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