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\n \n\n \n \n \n \n \n \n Control Barrier Function based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria.\n \n \n \n \n\n\n \n Reis, M. F.; Aguiar, A. P.; and Tabuada, P.\n\n\n \n\n\n\n arXiv:2003.07819 [cs, eess, math]. March 2020.\n arXiv: 2003.07819\n\n\n\n
\n\n\n\n \n \n $\"Control$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n\n\n\n

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@article{reis_control_2020,\n\ttitle = {Control {Barrier} {Function} based {Quadratic} {Programs} {Introduce} {Undesirable} {Asymptotically} {Stable} {Equilibria}},\n\turl = {http://arxiv.org/abs/2003.07819},\n\tabstract = {Control Lyapunov functions (CLFs) and control barrier functions (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs), guaranteeing safety in the form of trajectory invariance with respect to a given set. In this manuscript, we show that this framework can introduce equilibrium points (particularly at the boundary of the unsafe set) other than the minimum of the Lyapunov function into the closed-loop system. We derive explicit conditions under which these undesired equilibria (which can even appear in the simple case of linear systems with just one convex unsafe set) are asymptotically stable. To address this issue, we propose an extension to the QP-based controller unifying CLFs and CBFs that explicitly avoids undesirable equilibria on the boundary of the safe set. The solution is illustrated in the design of a collision-free controller.},\n\tlanguage = {en},\n\turldate = {2020-06-10},\n\tjournal = {arXiv:2003.07819 [cs, eess, math]},\n\tauthor = {Reis, Matheus F. and Aguiar, A. Pedro and Tabuada, Paulo},\n\tmonth = mar,\n\tyear = {2020},\n\tnote = {arXiv: 2003.07819},\n\tkeywords = {Electrical Engineering and Systems Science - Systems and Control, Mathematics - Optimization and Control},\n}\n\n

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\n \n\n \n \n \n \n \n \n Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions.\n \n \n \n \n\n\n \n Grandia, R.; Taylor, A. J.; Singletary, A.; Hutter, M.; and Ames, A. D.\n\n\n \n\n\n\n arXiv:2006.01229 [cs, eess]. June 2020.\n arXiv: 2006.01229\n\n\n\n
\n\n\n\n \n \n $\"Nonlinear$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n \n \n 15 downloads\n \n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n\n\n\n

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@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 = {2020-06-09},\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

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\n \n\n \n \n \n \n \n \n Control Barrier Function based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria.\n \n \n \n \n\n\n \n Reis, M. F.; Aguiar, A. P.; and Tabuada, P.\n\n\n \n\n\n\n arXiv:2003.07819 [cs, eess, math]. March 2020.\n arXiv: 2003.07819\n\n\n\n
\n\n\n\n \n \n $\"Control$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n\n\n\n

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@article{reis_control_2020-1,\n\ttitle = {Control {Barrier} {Function} based {Quadratic} {Programs} {Introduce} {Undesirable} {Asymptotically} {Stable} {Equilibria}},\n\turl = {http://arxiv.org/abs/2003.07819},\n\tabstract = {Control Lyapunov functions (CLFs) and control barrier functions (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs), guaranteeing safety in the form of trajectory invariance with respect to a given set. In this manuscript, we show that this framework can introduce equilibrium points (particularly at the boundary of the unsafe set) other than the minimum of the Lyapunov function into the closed-loop system. We derive explicit conditions under which these undesired equilibria (which can even appear in the simple case of linear systems with just one convex unsafe set) are asymptotically stable. To address this issue, we propose an extension to the QP-based controller unifying CLFs and CBFs that explicitly avoids undesirable equilibria on the boundary of the safe set. The solution is illustrated in the design of a collision-free controller.},\n\tlanguage = {en},\n\turldate = {2020-06-06},\n\tjournal = {arXiv:2003.07819 [cs, eess, math]},\n\tauthor = {Reis, Matheus F. and Aguiar, A. Pedro and Tabuada, Paulo},\n\tmonth = mar,\n\tyear = {2020},\n\tnote = {arXiv: 2003.07819},\n\tkeywords = {Electrical Engineering and Systems Science - Systems and Control, Mathematics - Optimization and Control},\n}\n\n

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\n \n\n \n \n \n \n \n \n An SQP method for equality constrained optimization on manifolds.\n \n \n \n \n\n\n \n Schiela, A.; and Ortiz, J.\n\n\n \n\n\n\n arXiv:2005.06844 [math]. May 2020.\n arXiv: 2005.06844\n\n\n\n
\n\n\n\n \n \n $\"An$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@article{schiela_sqp_2020,\n\ttitle = {An {SQP} method for equality constrained optimization on manifolds},\n\turl = {http://arxiv.org/abs/2005.06844},\n\tabstract = {We extend the class of SQP methods for equality constrained optimization to the setting of diﬀerentiable manifolds. The use of retractions and stratiﬁcations allows us to pull back the involved mappings to linear spaces. We study local quadratic convergence to minimizers. In addition we present a composite step method for globalization based on cubic regularization of the objective function and aﬃne covariant damped Newton method for feasibility. We show transition to fast local convergence of this scheme. We test our method on equilibrium problems in ﬁnite elasticity where the stable equilibrium position of an inextensible transversely isotropic elastic rod under dead load is sought.},\n\tlanguage = {en},\n\turldate = {2020-06-03},\n\tjournal = {arXiv:2005.06844 [math]},\n\tauthor = {Schiela, Anton and Ortiz, Julian},\n\tmonth = may,\n\tyear = {2020},\n\tnote = {arXiv: 2005.06844},\n\tkeywords = {49M37, 90C55, 90C06, Mathematics - Optimization and Control},\n}\n\n

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\n \n\n \n \n \n \n \n \n Task-Priority Control of Redundant Robotic Systems using Control Lyapunov and Control Barrier Function based Quadratic Programs.\n \n \n \n \n\n\n \n Basso, E. A.; and Pettersen, K. Y.\n\n\n \n\n\n\n arXiv:2001.07547 [cs, eess]. January 2020.\n arXiv: 2001.07547\n\n\n\n
\n\n\n\n \n \n $\"Task-Priority$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n\n\n\n

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@article{basso_task-priority_2020,\n\ttitle = {Task-{Priority} {Control} of {Redundant} {Robotic} {Systems} using {Control} {Lyapunov} and {Control} {Barrier} {Function} based {Quadratic} {Programs}},\n\turl = {http://arxiv.org/abs/2001.07547},\n\tabstract = {Redundant robotic systems are designed to accomplish multiple tasks simultaneously. Tasks are functions of the system conﬁguration, and can be divided into groups by their priority. System redundancy can be exploited by including lower-priority optimization tasks within the control framework. However, it is important that the inclusion of such lower-priority tasks does not have an eﬀect on higher-priority safety-related and operational tasks. This paper presents a novel task-priority framework based on a hierarchy of control Lyapunov function (CLF) and control barrier function (CBF) based quadratic programs (QPs). The proposed method guarantees strict priority among diﬀerent groups of tasks such as safety-related, operational and optimization tasks. Moreover, a soft priority measure in the form of penalty parameters can be employed to prioritize tasks at the same priority level. As opposed to kinematic control schemes, the proposed framework is a holistic approach to control of redundant robotic systems, which solves the redundancy resolution, dynamic control and control allocation problems simultaneously. Simulation results of a hyper-redundant articulated intervention autonomous underwater vehicle (AIAUV) is presented to validate the proposed framework.},\n\tlanguage = {en},\n\turldate = {2020-04-26},\n\tjournal = {arXiv:2001.07547 [cs, eess]},\n\tauthor = {Basso, Erlend A. and Pettersen, Kristin Y.},\n\tmonth = jan,\n\tyear = {2020},\n\tnote = {arXiv: 2001.07547},\n\tkeywords = {Computer Science - Robotics, Electrical Engineering and Systems Science - Systems and Control},\n}\n\n

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\n \n 2019\n \n \n (5)\n \n \n

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\n \n\n \n \n \n \n \n Do Intermediate Gaits Matter When Rapidly Accelerating?.\n \n \n \n\n\n \n Fisher, C.; Hubicki, C.; and Patel, A.\n\n\n \n\n\n\n IEEE Robotics and Automation Letters, 4(4): 3418–3424. October 2019.\n Conference Name: IEEE Robotics and Automation Letters\n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@article{fisher_intermediate_2019,\n\ttitle = {Do {Intermediate} {Gaits} {Matter} {When} {Rapidly} {Accelerating}?},\n\tvolume = {4},\n\tissn = {2377-3766},\n\tdoi = {10.1109/LRA.2019.2927952},\n\tabstract = {Transient locomotion is still poorly understood in terms of planning and implementation on robotic platforms, with most research concentrated on steady-state motion. In this letter, we investigate optimal rapid acceleration (positive and negative) maneuvers of a planar numerical quadruped and biped robot. The question we ask is whether legged robots should transition through discrete, intermediate gaits (walking to trot to bound) or plan a direct transition to the top-speed gait. We present numerical evidence supporting the energetic optimality of transitioning to a desired gait without intermediate gait transitions. Trajectories were generated from rest to steady state and vice versa. Two cost functions (cost of transport and a heat-based cost function) were analyzed and compared to observations made in nature. A full 30-m trajectory was generated and compared to the acceleration and deceleration results, which further supported transitioning directly to the desired gait. All the trajectories were observed to follow a sliding mass template model which, in future, can be used as a heuristic to plan these transient maneuvers.},\n\tnumber = {4},\n\tjournal = {IEEE Robotics and Automation Letters},\n\tauthor = {Fisher, Callen and Hubicki, Christian and Patel, Amir},\n\tmonth = oct,\n\tyear = {2019},\n\tnote = {Conference Name: IEEE Robotics and Automation Letters},\n\tkeywords = {Acceleration, Cost function, Legged locomotion, Legged robots, Steady-state, Trajectory, Transient analysis, biped robot, deceleration results, discrete gaits, gait analysis, heat-based cost function, intermediate gait, intermediate gait transitions, legged locomotion, legged robots, motion control, optimal rapid acceleration, optimization and optimal control, robot dynamics, robotic platforms, steady state, steady-state motion, top-speed gait, trajectory control, transient locomotion, transient maneuvers, under actuated robots},\n\tpages = {3418--3424},\n}\n\n

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\n \n\n \n \n \n \n \n Hybrid Nonsmooth Barrier Functions With Applications to Provably Safe and Composable Collision Avoidance for Robotic Systems.\n \n \n \n\n\n \n Glotfelter, P.; Buckley, I.; and Egerstedt, M.\n\n\n \n\n\n\n IEEE Robotics and Automation Letters, 4(2): 1303–1310. April 2019.\n Conference Name: IEEE Robotics and Automation Letters\n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@article{glotfelter_hybrid_2019,\n\ttitle = {Hybrid {Nonsmooth} {Barrier} {Functions} {With} {Applications} to {Provably} {Safe} and {Composable} {Collision} {Avoidance} for {Robotic} {Systems}},\n\tvolume = {4},\n\tcopyright = {Ryan},\n\tissn = {2377-3766},\n\tdoi = {10.1109/LRA.2019.2895125},\n\tabstract = {Robots are entering an age of ubiquity, and to operate effectively, these systems must typically satisfy a series of constraints (e.g., collision avoidance, obeying speed limits, maintaining connectivity). In addition, modern applications hinge on the completion of particular tasks, such as driving to a certain location or monitoring a crop patch. The dichotomy between satisfying constraints and completing objectives creates a need for constraint-satisfaction frameworks that are composable with a pre-existing primary objective. Barrier functions have recently emerged as a practical and the composable method for constraint satisfaction, and prior results demonstrate a system of Boolean logic for nonsmooth barrier functions as well as a composable controller-synthesis framework; however, this prior work does not consider dynamically changing constraints (e.g., a robot sensing and avoiding an obstacle). Consequently, the main theoretical contribution of this letter extends nonsmooth barrier functions to time-varying barrier functions with jumps. In a practical instantiation of the theoretical main results, this letter revisits a classic problem by formulating a collision-avoidance framework and composing it with a nominal controller. Experimental results show the efficacy of this framework on a light detection and ranging (LIDAR)-equipped differential-drive robot in a real-time obstacle-avoidance scenario.},\n\tnumber = {2},\n\tjournal = {IEEE Robotics and Automation Letters},\n\tauthor = {Glotfelter, Paul and Buckley, Ian and Egerstedt, Magnus},\n\tmonth = apr,\n\tyear = {2019},\n\tnote = {Conference Name: IEEE Robotics and Automation Letters},\n\tkeywords = {Agriculture, Autonomous vehicles, Collision avoidance, Optimization and optimal control, Robot kinematics, Tools, autonomous vehicle navigation, collision avoidance, composable controller-synthesis framework, composable method, constraint satisfaction, constraint theory, constraint-satisfaction frameworks, control system synthesis, crop patch, hybrid nonsmooth barrier functions, light detection, mobile robots, primary objective, real-time obstacle-avoidance scenario, robot safety, robot sensing, robotic systems, speed limits, time-varying barrier functions},\n\tpages = {1303--1310},\n}\n\n

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\n \n\n \n \n \n \n \n \n Passivity-Based Decentralized Control of Multi-Robot Systems With Delays Using Control Barrier Functions.\n \n \n \n \n\n\n \n Notomista, G.; Cai, X.; Yamauchi, J.; and Egerstedt, M.\n\n\n \n\n\n\n arXiv:1904.04801 [cs]. September 2019.\n arXiv: 1904.04801\n\n\n\n
\n\n\n\n \n \n $\"Passivity-Based$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n\n\n\n

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@article{notomista_passivity-based_2019,\n\ttitle = {Passivity-{Based} {Decentralized} {Control} of {Multi}-{Robot} {Systems} {With} {Delays} {Using} {Control} {Barrier} {Functions}},\n\tcopyright = {A},\n\turl = {http://arxiv.org/abs/1904.04801},\n\tabstract = {In this paper, we present a solution to the problem of coordinating multiple robots across a communication channel that experiences delays. The proposed approach leverages control barrier functions in order to ensure that the multi-robot system remains dissipative. This is achieved by encoding the dissipativity-preserving condition as a set invariance constraint. This constraint is then included in an optimization problem, whose objective is that of modifying, in a minimally invasive fashion, the nominal input to the robots. The formulated optimization problem is decentralized in the sense that, in order to be solved, it does not require the individual robots to have access to global information. Moreover, thanks to its convexity, each robot can solve it using fast and efficient algorithms. The effectiveness of the proposed control framework is demonstrated through the implementation of a formation control algorithm in presence of delays on a team of mobile robots.},\n\turldate = {2020-04-05},\n\tjournal = {arXiv:1904.04801 [cs]},\n\tauthor = {Notomista, Gennaro and Cai, Xiaoyi and Yamauchi, Junya and Egerstedt, Magnus},\n\tmonth = sep,\n\tyear = {2019},\n\tnote = {arXiv: 1904.04801},\n\tkeywords = {Electrical Engineering and Systems Science - Systems and Control},\n}\n\n

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\n \n\n \n \n \n \n \n \n Composition of Safety Constraints With Applications to Decentralized Fixed-Wing Collision Avoidance.\n \n \n \n \n\n\n \n Squires, E.; Pierpaoli, P.; Konda, R.; Coogan, S.; and Egerstedt, M.\n\n\n \n\n\n\n arXiv:1906.03771 [cs]. June 2019.\n arXiv: 1906.03771\n\n\n\n
\n\n\n\n \n \n $\"Composition$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n\n\n\n

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@article{squires_composition_2019,\n\ttitle = {Composition of {Safety} {Constraints} {With} {Applications} to {Decentralized} {Fixed}-{Wing} {Collision} {Avoidance}},\n\tcopyright = {5/10},\n\turl = {http://arxiv.org/abs/1906.03771},\n\tabstract = {In this paper we discuss how to construct a barrier certiﬁcate for a control afﬁne system subject to actuator constraints and motivate this discussion by examining collision avoidance for ﬁxed-wing unmanned aerial vehicles (UAVs). In particular, the theoretical development in this paper is used to create a barrier certiﬁcate that ensures that two UAVs will not collide for all future times assuming the vehicles start in a safe starting conﬁguration. We then extend this development by discussing how to ensure that multiple safety constraints are simultaneously satisﬁed in a decentralized manner (e.g., ensure robot distances are above some threshold for all pairwise combinations of UAVs for all future times) while ensuring output actuator commands are within speciﬁed limits. We validate the theoretical developments of this paper in the simulator SCRIMMAGE with a simulation of 20 UAVs that maintain safe distances from each other even though their nominal paths would otherwise cause a collision.},\n\tlanguage = {en},\n\turldate = {2020-04-01},\n\tjournal = {arXiv:1906.03771 [cs]},\n\tauthor = {Squires, Eric and Pierpaoli, Pietro and Konda, Rohit and Coogan, Sam and Egerstedt, Magnus},\n\tmonth = jun,\n\tyear = {2019},\n\tnote = {arXiv: 1906.03771},\n\tkeywords = {Computer Science - Robotics},\n}\n\n

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\n \n\n \n \n \n \n \n Control Barrier Functions: Theory and Applications.\n \n \n \n\n\n \n Ames, A. D.; Coogan, S.; Egerstedt, M.; Notomista, G.; Sreenath, K.; and Tabuada, P.\n\n\n \n\n\n\n In 2019 18th European Control Conference (ECC), pages 3420–3431, June 2019. \n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n \n \n 25 downloads\n \n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@inproceedings{ames_control_2019,\n\ttitle = {Control {Barrier} {Functions}: {Theory} and {Applications}},\n\tcopyright = {5},\n\tshorttitle = {Control {Barrier} {Functions}},\n\tdoi = {10.23919/ECC.2019.8796030},\n\tabstract = {This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.},\n\tbooktitle = {2019 18th {European} {Control} {Conference} ({ECC})},\n\tauthor = {Ames, Aaron D. and Coogan, Samuel and Egerstedt, Magnus and Notomista, Gennaro and Sreenath, Koushil and Tabuada, Paulo},\n\tmonth = jun,\n\tyear = {2019},\n\tkeywords = {control barrier functions, optimisation, optimization, robotic systems, robots, safety properties, safety-critical controllers},\n\tpages = {3420--3431},\n}\n

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\n \n\n \n \n \n \n \n A Parametric MPC Approach to Balancing the Cost of Abstraction for Differential-Drive Mobile Robots.\n \n \n \n\n\n \n Glotfelter, P.; and Egerstedt, M.\n\n\n \n\n\n\n In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages 732–737, May 2018. \n ISSN: 2577-087X\n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@inproceedings{glotfelter_parametric_2018,\n\ttitle = {A {Parametric} {MPC} {Approach} to {Balancing} the {Cost} of {Abstraction} for {Differential}-{Drive} {Mobile} {Robots}},\n\tcopyright = {8/10},\n\tdoi = {10.1109/ICRA.2018.8461234},\n\tabstract = {When designing control strategies for differential-drive mobile robots, one standard tool is the consideration of a point at a fixed distance along a line orthogonal to the wheel axis instead of the full pose of the vehicle. This abstraction supports replacing the non-holonomic, three-state unicycle model with a much simpler two-state single-integrator model (i.e., a velocity-controlled point). Yet this transformation comes at a performance cost, through the robot's precision and maneuverability. This work contains derivations for expressions of these precision and maneuverability costs in terms of the transformation's parameters. Furthermore, these costs show that only selecting the parameter once over the course of an application may cause an undue loss of precision. Model Predictive Control (MPC) represents one such method to ameliorate this condition. However, MPC typically realizes a control signal, rather than a parameter, so this work also proposes a Parametric Model Predictive Control (PMPC) method for parameter and sampling horizon optimization. Experimental results are presented that demonstrate the effects of the parameterization on the deployment of algorithms developed for the single-integrator model on actual differential-drive mobile robots.},\n\tbooktitle = {2018 {IEEE} {International} {Conference} on {Robotics} and {Automation} ({ICRA})},\n\tauthor = {Glotfelter, Paul and Egerstedt, Magnus},\n\tmonth = may,\n\tyear = {2018},\n\tnote = {ISSN: 2577-087X},\n\tkeywords = {Measurement, Mobile robots, Parametric MPC approach, Parametric Model Predictive Control method, Parametric statistics, Predictive control, Robot kinematics, Wheels, control signal, differential-drive mobile robots, maneuverability costs, mobile robots, motion control, predictive control, three-state unicycle model, two-state single-integrator model},\n\tpages = {732--737},\n}\n\n

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\n \n\n \n \n \n \n \n Towards a Framework for Realizable Safety Critical Control through Active Set Invariance.\n \n \n \n\n\n \n Gurriet, T.; Singletary, A.; Reher, J.; Ciarletta, L.; Feron, E.; and Ames, A.\n\n\n \n\n\n\n In 2018 ACM/IEEE 9th International Conference on Cyber-Physical Systems (ICCPS), pages 98–106, April 2018. \n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n \n \n 3 downloads\n \n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@inproceedings{gurriet_towards_2018,\n\ttitle = {Towards a {Framework} for {Realizable} {Safety} {Critical} {Control} through {Active} {Set} {Invariance}},\n\tcopyright = {6.5/10},\n\tdoi = {10.1109/ICCPS.2018.00018},\n\tabstract = {This paper presents initial results towards a realizable framework for the safety critical controlled invariance of cyber-physical systems. The main contribution of this paper is the development of a control barrier function based methodology which can be used to enforce set invariance on systems in the presence of non-linear disturbances and uncertainty. The first part of this work is a review of the current methods available for finding viable sets and how they are linked to practical choices regarding safety. Their limitations and directions towards improvements when it comes to handling model uncertainty are also highlighted. The second part of this work is the formulation of a condition which can guarantee set invariance in the presence of generic uncertain in the dynamics. An associated optimization problem to enforce that condition is proposed and a method to convexify the problem and make it solvable in real-time is formally presented. The effectiveness of the proposed framework is illustrated experimentally on a two-wheeled inverted pendulum.},\n\tbooktitle = {2018 {ACM}/{IEEE} 9th {International} {Conference} on {Cyber}-{Physical} {Systems} ({ICCPS})},\n\tauthor = {Gurriet, Thomas and Singletary, Andrew and Reher, Jacob and Ciarletta, Laurent and Feron, Eric and Ames, Aaron},\n\tmonth = apr,\n\tyear = {2018},\n\tkeywords = {Barrier functions, Control systems, Cyber-physical systems, Kernel, Lyapunov methods, Non linear control, Optimization, Real time optimization, Safety, Set invariance, Uncertainty, active set invariance, control barrier function based methodology, control system synthesis, cyber-physical systems, model uncertainty, nonlinear control systems, nonlinear disturbances, optimisation, optimization problem, pendulums, realizable framework, realizable safety critical control, safety, safety critical controlled invariance, two-wheeled inverted pendulum, uncertain systems, wheels},\n\tpages = {98--106},\n}\n\n

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\n \n 2017\n \n \n (4)\n \n \n

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\n \n\n \n \n \n \n \n \n Transcription Methods for Trajectory Optimization: a beginners tutorial.\n \n \n \n \n\n\n \n Kelly, M. P.\n\n\n \n\n\n\n arXiv:1707.00284 [math]. July 2017.\n arXiv: 1707.00284\n\n\n\n
\n\n\n\n \n \n $\"Transcription$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n\n\n\n

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@article{kelly_transcription_2017,\n\ttitle = {Transcription {Methods} for {Trajectory} {Optimization}: a beginners tutorial},\n\tcopyright = {5},\n\tshorttitle = {Transcription {Methods} for {Trajectory} {Optimization}},\n\turl = {http://arxiv.org/abs/1707.00284},\n\tabstract = {This report is an introduction to transcription methods for trajectory optimization techniques. The ﬁrst few sections describe the two classes of transcription methods (shooting \\& simultaneous) that are used to convert the trajectory optimization problem into a general constrained optimization form. The middle of the report discusses a few extensions to the basic methods, including how to deal with hybrid systems (such as walking robots). The ﬁnal section goes over a variety of implementation details.},\n\tlanguage = {en},\n\turldate = {2020-04-14},\n\tjournal = {arXiv:1707.00284 [math]},\n\tauthor = {Kelly, Matthew P.},\n\tmonth = jul,\n\tyear = {2017},\n\tnote = {arXiv: 1707.00284},\n\tkeywords = {Mathematics - Optimization and Control},\n}\n\n

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\n \n\n \n \n \n \n \n Supervised learning for stabilizing underactuated bipedal robot locomotion, with outdoor experiments on the wave field.\n \n \n \n\n\n \n Da, X.; Hartley, R.; and Grizzle, J. W.\n\n\n \n\n\n\n In 2017 IEEE International Conference on Robotics and Automation (ICRA), pages 3476–3483, May 2017. \n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@inproceedings{da_supervised_2017,\n\ttitle = {Supervised learning for stabilizing underactuated bipedal robot locomotion, with outdoor experiments on the wave field},\n\tcopyright = {4.5},\n\tdoi = {10.1109/ICRA.2017.7989397},\n\tabstract = {Supervised learning is used to build a control policy for robust, stable, dynamic walking of an underactuated bipedal robot. The training and testing sets consist of controllers based on a full dynamic model, virtual constraints, and parameter optimization to meet torque limits, friction cone, and environmental conditions. The controllers are designed to induce locally exponentially stable periodic walking gaits at various speeds, both forward and backward, and for various constant ground slopes. They are also designed to induce aperiodic gaits that transition among a subset of the periodic gaits in a fixed number of steps. In experiments, the learned policy allows a 3D bipedal robot to recover from a significant kick. It also enables the robot to walk down a 22 degree slope and walk on sinusoidally varying terrain, all without using a camera. During the development of these results, it is demonstrated that supervised learning of locally exponentially stable controllers can result in a loss of stability and a means to avoid this is suggested.},\n\tbooktitle = {2017 {IEEE} {International} {Conference} on {Robotics} and {Automation} ({ICRA})},\n\tauthor = {Da, Xingye and Hartley, Ross and Grizzle, Jessy W.},\n\tmonth = may,\n\tyear = {2017},\n\tkeywords = {3D bipedal robot, Legged locomotion, Optimization, Robot kinematics, Supervised learning, Testing, Training, aperiodic gaits, control policy, control system synthesis, controllers, dynamic walking, environmental conditions, friction cone, full dynamic model, learning (artificial intelligence), legged locomotion, parameter optimization, stability, stabilizing underactuated bipedal robot locomotion, stable controllers, stable periodic walking gaits, supervised learning, torque limits, virtual constraints, wave field},\n\tpages = {3476--3483},\n}\n\n

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\n \n\n \n \n \n \n \n \n Dynamic Walking on Randomly-Varying Discrete Terrain with One-step Preview.\n \n \n \n \n\n\n \n Nguyen, Q.; Agrawal, A.; Da, X.; Martin, W.; Geyer, H.; Grizzle, J.; and Sreenath, K.\n\n\n \n\n\n\n In Robotics: Science and Systems XIII, July 2017. Robotics: Science and Systems Foundation\n \n\n\n\n
\n\n\n\n \n \n $\"Dynamic$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

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@inproceedings{nguyen_dynamic_2017,\n\ttitle = {Dynamic {Walking} on {Randomly}-{Varying} {Discrete} {Terrain} with {One}-step {Preview}},\n\tcopyright = {4.8},\n\tisbn = {978-0-9923747-3-0},\n\turl = {http://www.roboticsproceedings.org/rss13/p72.pdf},\n\tdoi = {10.15607/RSS.2017.XIII.072},\n\tabstract = {An inspiration for developing a bipedal walking system is the ability to navigate rough terrain with discrete footholds like stepping stones. In this paper, we present a novel methodology to overcome the problem of dynamic walking over stepping stones with signiﬁcant random changes to step length and step height at each step. Using a 2-step gait optimization, we not only consider the desired location of the next footstep but also the current conﬁguration of the robot, thereby resolving the problem of step transition when we switch between different walking gaits. We then use gait interpolation to generate the desired walking gait in real-time. We demonstrate the method on a planar dynamical walking model of ATRIAS, an underactuated bipedal robot walking over a randomly generated stepping stones with step length and step height changing in the range of [30:80] (cm) and [30:30] (cm) respectively. Experimental validation on the real robot was also successful for the problem of dynamic walking (a) on stepping stones with step lengths varied within [23:78] (cm) and average walking speed of 0.6 (m/s).},\n\tlanguage = {en},\n\turldate = {2020-04-08},\n\tbooktitle = {Robotics: {Science} and {Systems} {XIII}},\n\tpublisher = {Robotics: Science and Systems Foundation},\n\tauthor = {Nguyen, Quan and Agrawal, Ayush and Da, Xingye and Martin, William and Geyer, Hartmut and Grizzle, Jessy and Sreenath, Koushil},\n\tmonth = jul,\n\tyear = {2017},\n}\n\n

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\n \n\n \n \n \n \n \n Safe certificate-based maneuvers for teams of quadrotors using differential flatness.\n \n \n \n\n\n \n Wang, L.; Ames, A. D.; and Egerstedt, M.\n\n\n \n\n\n\n In 2017 IEEE International Conference on Robotics and Automation (ICRA), pages 3293–3298, May 2017. \n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n \n \n 3 downloads\n \n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@inproceedings{wang_safe_2017,\n\ttitle = {Safe certificate-based maneuvers for teams of quadrotors using differential flatness},\n\tdoi = {10.1109/ICRA.2017.7989375},\n\tabstract = {Safety Barrier Certificates that ensure collision-free maneuvers for teams of differential flatness-based quadrotors are presented in this paper. Synthesized with control barrier functions, the certificates are used to modify the nominal trajectory in a minimally invasive way to avoid collisions. The proposed collision avoidance strategy complements existing flight control and planning algorithms by providing trajectory modifications with provable safety guarantees. The effectiveness of this strategy is supported both by the theoretical results and experimental validation on a team of five quadrotors.},\n\tbooktitle = {2017 {IEEE} {International} {Conference} on {Robotics} and {Automation} ({ICRA})},\n\tauthor = {Wang, Li and Ames, Aaron D. and Egerstedt, Magnus},\n\tmonth = may,\n\tyear = {2017},\n\tkeywords = {Collision avoidance, Minimally invasive surgery, Planning, Propellers, Safety, Shape, Trajectory, air safety, aircraft control, autonomous aerial vehicles, collision avoidance, collision avoidance strategy, collision-free maneuver, control barrier function, differential flatness-based quadrotors, flight control, flight planning algorithm, helicopters, mobile robots, multi-robot systems, nominal trajectory, provable safety guarantee, quadrotor team, safe certificate-based maneuver, safety barrier certificate, trajectory control, trajectory modification},\n\tpages = {3293--3298},\n}\n\n

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\n \n 2016\n \n \n (1)\n \n \n

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\n \n\n \n \n \n \n \n Optimization and stabilization of trajectories for constrained dynamical systems.\n \n \n \n\n\n \n Posa, M.; Kuindersma, S.; and Tedrake, R.\n\n\n \n\n\n\n In 2016 IEEE International Conference on Robotics and Automation (ICRA), pages 1366–1373, May 2016. \n \n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@inproceedings{posa_optimization_2016,\n\ttitle = {Optimization and stabilization of trajectories for constrained dynamical systems},\n\tdoi = {10.1109/ICRA.2016.7487270},\n\tabstract = {Contact constraints, such as those between a foot and the ground or a hand and an object, are inherent in many robotic tasks. These constraints define a manifold of feasible states; while well understood mathematically, they pose numerical challenges to many algorithms for planning and controlling whole-body dynamic motions. In this paper, we present an approach to the synthesis and stabilization of complex trajectories for both fully-actuated and underactuated robots subject to contact constraints. We introduce a trajectory optimization algorithm (DIRCON) that extends the direct collocation method, naturally incorporating manifold constraints to produce a nominal trajectory with third-order integration accuracy-a critical feature for achieving reliable tracking control. We adapt the classical time-varying linear quadratic regulator to produce a local cost-to-go in the manifold tangent plane. Finally, we descend the cost-to-go using a quadratic program that incorporates unilateral friction and torque constraints. This approach is demonstrated on three complex walking and climbing locomotion examples in simulation.},\n\tbooktitle = {2016 {IEEE} {International} {Conference} on {Robotics} and {Automation} ({ICRA})},\n\tauthor = {Posa, Michael and Kuindersma, Scott and Tedrake, Russ},\n\tmonth = may,\n\tyear = {2016},\n\tkeywords = {DIRCON, Heuristic algorithms, Legged locomotion, Manifolds, Robot kinematics, Trajectory optimization, climbing locomotion, complex trajectory stabilization, complex trajectory synthesis, complex walking locomotion, constrained dynamical systems, contact constraints, direct collocation method, friction, fully-actuated robot, legged locomotion, linear quadratic control, manifold tangent plane, motion control, path planning, quadratic program, quadratic programming, robot dynamics, robotic tasks, third-order integration, time-varying linear quadratic regulator, time-varying systems, torque constraints, tracking control, trajectory optimization algorithm, underactuated robot, unilateral friction, whole-body dynamic motion control, whole-body dynamic motion planning},\n\tpages = {1366--1373},\n}\n\n

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\n \n\n \n \n \n \n \n \n The invariant extended Kalman filter as a stable observer.\n \n \n \n \n\n\n \n Barrau, A.; and Bonnabel, S.\n\n\n \n\n\n\n arXiv:1410.1465 [cs]. October 2015.\n arXiv: 1410.1465\n\n\n\n
\n\n\n\n \n \n $\"The$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n\n\n\n

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@article{barrau_invariant_2015,\n\ttitle = {The invariant extended {Kalman} filter as a stable observer},\n\turl = {http://arxiv.org/abs/1410.1465},\n\tabstract = {We analyze the convergence aspects of the invariant extended Kalman ﬁlter (IEKF), when the latter is used as a deterministic non-linear observer on Lie groups, for continuoustime systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we ﬁrst generalize this result by characterizing the (much broader) class of systems for which this property holds. Then, we leverage the result to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging.},\n\tlanguage = {en},\n\turldate = {2020-04-21},\n\tjournal = {arXiv:1410.1465 [cs]},\n\tauthor = {Barrau, Axel and Bonnabel, Silvère},\n\tmonth = oct,\n\tyear = {2015},\n\tnote = {arXiv: 1410.1465},\n\tkeywords = {Electrical Engineering and Systems Science - Systems and Control},\n}\n\n

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\n \n\n \n \n \n \n \n \n Do limit cycles matter in the long run? Stable orbits and sliding-mass dynamics emerge in task-optimal locomotion.\n \n \n \n \n\n\n \n Hubicki, C.; Jones, M.; Daley, M.; and Hurst, J.\n\n\n \n\n\n\n In 2015 IEEE International Conference on Robotics and Automation (ICRA), pages 5113–5120, Seattle, WA, USA, May 2015. IEEE\n \n\n\n\n
\n\n\n\n \n \n $\"Do$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

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@inproceedings{hubicki_limit_2015,\n\taddress = {Seattle, WA, USA},\n\ttitle = {Do limit cycles matter in the long run? {Stable} orbits and sliding-mass dynamics emerge in task-optimal locomotion},\n\tcopyright = {9/10},\n\tisbn = {978-1-4799-6923-4},\n\tshorttitle = {Do limit cycles matter in the long run?},\n\turl = {http://ieeexplore.ieee.org/document/7139911/},\n\tdoi = {10.1109/ICRA.2015.7139911},\n\tabstract = {We investigate the task-optimality of legged limit cycles and present numerical evidence supporting a simple general locomotion-planning template. Limit cycles have been foundational to the control and analysis of legged systems, but as robots move toward completing real-world tasks, are limit cycles practical in the long run? We address this question both ﬁguratively and literally by solving for optimal strategies for long-horizon tasks spanning as many as 20 running steps. These scenarios were designed to embody practical locomotion tasks, such as evading a pursuer, and were formulated with minimal constraints (complete the task, minimize energy cost, and don’t fall). By leveraging large-scale constrained optimization techniques, we numerically solve the trajectory for a reducedorder running model to optimally complete each scenario. We ﬁnd, in the tested scenarios in ﬂat terrain, that near-limitcycle behaviors emerge after a transient period of acceleration and deceleration, suggesting limit cycles may be a useful, near-optimal planning target. On rough terrain, enforcing a limit cycle on every step only degrades gait economy by 25\\% compared to optimal 20-step look-ahead planning. When perturbing the scenario with a single “bump” in the road, the model converged in a manner giving the appearance of an asymptotically stable orbit, despite not explicitly enforcing asymptotic stability. Further, we show that the transient periods of acceleration and deceleration may be near-optimally approximated by planning with a simple “sliding mass” template. These results support the notion that limit cycles can be useful approximations of task-optimal behavior, and thus are useful near-term targets for long-term planning.},\n\tlanguage = {en},\n\turldate = {2020-04-14},\n\tbooktitle = {2015 {IEEE} {International} {Conference} on {Robotics} and {Automation} ({ICRA})},\n\tpublisher = {IEEE},\n\tauthor = {Hubicki, Christian and Jones, Mikhail and Daley, Monica and Hurst, Jonathan},\n\tmonth = may,\n\tyear = {2015},\n\tpages = {5113--5120},\n}\n\n

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\n \n\n \n \n \n \n \n Control barrier function based quadratic programs with application to bipedal robotic walking.\n \n \n \n\n\n \n Hsu, S.; Xu, X.; and Ames, A. D.\n\n\n \n\n\n\n In 2015 American Control Conference (ACC), pages 4542–4548, July 2015. \n ISSN: 2378-5861\n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n \n \n 2 downloads\n \n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@inproceedings{hsu_control_2015,\n\ttitle = {Control barrier function based quadratic programs with application to bipedal robotic walking},\n\tcopyright = {10/10},\n\tdoi = {10.1109/ACC.2015.7172044},\n\tabstract = {This paper presents a methodology for the development of control barrier functions (CBFs) through a backstepping inspired approach. Given a set defined as the superlevel set of a function, h, the main result is a constructive means for generating control barrier functions that guarantee forward invariance of this set. In particular, if the function defining the set has relative degree n, an iterative methodology utilizing higher order derivatives of h provably results in a control barrier function that can be explicitly derived. To demonstrate these formal results, they are applied in the context of bipedal robotic walking. Physical constraints, e.g., joint limits, are represented by control barrier functions and unified with control objectives expressed through control Lyapunov functions (CLFs) via quadratic program (QP) based controllers. The end result is the generation of stable walking satisfying physical realizability constraints for a model of the bipedal robot AMBER2.},\n\tbooktitle = {2015 {American} {Control} {Conference} ({ACC})},\n\tauthor = {Hsu, Shao-Chen and Xu, Xiangru and Ames, Aaron D.},\n\tmonth = jul,\n\tyear = {2015},\n\tnote = {ISSN: 2378-5861},\n\tkeywords = {Backstepping, CBF, CLF, Context, Foot, Legged locomotion, Lyapunov methods, Mathematical model, QP based controllers, backstepping inspired approach, bipedal robot AMBER2, bipedal robotic walking, control Lyapunov functions, control barrier function, control nonlinearities, forward invariance, higher order derivatives, invariance, iterative methodology, iterative methods, joint limits, legged locomotion, physical realizability constraints, quadratic programming, quadratic programs, stable walking},\n\tpages = {4542--4548},\n}\n\n

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\n \n\n \n \n \n \n \n \n Nonholonomic virtual constraints for dynamic walking.\n \n \n \n \n\n\n \n Griffin, B.; and Grizzle, J.\n\n\n \n\n\n\n In 2015 54th IEEE Conference on Decision and Control (CDC), pages 4053–4060, Osaka, December 2015. IEEE\n \n\n\n\n
\n\n\n\n \n \n $\"Nonholonomic$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

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@inproceedings{griffin_nonholonomic_2015,\n\taddress = {Osaka},\n\ttitle = {Nonholonomic virtual constraints for dynamic walking},\n\tcopyright = {3.5/10},\n\tisbn = {978-1-4799-7886-1},\n\turl = {http://ieeexplore.ieee.org/document/7402850/},\n\tdoi = {10.1109/CDC.2015.7402850},\n\tabstract = {Virtual constraints are functional relations (i.e., constraints) on the state variables of a robot’s model that are achieved through the action of actuators and feedback control instead of physical contact forces. They are called virtual because they can be re-programmed on the ﬂy without modifying any physical connections among the links of the robot or its environment. Previous analytical and experimental work has established that vector relative degree two virtual holonomic (i.e., only conﬁguration dependent) constraints are a powerful means to synchronize the links of a bipedal robot so as to achieve walking and running motions over a variety of terrain proﬁles. This paper introduces a class of virtual nonholonomic constraints that depend on velocity through (generalized) angular momentum, while maintaining the property of being relative degree two. This additional freedom is shown to yield control solutions that handle a wider range of gait perturbations arising from terrain variations and exogenous forces. Moreover, including angular momentum in the virtual constraints allows foot placement control to be rigorously designed on the basis of the full dynamic model of the biped, instead of on the basis of an inverted pendulum approximation of its center of mass, as is commonly done in the bipedal robotics literature. This new class of control laws is shown in simulation to be robust to a variety of common gait disturbances.},\n\tlanguage = {en},\n\turldate = {2020-03-29},\n\tbooktitle = {2015 54th {IEEE} {Conference} on {Decision} and {Control} ({CDC})},\n\tpublisher = {IEEE},\n\tauthor = {Griffin, Brent and Grizzle, Jessy},\n\tmonth = dec,\n\tyear = {2015},\n\tpages = {4053--4060},\n}\n\n

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\n \n\n \n \n \n \n \n \n Safety-Critical Control for Dynamical Bipedal Walking with Precise Footstep Placement**This work is partially supported through funding from the Google Faculty Award and NSF Grant IIS-1464337.\n \n \n \n \n\n\n \n Nguyen, Q.; and Sreenath, K.\n\n\n \n\n\n\n IFAC-PapersOnLine, 48(27): 147–154. January 2015.\n \n\n\n\n
\n\n\n\n \n \n $\"Safety-Critical$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@article{nguyen_safety-critical_2015,\n\tseries = {Analysis and {Design} of {Hybrid} {Systems} {ADHS}},\n\ttitle = {Safety-{Critical} {Control} for {Dynamical} {Bipedal} {Walking} with {Precise} {Footstep} {Placement}**{This} work is partially supported through funding from the {Google} {Faculty} {Award} and {NSF} {Grant} {IIS}-1464337.},\n\tvolume = {48},\n\tcopyright = {7/10},\n\tissn = {2405-8963},\n\turl = {http://www.sciencedirect.com/science/article/pii/S2405896315024258},\n\tdoi = {10.1016/j.ifacol.2015.11.167},\n\tabstract = {This paper presents a novel methodology to achieve dynamic walking for underactu-ated and hybrid dynamical bipedal robots subject to safety-critical position-based constraints. The proposed controller is based on the combination of control Barrier functions and control Lyapunov functions implemented as a state-based online quadratic program to achieve stability under input and state constraints, while simultaneously enforcing safety. The main contribution of this paper is the control design to enable stable dynamical bipedal walking subject to strict safety constraints that arise due to walking over a terrain with randomly generated discrete footholds and overhead obstacles. Evaluation of our proposed control design is presented on a model of RABBIT, a fve-link planar underacted bipedal robot with point feet.},\n\tlanguage = {en},\n\tnumber = {27},\n\turldate = {2020-04-04},\n\tjournal = {IFAC-PapersOnLine},\n\tauthor = {Nguyen, Quan and Sreenath, Koushil},\n\tmonth = jan,\n\tyear = {2015},\n\tkeywords = {Lyapunov function, Nonlinear control, Quadratic programming, Safety-critical},\n\tpages = {147--154},\n}\n\n

\n

\n\n\n\n\n\n

\n\n\n

\n \n\n \n \n \n \n \n \n Control Barrier Certificates for Safe Swarm Behavior.\n \n \n \n \n\n\n \n Borrmann, U.; Wang, L.; Ames, A. D.; and Egerstedt, M.\n\n\n \n\n\n\n IFAC-PapersOnLine, 48(27): 68–73. 2015.\n \n\n\n\n
\n\n\n\n \n \n $\"Control$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

\n

@article{borrmann_control_2015,\n\ttitle = {Control {Barrier} {Certificates} for {Safe} {Swarm} {Behavior}},\n\tvolume = {48},\n\tcopyright = {8/10},\n\tissn = {24058963},\n\turl = {https://linkinghub.elsevier.com/retrieve/pii/S240589631502412X},\n\tdoi = {10.1016/j.ifacol.2015.11.154},\n\tabstract = {Multi-agent robotics involves the coordination of large numbers of robots, which leads to signiﬁcant challenges in terms of collision avoidance. This paper generates provably collision free swarm behaviours by constructing swarm safety control barrier certiﬁcates. The safety barrier, implemented via an optimization-based controller, serves as a low level safety controller formally ensuring the forward invariance of the safe operating set. In addition, the proposed method naturally combines the goals of collision avoidance and interference with the coordination laws in a uniﬁed and computationally eﬃcient manner. The centralized version of safety barrier certiﬁcate is designed on double integrator dynamic model, and then a decentralized formulation is proposed as a less computationally intensive and more scalable solution. The safety barrier certiﬁcate is validated in simulation and implemented experimentally on multiple mobile robots; the proposed optimization-based controller successfully generates collision free control commands with minimal overall impact on the coordination control laws.},\n\tlanguage = {en},\n\tnumber = {27},\n\turldate = {2020-03-31},\n\tjournal = {IFAC-PapersOnLine},\n\tauthor = {Borrmann, Urs and Wang, Li and Ames, Aaron D. and Egerstedt, Magnus},\n\tyear = {2015},\n\tpages = {68--73},\n}\n\n

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\n\n\n\n\n\n

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\n \n 2014\n \n \n (1)\n \n \n

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\n \n \n

\n \n\n \n \n \n \n \n \n Whole-body motion planning with centroidal dynamics and full kinematics.\n \n \n \n \n\n\n \n Dai, H.; Valenzuela, A.; and Tedrake, R.\n\n\n \n\n\n\n In 2014 IEEE-RAS International Conference on Humanoid Robots, pages 295–302, Madrid, November 2014. IEEE\n \n\n\n\n
\n\n\n\n \n \n $\"Whole-body$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

\n

@inproceedings{dai_whole-body_2014,\n\taddress = {Madrid},\n\ttitle = {Whole-body motion planning with centroidal dynamics and full kinematics},\n\tisbn = {978-1-4799-7174-9},\n\turl = {http://ieeexplore.ieee.org/document/7041375/},\n\tdoi = {10.1109/HUMANOIDS.2014.7041375},\n\tabstract = {To plan dynamic, whole-body motions for robots, one conventionally faces the choice between a complex, fullbody dynamic model containing every link and actuator of the robot, or a highly simpliﬁed model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We exploit the fact that while the full dynamics of humanoid robots are complicated, their centroidal dynamics (the evolution of the angular momentum and the center of mass (COM) position) are much simpler. By treating the dynamics of the robot in centroidal form and directly optimizing the joint trajectories for the actuated degrees of freedom, we arrive at a method that enjoys simpler dynamics, while still having the expressiveness required to handle kinematic constraints such as collision avoidance or reaching to a target. We further require that the robot’s COM and angular momentum as computed from the joint trajectories match those given by the centroidal dynamics. This ensures that the dynamics considered by our optimization are equivalent to the full dynamics of the robot, provided that the robot’s actuators can supply sufﬁcient torque. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot. Additionally, we show that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance.},\n\tlanguage = {en},\n\turldate = {2020-12-10},\n\tbooktitle = {2014 {IEEE}-{RAS} {International} {Conference} on {Humanoid} {Robots}},\n\tpublisher = {IEEE},\n\tauthor = {Dai, Hongkai and Valenzuela, Andres and Tedrake, Russ},\n\tmonth = nov,\n\tyear = {2014},\n\tpages = {295--302},\n}\n\n

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\n \n 2013\n \n \n (4)\n \n \n

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\n \n \n

\n \n\n \n \n \n \n \n \n The zero dynamics of a nonlinear system: From the origin to the latest progresses of a long successful story.\n \n \n \n \n\n\n \n Isidori, A.\n\n\n \n\n\n\n European Journal of Control, 19(5): 369–378. September 2013.\n \n\n\n\n
\n\n\n\n \n \n $\"The$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

\n

@article{isidori_zero_2013,\n\ttitle = {The zero dynamics of a nonlinear system: {From} the origin to the latest progresses of a long successful story},\n\tvolume = {19},\n\tcopyright = {4.5},\n\tissn = {09473580},\n\tshorttitle = {The zero dynamics of a nonlinear system},\n\turl = {https://linkinghub.elsevier.com/retrieve/pii/S0947358013000836},\n\tdoi = {10.1016/j.ejcon.2013.05.014},\n\tabstract = {The concept of zero dynamics of a nonlinear system was introduced about thirty years ago as nonlinear analogue of the concept of transmission zero of the transfer function of a system. This paper reviews a few historical landmarks in the development of this concept and then addresses some current challenging issues, such as the development of global and coordinate free version of a standard output-feedback design paradigm, the analysis of problems of stabilization and tracking in the presence of unstable zero dynamics, and extensions to multivariable systems.},\n\tlanguage = {en},\n\tnumber = {5},\n\turldate = {2020-04-23},\n\tjournal = {European Journal of Control},\n\tauthor = {Isidori, Alberto},\n\tmonth = sep,\n\tyear = {2013},\n\tpages = {369--378},\n}\n\n

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\n\n\n\n\n\n

\n\n\n

\n \n\n \n \n \n \n \n \n Simulation of Aperiodic Bipedal Sprinting.\n \n \n \n \n\n\n \n Celik, H.; and Piazza, S. J.\n\n\n \n\n\n\n Journal of Biomechanical Engineering, 135(8): 081008. August 2013.\n \n\n\n\n
\n\n\n\n \n \n $\"Simulation$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

\n

@article{celik_simulation_2013,\n\ttitle = {Simulation of {Aperiodic} {Bipedal} {Sprinting}},\n\tvolume = {135},\n\tissn = {0148-0731, 1528-8951},\n\turl = {https://asmedigitalcollection.asme.org/biomechanical/article/doi/10.1115/1.4024577/371078/Simulation-of-Aperiodic-Bipedal-Sprinting},\n\tdoi = {10.1115/1.4024577},\n\tabstract = {Synthesis of legged locomotion through dynamic simulation is useful for exploration of the mechanical and control variables that contribute to efficient gait. Most previous simulations have made use of periodicity constraints, a sensible choice for investigations of steady-state walking or running. Sprinting from rest, however, is aperiodic by nature and this aperiodicity is central to the goal of the movement, as performance is determined in large part by a rapid acceleration phase early in the race. The purpose of this study was to create a novel simulation of aperiodic sprinting using a modified spring-loaded inverted pendulum (SLIP) biped model. The optimal control problem was to find the set of controls that minimized the time for the model to run 20 m, and this problem was solved using a direct multiple shooting algorithm that converts the original continuous time problem into piecewise discrete subproblems. The resulting nonlinear programming problem was solved iteratively using a sequential quadratic programming method. The starting point for the optimizer was an initial guess simulation that was a slow alternating-gait “jogging” simulation developed using proportional-derivative feedback to control trunk attitude, swing leg angle, and leg retraction and extension. The optimized aperiodic sprint simulation solution yielded a substantial improvement in locomotion time over the initial guess (2.79 s versus 6.64 s). Following optimization, the model produced forward impulses at the start of the sprint that were four times greater than those of the initial guess simulation, producing more rapid acceleration. Several gait features demonstrated in the optimized sprint simulation correspond to behaviors of human sprinters: forward trunk lean at the start; straightening of the trunk during acceleration; and a dive at the finish. Optimization resulted in reduced foot contact times (0.065 s versus 0.210 s), but contact times early in the optimized simulation were longer to facilitate acceleration. The present study represents the first simulation of multistep aperiodic sprinting with optimal controls. Although the minimized objective function was simple, the model replicated several complex behaviors such as modulation of the foot contact and executing a forward dive at the finish line. None of these observed behaviors were imposed explicitly by constraints but rather were “discovered” by the optimizer. These methods will be extended by addition of musculotendon actuators and joints in order to gain understanding of the influence of musculoskeletal mechanics on gait speed.},\n\tlanguage = {en},\n\tnumber = {8},\n\turldate = {2020-04-14},\n\tjournal = {Journal of Biomechanical Engineering},\n\tauthor = {Celik, Huseyin and Piazza, Stephen J.},\n\tmonth = aug,\n\tyear = {2013},\n\tpages = {081008},\n}\n\n

\n

\n\n\n

\n Synthesis of legged locomotion through dynamic simulation is useful for exploration of the mechanical and control variables that contribute to efficient gait. Most previous simulations have made use of periodicity constraints, a sensible choice for investigations of steady-state walking or running. Sprinting from rest, however, is aperiodic by nature and this aperiodicity is central to the goal of the movement, as performance is determined in large part by a rapid acceleration phase early in the race. The purpose of this study was to create a novel simulation of aperiodic sprinting using a modified spring-loaded inverted pendulum (SLIP) biped model. The optimal control problem was to find the set of controls that minimized the time for the model to run 20 m, and this problem was solved using a direct multiple shooting algorithm that converts the original continuous time problem into piecewise discrete subproblems. The resulting nonlinear programming problem was solved iteratively using a sequential quadratic programming method. The starting point for the optimizer was an initial guess simulation that was a slow alternating-gait “jogging” simulation developed using proportional-derivative feedback to control trunk attitude, swing leg angle, and leg retraction and extension. The optimized aperiodic sprint simulation solution yielded a substantial improvement in locomotion time over the initial guess (2.79 s versus 6.64 s). Following optimization, the model produced forward impulses at the start of the sprint that were four times greater than those of the initial guess simulation, producing more rapid acceleration. Several gait features demonstrated in the optimized sprint simulation correspond to behaviors of human sprinters: forward trunk lean at the start; straightening of the trunk during acceleration; and a dive at the finish. Optimization resulted in reduced foot contact times (0.065 s versus 0.210 s), but contact times early in the optimized simulation were longer to facilitate acceleration. The present study represents the first simulation of multistep aperiodic sprinting with optimal controls. Although the minimized objective function was simple, the model replicated several complex behaviors such as modulation of the foot contact and executing a forward dive at the finish line. None of these observed behaviors were imposed explicitly by constraints but rather were “discovered” by the optimizer. These methods will be extended by addition of musculotendon actuators and joints in order to gain understanding of the influence of musculoskeletal mechanics on gait speed.\n

\n\n\n

\n \n\n \n \n \n \n \n \n Towards the Unification of Locomotion and Manipulation through Control Lyapunov Functions and Quadratic Programs.\n \n \n \n \n\n\n \n Ames, A. D.; and Powell, M.\n\n\n \n\n\n\n In Tarraf, D. C., editor(s), Control of Cyber-Physical Systems, volume 449, pages 219–240. Springer International Publishing, Heidelberg, 2013.\n Series Title: Lecture Notes in Control and Information Sciences\n\n\n\n
\n\n\n\n \n \n $\"Towards$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n \n \n 3 downloads\n \n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

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@incollection{tarraf_towards_2013,\n\taddress = {Heidelberg},\n\ttitle = {Towards the {Unification} of {Locomotion} and {Manipulation} through {Control} {Lyapunov} {Functions} and {Quadratic} {Programs}},\n\tvolume = {449},\n\tcopyright = {9.5/10},\n\tisbn = {978-3-319-01158-5 978-3-319-01159-2},\n\turl = {http://link.springer.com/10.1007/978-3-319-01159-2_12},\n\tabstract = {This paper presents the ﬁrst steps toward unifying locomotion controllers and algorithms with whole-body control and manipulation. A theoretical framework for this uniﬁcation will be given based upon quadratic programs utilizing control Lyapunov functions. In particular, we will ﬁrst consider output based feedback linearization strategies for locomotion together with whole-body control methods for manipulation. We will show that these two traditionally disjoint methods are equivalent through the correct choice of controller. We will then present a method for unifying these two methodologies through the use of control Lyapunov functions presented in the form of a quadratic program. In addition, it will be shown that these controllers can be combined with force-based control to achieve locomotion and force-based manipulation in a single framework. Finally, simulation results will be presented demonstrating the validity of the proposed framework.},\n\tlanguage = {en},\n\turldate = {2020-04-07},\n\tbooktitle = {Control of {Cyber}-{Physical} {Systems}},\n\tpublisher = {Springer International Publishing},\n\tauthor = {Ames, Aaron D. and Powell, Matthew},\n\teditor = {Tarraf, Danielle C.},\n\tyear = {2013},\n\tdoi = {10.1007/978-3-319-01159-2_12},\n\tnote = {Series Title: Lecture Notes in Control and Information Sciences},\n\tpages = {219--240},\n}\n\n

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\n\n\n\n\n\n

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\n \n\n \n \n \n \n \n \n Optimal control of underactuated mechanical systems with symmetries.\n \n \n \n \n\n\n \n \n\n\n \n\n\n\n 2013.\n \n\n\n\n
\n\n\n\n \n \n $\"Optimal$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

\n

@misc{noauthor_optimal_2013,\n\ttitle = {Optimal control of underactuated mechanical systems with symmetries},\n\turl = {http://aimsciences.org/article/doi/10.3934/proc.2013.2013.149},\n\tlanguage = {en},\n\turldate = {2020-03-25},\n\tyear = {2013},\n\tdoi = {10.3934/proc.2013.2013.149},\n}\n\n

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\n \n 2012\n \n \n (1)\n \n \n

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\n \n \n

\n \n\n \n \n \n \n \n \n Synthesis and stabilization of complex behaviors through online trajectory optimization.\n \n \n \n \n\n\n \n Tassa, Y.; Erez, T.; and Todorov, E.\n\n\n \n\n\n\n In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 4906–4913, Vilamoura-Algarve, Portugal, October 2012. IEEE\n \n\n\n\n
\n\n\n\n \n \n $\"Synthesis$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

\n

@inproceedings{tassa_synthesis_2012,\n\taddress = {Vilamoura-Algarve, Portugal},\n\ttitle = {Synthesis and stabilization of complex behaviors through online trajectory optimization},\n\tisbn = {978-1-4673-1736-8 978-1-4673-1737-5 978-1-4673-1735-1},\n\turl = {http://ieeexplore.ieee.org/document/6386025/},\n\tdoi = {10.1109/IROS.2012.6386025},\n\tabstract = {We present an online trajectory optimization method and software platform applicable to complex humanoid robots performing challenging tasks such as getting up from an arbitrary pose on the ground and recovering from large disturbances using dexterous acrobatic maneuvers. The resulting behaviors, illustrated in the attached video, are computed only 7 x slower than real time, on a standard PC. The video also shows results on the acrobot problem, planar swimming and one-legged hopping. These simpler problems can already be solved in real time, without pre-computing anything.},\n\tlanguage = {en},\n\turldate = {2020-06-24},\n\tbooktitle = {2012 {IEEE}/{RSJ} {International} {Conference} on {Intelligent} {Robots} and {Systems}},\n\tpublisher = {IEEE},\n\tauthor = {Tassa, Yuval and Erez, Tom and Todorov, Emanuel},\n\tmonth = oct,\n\tyear = {2012},\n\tpages = {4906--4913},\n}\n\n

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\n\n\n\n\n\n

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\n \n 2011\n \n \n (1)\n \n \n

\n

\n \n \n

\n \n\n \n \n \n \n \n Consensus in Directed Networks of Agents With Nonlinear Dynamics.\n \n \n \n\n\n \n Yu, W.; Chen, G.; and Cao, M.\n\n\n \n\n\n\n IEEE Transactions on Automatic Control, 56(6): 1436–1441. June 2011.\n Conference Name: IEEE Transactions on Automatic Control\n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@article{yu_consensus_2011,\n\ttitle = {Consensus in {Directed} {Networks} of {Agents} {With} {Nonlinear} {Dynamics}},\n\tvolume = {56},\n\tcopyright = {A},\n\tissn = {1558-2523},\n\tdoi = {10.1109/TAC.2011.2112477},\n\tabstract = {This technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network. Both local and global consensus are defined and investigated. Techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus. The local consensus problem is first studied via a combination of the tools of complex analysis, local consensus manifold approach, and Lyapunov methods. A generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees, for which ideas from algebraic graph theory, matrix theory, and Lyapunov methods are utilized.},\n\tnumber = {6},\n\tjournal = {IEEE Transactions on Automatic Control},\n\tauthor = {Yu, Wenwu and Chen, Guanrong and Cao, Ming},\n\tmonth = jun,\n\tyear = {2011},\n\tnote = {Conference Name: IEEE Transactions on Automatic Control},\n\tkeywords = {Algebraic graph theory, Complex networks, Eigenvalues and eigenfunctions, Laplace equations, Lyapunov function, Lyapunov methods, Manifolds, Multiagent systems, Nonlinear dynamical systems, Synchronization, agent directed networks, algebraic graph theory, complex network, consensus, consensus problem, cooperative agents, generalized algebraic connectivity, graph theory, matrix algebra, matrix theory, nonlinear dynamical systems, nonlinear dynamics, spanning trees, sufficient conditions, synchronization},\n\tpages = {1436--1441},\n}\n\n

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\n \n 2010\n \n \n (2)\n \n \n

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\n \n \n

\n \n\n \n \n \n \n \n \n Passivity-based output synchronization of networked Euler-Lagrange systems subject to nonholonomic constraints.\n \n \n \n \n\n\n \n Han Yu; and Antsaklis, P. J\n\n\n \n\n\n\n In Proceedings of the 2010 American Control Conference, pages 208–213, Baltimore, MD, June 2010. IEEE\n \n\n\n\n
\n\n\n\n \n \n $\"Passivity-based$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

\n

@inproceedings{han_yu_passivity-based_2010,\n\taddress = {Baltimore, MD},\n\ttitle = {Passivity-based output synchronization of networked {Euler}-{Lagrange} systems subject to nonholonomic constraints},\n\tcopyright = {A},\n\tisbn = {978-1-4244-7427-1 978-1-4244-7426-4 978-1-4244-7425-7},\n\turl = {http://ieeexplore.ieee.org/document/5530541/},\n\tdoi = {10.1109/ACC.2010.5530541},\n\turldate = {2020-04-05},\n\tbooktitle = {Proceedings of the 2010 {American} {Control} {Conference}},\n\tpublisher = {IEEE},\n\tauthor = {{Han Yu} and Antsaklis, Panos J},\n\tmonth = jun,\n\tyear = {2010},\n\tpages = {208--213},\n}\n\n

\n

\n\n\n\n

\n\n\n

\n \n\n \n \n \n \n \n Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics.\n \n \n \n\n\n \n Yu, W.; Chen, G.; Cao, M.; and Kurths, J.\n\n\n \n\n\n\n IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40(3): 881–891. June 2010.\n Conference Name: IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)\n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@article{yu_second-order_2010,\n\ttitle = {Second-{Order} {Consensus} for {Multiagent} {Systems} {With} {Directed} {Topologies} and {Nonlinear} {Dynamics}},\n\tvolume = {40},\n\tcopyright = {A},\n\tissn = {1941-0492},\n\tdoi = {10.1109/TSMCB.2009.2031624},\n\tabstract = {This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching second-order consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis.},\n\tnumber = {3},\n\tjournal = {IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)},\n\tauthor = {Yu, Wenwu and Chen, Guanrong and Cao, Ming and Kurths, Jürgen},\n\tmonth = jun,\n\tyear = {2010},\n\tnote = {Conference Name: IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)},\n\tkeywords = {Algebraic connectivity, Algorithms, Analytical models, Artificial Intelligence, Computer Simulation, Control systems, Decision Support Techniques, Graph theory, Lyapunov control approach, Lyapunov methods, Matrices, Models, Theoretical, Multiagent systems, Network topology, Nonlinear Dynamics, Nonlinear control systems, Sufficient conditions, Time varying systems, Tree graphs, algebraic graph theory, directed spanning tree, directed topologies, generalized algebraic connectivity, matrix algebra, matrix theory, mobile robots, multi-agent systems, multiagent system, multiagent systems, nonlinear dynamical systems, nonlinear dynamics, position-velocity consensus, second-order consensus, strongly connected network, trees (mathematics)},\n\tpages = {881--891},\n}\n\n

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\n \n 2008\n \n \n (1)\n \n \n

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\n \n \n

\n \n\n \n \n \n \n \n \n BigDog, the Rough-Terrain Quadruped Robot.\n \n \n \n \n\n\n \n Raibert, M.; Blankespoor, K.; Nelson, G.; and Playter, R.\n\n\n \n\n\n\n IFAC Proceedings Volumes, 41(2): 10822–10825. January 2008.\n 1\n\n\n\n
\n\n\n\n \n \n $\"BigDog,$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

\n

@article{raibert_bigdog_2008,\n\tseries = {17th {IFAC} {World} {Congress}},\n\ttitle = {{BigDog}, the {Rough}-{Terrain} {Quadruped} {Robot}},\n\tvolume = {41},\n\tcopyright = {1/10},\n\tissn = {1474-6670},\n\turl = {http://www.sciencedirect.com/science/article/pii/S1474667016407020},\n\tdoi = {10.3182/20080706-5-KR-1001.01833},\n\tabstract = {Less than half the Earth's landmass is accessible to existing wheeled and tracked vehicles. But people and animals using their legs can go almost anywhere. Our mission at Boston Dynamics is to develop a new breed of rough-terrain robots that capture the mobility, autonomy and speed of living creatures. Such robots will travel in outdoor terrain that is too steep, rutted, rocky, wet, muddy, and snowy for conventional vehicles. They will travel in cities and in our homes, doing chores and providing care, where steps, stairways and household clutter limit the utility of wheeled vehicles. Robots meeting these goals will have terrain sensors, sophisticated computing and power systems, advanced actuators and dynamic controls. We will give a status report on BigDog, an example of such rough-terrain robots.},\n\tnumber = {2},\n\turldate = {2019-09-30},\n\tjournal = {IFAC Proceedings Volumes},\n\tauthor = {Raibert, Marc and Blankespoor, Kevin and Nelson, Gabriel and Playter, Rob},\n\tmonth = jan,\n\tyear = {2008},\n\tnote = {1},\n\tpages = {10822--10825},\n}\n\n

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\n\n\n\n\n\n

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\n \n 2007\n \n \n (1)\n \n \n

\n

\n \n \n

\n \n\n \n \n \n \n \n A Disturbance Rejection Measure for Limit Cycle Walkers: The Gait Sensitivity Norm.\n \n \n \n\n\n \n Hobbelen, D. G. E.; and Wisse, M.\n\n\n \n\n\n\n IEEE Transactions on Robotics, 23(6): 1213–1224. December 2007.\n Conference Name: IEEE Transactions on Robotics\n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

\n

@article{hobbelen_disturbance_2007,\n\ttitle = {A {Disturbance} {Rejection} {Measure} for {Limit} {Cycle} {Walkers}: {The} {Gait} {Sensitivity} {Norm}},\n\tvolume = {23},\n\tissn = {1941-0468},\n\tshorttitle = {A {Disturbance} {Rejection} {Measure} for {Limit} {Cycle} {Walkers}},\n\tdoi = {10.1109/TRO.2007.904908},\n\tabstract = {The construction of more capable bipedal robots highly depends on the ability to measure their performance. This performance is often measured in terms of speed or energy efficiency, but these properties are secondary to the robot's ability to prevent falling given the inevitable presence of disturbances, i.e., its disturbance rejection. Existing disturbance rejection measures (zero moment point, basin of attraction, Floquet multipliers) are unsatisfactory due to conservative assumptions, long computation times, or bad correlation to actual disturbance rejection. This paper introduces a new measure called the Gait Sensitivity Norm that combines a short calculation time with good correlation to actual disturbance rejection. It is especially suitable for implementation on limit cycle walkers, a class of bipeds that currently excels in terms of energy efficiency, but still has limited disturbance rejection capabilities. The paper contains an explanation of the Gait Sensitivity Norm and a validation of its value on a simple walking model as well as on a real bipedal robot. The disturbance rejection of the simple model is studied for variations of floor slope, foot radius, and hip spring stiffness. We show that the calculation speed is as fast as the standard Floquet multiplier analysis, while the actual disturbance rejection is correctly predicted with 93\\% correlation on average.},\n\tnumber = {6},\n\tjournal = {IEEE Transactions on Robotics},\n\tauthor = {Hobbelen, Daan G. E. and Wisse, Martijn},\n\tmonth = dec,\n\tyear = {2007},\n\tnote = {Conference Name: IEEE Transactions on Robotics},\n\tkeywords = {Biped, Energy efficiency, Energy measurement, Floors, Foot, Hip, Legged locomotion, Limit-cycles, Robot sensing systems, Time measurement, Velocity measurement, bipedal robots, controllability, disturbance rejection, disturbance rejection measure, energy efficiency, floor slope, foot radius, gait sensitivity norm, hip spring stiffness, legged locomotion, limit cycle walkers, optimal control, passive dynamic walking, performance index, performance measures, robot dynamics, robot performance measure, stability, walking model},\n\tpages = {1213--1224},\n}\n\n

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\n \n 2006\n \n \n (2)\n \n \n

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\n \n\n \n \n \n \n \n Capture Point: A Step toward Humanoid Push Recovery.\n \n \n \n\n\n \n Pratt, J.; Carff, J.; Drakunov, S.; and Goswami, A.\n\n\n \n\n\n\n In 2006 6th IEEE-RAS International Conference on Humanoid Robots, pages 200–207, December 2006. \n ISSN: 2164-0580\n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

\n

@inproceedings{pratt_capture_2006,\n\ttitle = {Capture {Point}: {A} {Step} toward {Humanoid} {Push} {Recovery}},\n\tcopyright = {2/10},\n\tshorttitle = {Capture {Point}},\n\tdoi = {10.1109/ICHR.2006.321385},\n\tabstract = {It is known that for a large magnitude push a human or a humanoid robot must take a step to avoid a fall. Despite some scattered results, a principled approach towards "when and where to take a step" has not yet emerged. Towards this goal, we present methods for computing capture points and the capture region, the region on the ground where a humanoid must step to in order to come to a complete stop. The intersection between the capture region and the base of support determines which strategy the robot should adopt to successfully stop in a given situation. Computing the capture region for a humanoid, in general, is very difficult. However, with simple models of walking, computation of the capture region is simplified. We extend the well-known linear inverted pendulum model to include a flywheel body and show how to compute exact solutions of the capture region for this model. Adding rotational inertia enables the humanoid to control its centroidal angular momentum, much like the way human beings do, significantly enlarging the capture region. We present simulations of a simple planar biped that can recover balance after a push by stepping to the capture region and using internal angular momentum. Ongoing work involves applying the solution from the simple model as an approximate solution to more complex simulations of bipedal walking, including a 3D biped with distributed mass.},\n\tbooktitle = {2006 6th {IEEE}-{RAS} {International} {Conference} on {Humanoid} {Robots}},\n\tauthor = {Pratt, Jerry and Carff, John and Drakunov, Sergey and Goswami, Ambarish},\n\tmonth = dec,\n\tyear = {2006},\n\tnote = {ISSN: 2164-0580},\n\tkeywords = {Acceleration, Biological system modeling, Closed-form solution, Cognition, Computational modeling, Flywheels, Foot, Humanoid robots, Humans, Legged locomotion, biped robot, capture point, capture region, centroidal angular momentum, flywheel body, humanoid push recovery, humanoid robot, humanoid robots, legged locomotion, linear inverted pendulum model, nonlinear control systems, position control, rotational inertia, torque control},\n\tpages = {200--207},\n}\n\n

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\n\n\n\n\n\n

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\n \n\n \n \n \n \n \n \n Passivity-Based Control of Multi-Agent Systems.\n \n \n \n \n\n\n \n Chopra, N.; and Spong, M. W.\n\n\n \n\n\n\n In Kawamura, S.; and Svinin, M., editor(s), Advances in Robot Control, pages 107–134. Springer Berlin Heidelberg, Berlin, Heidelberg, 2006.\n \n\n\n\n
\n\n\n\n \n \n $\"Passivity-Based$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n\n\n\n

\n

@incollection{kawamura_passivity-based_2006,\n\taddress = {Berlin, Heidelberg},\n\ttitle = {Passivity-{Based} {Control} of {Multi}-{Agent} {Systems}},\n\tcopyright = {A},\n\tisbn = {978-3-540-37346-9},\n\turl = {http://link.springer.com/10.1007/978-3-540-37347-6_6},\n\tabstract = {In this paper we study passivity-based control for the problem of coordination and synchronization of multi-agent systems. We treat agents described by aﬃne nonlinear systems that are input-output passive and that exchange information over a network described by an interconnection graph. We treat both linear interconnections on balanced, directed graphs and nonlinear interconnections on undirected graphs. We present synchronization results for both ﬁxed and switching graphs. Finally, we treat the realistic case of time delay in the communication of information among agents. Our results unify several existing results from the literature on multi-agent systems.},\n\tlanguage = {en},\n\turldate = {2020-04-05},\n\tbooktitle = {Advances in {Robot} {Control}},\n\tpublisher = {Springer Berlin Heidelberg},\n\tauthor = {Chopra, Nikhil and Spong, Mark W.},\n\teditor = {Kawamura, Sadao and Svinin, Mikhail},\n\tyear = {2006},\n\tdoi = {10.1007/978-3-540-37347-6_6},\n\tkeywords = {Passivity},\n\tpages = {107--134},\n}\n\n

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\n \n 2004\n \n \n (1)\n \n \n

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\n \n \n

\n \n\n \n \n \n \n \n \n On the concept of virtual constraints as a tool for walking robot control and balancing.\n \n \n \n \n\n\n \n Canudas-de-Wit, C.\n\n\n \n\n\n\n Annual Reviews in Control, 28(2): 157–166. January 2004.\n \n\n\n\n
\n\n\n\n \n \n $\"On$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

\n

@article{canudas-de-wit_concept_2004,\n\ttitle = {On the concept of virtual constraints as a tool for walking robot control and balancing},\n\tvolume = {28},\n\tissn = {13675788},\n\turl = {https://linkinghub.elsevier.com/retrieve/pii/S1367578804000379},\n\tdoi = {10.1016/j.arcontrol.2004.03.002},\n\tabstract = {In this paper we review a class of control methods for the walking control and the balancing problem. The methods under review are based on the notion of virtual constraints which are forced by feedback. The paper describes several examples where this notion has been used, in a variety of control problems, as a main tool for constructing orbitally stable feedback laws. We also underline the main stability mechanisms behind such approaches, and present the Rabbit 7-DOF walking robot which has been used as a testbed robot for studying controllers based on these concepts.},\n\tlanguage = {en},\n\tnumber = {2},\n\turldate = {2020-04-08},\n\tjournal = {Annual Reviews in Control},\n\tauthor = {Canudas-de-Wit, Carlos},\n\tmonth = jan,\n\tyear = {2004},\n\tpages = {157--166},\n}\n\n

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\n \n 2003\n \n \n (1)\n \n \n

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\n \n\n \n \n \n \n \n Gait transitions for walking and running of biped robots.\n \n \n \n\n\n \n Kwon, O.; and Park, J. H.\n\n\n \n\n\n\n In 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422), volume 1, pages 1350–1355 vol.1, September 2003. \n ISSN: 1050-4729\n\n\n\n
\n\n\n\n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n

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@inproceedings{ohung_kwon_gait_2003,\n\ttitle = {Gait transitions for walking and running of biped robots},\n\tvolume = {1},\n\tdoi = {10.1109/ROBOT.2003.1241779},\n\tabstract = {In this paper, we propose a gait transition algorithm between walking and running for fast movement of a biped robot. Firstly, considering that walking and running differ in the oscillations of the body and legs that occur during each step or stride, the transitionary trajectory is constructed by the transformations of the velocities of hip link, the step height and stride of the feet, and the duration of the step using interpolating polynomials. And in order to increase the compliance about the environment and to absorb the impact force in the landing event, the impedance controller is designed for walking and running biped robot. The effectiveness and the performance of the proposed gait patterns are shown in computer simulations with a 19-DOF biped robot and a 6-DOF elastic pad model.},\n\tbooktitle = {2003 {IEEE} {International} {Conference} on {Robotics} and {Automation} ({Cat}. {No}.{03CH37422})},\n\tauthor = {Ohung Kwon and Jong Hyeon Park},\n\tmonth = sep,\n\tyear = {2003},\n\tnote = {ISSN: 1050-4729},\n\tkeywords = {6-DOF elastic pad model, Computer simulation, Hip, Humans, Impedance, Leg, Legged locomotion, Mechanical engineering, Motion control, Polynomials, Robots, computer simulations, gait analysis, gait transition algorithm, hip link velocity, impedance controller, interpolating polynomials, legged locomotion, robot kinematics, running robots, transitionary trajectory, walking biped robots},\n\tpages = {1350--1355 vol.1},\n}\n\n

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\n \n 2000\n \n \n (1)\n \n \n

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\n \n\n \n \n \n \n \n \n An Elementary Introduction to Groups and Representations.\n \n \n \n \n\n\n \n Hall, B. C.\n\n\n \n\n\n\n arXiv:math-ph/0005032. May 2000.\n arXiv: math-ph/0005032\n\n\n\n
\n\n\n\n \n \n $\"An$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n \n \n \n \n \n \n\n\n\n

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@article{hall_elementary_2000,\n\ttitle = {An {Elementary} {Introduction} to {Groups} and {Representations}},\n\turl = {http://arxiv.org/abs/math-ph/0005032},\n\tabstract = {These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions and examples of Lie groups and Lie algebras, the relationship between Lie groups and Lie algebras via the exponential mapping, the basics of representations theory, the Baker-Campbell-Hausdorff formula, a detailed study of the representations of SU(3), and a brief survey of the representation theory of general semisimple groups.},\n\tlanguage = {en},\n\turldate = {2020-04-21},\n\tjournal = {arXiv:math-ph/0005032},\n\tauthor = {Hall, Brian C.},\n\tmonth = may,\n\tyear = {2000},\n\tnote = {arXiv: math-ph/0005032},\n\tkeywords = {81R05, 22E30, Mathematical Physics},\n}\n\n

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\n \n 1998\n \n \n (1)\n \n \n

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\n \n\n \n \n \n \n \n A benchmark problem for nonlinear control design.\n \n \n \n\n\n \n Bupp, R. T; Bernstein, D. S; and Coppola, V. T\n\n\n \n\n\n\n Int. J. Robust Nonlinear Control,4. 1998.\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

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@article{bupp_benchmark_1998,\n\ttitle = {A benchmark problem for nonlinear control design},\n\tlanguage = {en},\n\tjournal = {Int. J. Robust Nonlinear Control},\n\tauthor = {Bupp, Robert T and Bernstein, Dennis S and Coppola, Vincent T},\n\tyear = {1998},\n\tpages = {4},\n}\n\n

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\n \n undefined\n \n \n (4)\n \n \n

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\n \n\n \n \n \n \n \n Offline motion libraries and online MPC for advanced mobility skills.\n \n \n \n\n\n \n Bjelonic, M.; Grandia, R.; Geilinger, M.; Harley, O.; Medeiros, V. S; Pajovic, V.; Jelavic, E.; Coros, S.; and Hutter, M.\n\n\n \n\n\n\n The International Journal of Robotics Research,22. .\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n \n \n abstract \n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

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@article{bjelonic_offline_nodate,\n\ttitle = {Offline motion libraries and online {MPC} for advanced mobility skills},\n\tabstract = {We describe an optimization-based framework to perform complex locomotion skills for robots with legs and wheels. The generation of complex motions over a long-time horizon often requires ofﬂine computation due to current computing constraints and is mostly accomplished through trajectory optimization (TO). In contrast, model predictive control (MPC) focuses on the online computation of trajectories, robust even in the presence of uncertainty, albeit mostly over shorter time horizons and is prone to generating nonoptimal solutions over the horizon of the task’s goals. Our article’s contributions overcome this trade-off by combining ofﬂine motion libraries and online MPC, uniting a complex, long-time horizon plan with reactive, short-time horizon solutions. We start from ofﬂine trajectories that can be, for example, generated by TO or sampling-based methods. Also, multiple ofﬂine trajectories can be composed out of a motion library into a single maneuver. We then use these ofﬂine trajectories as the cost for the online MPC, allowing us to smoothly blend between multiple composed motions even in the presence of discontinuous transitions. The MPC optimizes from the measured state, resulting in feedback control, which robustiﬁes the task’s execution by reacting to disturbances and looking ahead at the ofﬂine trajectory. With our contribution, motion designers can choose their favorite method to iterate over behavior designs ofﬂine without tuning robot experiments, enabling them to author new behaviors rapidly. Our experiments demonstrate complex and dynamic motions on our traditional quadrupedal robot ANYmal and its roller-walking version. Moreover, the article’s ﬁndings contribute to evaluating ﬁve planning algorithms.},\n\tlanguage = {en},\n\tjournal = {The International Journal of Robotics Research},\n\tauthor = {Bjelonic, Marko and Grandia, Ruben and Geilinger, Moritz and Harley, Oliver and Medeiros, Vivian S and Pajovic, Vuk and Jelavic, Edo and Coros, Stelian and Hutter, Marco},\n\tpages = {22},\n}\n\n

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\n \n\n \n \n \n \n \n \n Library Genesis.\n \n \n \n \n\n\n \n \n\n\n \n\n\n\n \n \n\n\n\n
\n\n\n\n \n \n $\"Library$ Paper\n \n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

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@misc{noauthor_library_nodate,\n\ttitle = {Library {Genesis}},\n\turl = {https://libgen.lc/ads.php?md5=C9D74012D37598766968321C5572115F},\n\turldate = {2020-06-08},\n}\n\n

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\n \n\n \n \n \n \n \n An Introduction to Distributions and Foliations.\n \n \n \n\n\n \n Otten, S.\n\n\n \n\n\n\n ,9. .\n \n\n\n\n
\n\n\n\n \n\n \n\n \n link\n \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

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@article{otten_introduction_nodate,\n\ttitle = {An {Introduction} to {Distributions} and {Foliations}},\n\tcopyright = {10/10},\n\tlanguage = {en},\n\tauthor = {Otten, Samuel},\n\tpages = {9},\n}\n\n

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\n \n\n \n \n \n \n \n \n CONSTRUCTIVE SAFETY USING CONTROL BARRIER FUNCTIONS \\textbar Elsevier Enhanced Reader.\n \n \n \n \n\n\n \n \n\n\n \n\n\n\n \n Library Catalog: reader.elsevier.com\n\n\n\n
\n\n\n\n \n \n $\"CONSTRUCTIVE$ Paper\n \n \n\n \n \n doi\n \n \n\n \n link\n \n \n\n bibtex\n \n\n \n\n \n\n \n \n \n \n \n \n \n\n \n \n \n\n\n\n

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@misc{noauthor_constructive_nodate,\n\ttitle = {{CONSTRUCTIVE} {SAFETY} {USING} {CONTROL} {BARRIER} {FUNCTIONS} {\\textbar} {Elsevier} {Enhanced} {Reader}},\n\tcopyright = {Ryan},\n\turl = {https://reader.elsevier.com/reader/sd/pii/S1474667016355690?token=B06567AA85D6783B62BACD1115700D383C03F1B91391E64275D8E69A2AF38638AEE3BBC242BFACE509AF2518A08E22EA},\n\tlanguage = {en},\n\turldate = {2020-04-08},\n\tdoi = {10.3182/20070822-3-ZA-2920.00076},\n\tnote = {Library Catalog: reader.elsevier.com},\n}\n\n

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