artstein-stabilizationwithrelaxedcontrols', 'https://reader.elsevier.com/reader/sd/pii/0362546X83900494?token=B88DBE74ECF120DBA01EA046831622DD7E545B033FA36243E3552AA41910AC40C4AC00AEF64C05628DED2123DF4CD220', event);\">\n    STABILIZATION WITH RELAXED CONTROLS.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Artstein\n</span>\n\n  \n\n</span>\n\n   \n  <span class=\"note\">ISSN: 10.1016/0362-546X(83)90049-4 Library Catalog: reader.elsevier.com</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://reader.elsevier.com/reader/sd/pii/0362546X83900494?token=B88DBE74ECF120DBA01EA046831622DD7E545B033FA36243E3552AA41910AC40C4AC00AEF64C05628DED2123DF4CD220\"\n     onclick=\"log_download('artstein-stabilizationwithrelaxedcontrols', 'https://reader.elsevier.com/reader/sd/pii/0362546X83900494?token=B88DBE74ECF120DBA01EA046831622DD7E545B033FA36243E3552AA41910AC40C4AC00AEF64C05628DED2123DF4CD220', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"STABILIZATION WITH RELAXED CONTROLS [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/0362-546X(83)90049-4\"\n     onclick=\"log_download('artstein-stabilizationwithrelaxedcontrols', 'http://doi.org/10.1016/0362-546X(83)90049-4', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/artstein-stabilizationwithrelaxedcontrols\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('artstein-stabilizationwithrelaxedcontrols')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{artstein_stabilization_nodate,\n\ttitle = {{STABILIZATION} {WITH} {RELAXED} {CONTROLS}},\n\tshorttitle = {{PII}},\n\turl = {https://reader.elsevier.com/reader/sd/pii/0362546X83900494?token=B88DBE74ECF120DBA01EA046831622DD7E545B033FA36243E3552AA41910AC40C4AC00AEF64C05628DED2123DF4CD220},\n\tlanguage = {en},\n\turldate = {2020-06-22},\n\tauthor = {Artstein},\n\tdoi = {10.1016/0362-546X(83)90049-4},\n\tnote = {ISSN: 10.1016/0362-546X(83)90049-4\nLibrary Catalog: reader.elsevier.com},\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"anonymous-pathfollowingforlinearsystemswithunstablezerodynamics\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://reader.elsevier.com/reader/sd/pii/S0005109806002196?token=22AE7F0A9F0CADCFAE496B41BFC0C9359622CC05594126822D2F63027DD83F339905E4DEA4652A25699EFA5AE0ACAD4B\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'anonymous-pathfollowingforlinearsystemswithunstablezerodynamics', 'https://reader.elsevier.com/reader/sd/pii/S0005109806002196?token=22AE7F0A9F0CADCFAE496B41BFC0C9359622CC05594126822D2F63027DD83F339905E4DEA4652A25699EFA5AE0ACAD4B', event);\">\n    Path-following for linear systems with unstable zero dynamics.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  \n</span>\n\n  \n\n</span>\n\n   \n  <span class=\"note\">Library Catalog: reader.elsevier.com</span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://reader.elsevier.com/reader/sd/pii/S0005109806002196?token=22AE7F0A9F0CADCFAE496B41BFC0C9359622CC05594126822D2F63027DD83F339905E4DEA4652A25699EFA5AE0ACAD4B\"\n     onclick=\"log_download('anonymous-pathfollowingforlinearsystemswithunstablezerodynamics', 'https://reader.elsevier.com/reader/sd/pii/S0005109806002196?token=22AE7F0A9F0CADCFAE496B41BFC0C9359622CC05594126822D2F63027DD83F339905E4DEA4652A25699EFA5AE0ACAD4B', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Path-following for linear systems with unstable zero dynamics [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1016/j.automatica.2006.05.014\"\n     onclick=\"log_download('anonymous-pathfollowingforlinearsystemswithunstablezerodynamics', 'http://doi.org/10.1016/j.automatica.2006.05.014', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/anonymous-pathfollowingforlinearsystemswithunstablezerodynamics\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('anonymous-pathfollowingforlinearsystemswithunstablezerodynamics')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{noauthor_path-following_nodate,\n\ttitle = {Path-following for linear systems with unstable zero dynamics},\n\tshorttitle = {doi},\n\turl = {https://reader.elsevier.com/reader/sd/pii/S0005109806002196?token=22AE7F0A9F0CADCFAE496B41BFC0C9359622CC05594126822D2F63027DD83F339905E4DEA4652A25699EFA5AE0ACAD4B},\n\tlanguage = {en},\n\turldate = {2020-06-09},\n\tdoi = {10.1016/j.automatica.2006.05.014},\n\tnote = {Library Catalog: reader.elsevier.com},\n}\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"singletary-gurriet-nilsson-ames-safetycriticalrapidaerialexplorationofunknownenvironments\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  Safety-Critical Rapid Aerial Exploration of Unknown Environments.\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Singletary, A.; Gurriet, T.; Nilsson, P.;  and Ames, A.\n</span>\n\n  \n\n</span>\n\n  ,7.  .\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/singletary-gurriet-nilsson-ames-safetycriticalrapidaerialexplorationofunknownenvironments\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('singletary-gurriet-nilsson-ames-safetycriticalrapidaerialexplorationofunknownenvironments')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{singletary_safety-critical_nodate,\n\ttitle = {Safety-{Critical} {Rapid} {Aerial} {Exploration} of {Unknown} {Environments}},\n\tabstract = {This paper details a novel approach to collision avoidance for aerial vehicles that enables high-speed flight in uncertain environments. This framework is applied at the controller level and provides safety regardless of the planner that is used. The method is shown to be robust to state uncertainty and disturbances, and is computed entirely online utilizing the full nonlinear system dynamics. The effectiveness of this method is shown in a high-fidelity simulation of a quadrotor with onboard sensors rapidly and safely exploring a cave environment utilizing a simple planner.},\n\tlanguage = {en},\n\tauthor = {Singletary, Andrew and Gurriet, Thomas and Nilsson, Petter and Ames, Aaron},\n\tpages = {7},\n}\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This paper details a novel approach to collision avoidance for aerial vehicles that enables high-speed flight in uncertain environments. This framework is applied at the controller level and provides safety regardless of the planner that is used. The method is shown to be robust to state uncertainty and disturbances, and is computed entirely online utilizing the full nonlinear system dynamics. The effectiveness of this method is shown in a high-fidelity simulation of a quadrotor with onboard sensors rapidly and safely exploring a cave environment utilizing a simple planner.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n\n\n\n  </div>\n\n\n  <!-- Modal -->\n\n  <!-- <iframe id=\"bibbase_network_frame\" -->\n  <!--         src=\"//bibbase.org/network/control\" -->\n  <!--         style=\"display: none;\"> -->\n  <!-- </iframe> -->\n\n</div>\n"}; document.write(bibbase_data.data);