A hybrid dynamical extension of averaging and its application to the analysis of legged gait stability

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General Robotics, Automation, Sensing and Perception Laboratory
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GRASP
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Electrical and Computer Engineering
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Systems Engineering
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This work was supported in part by NSF grant #1028237, in part by the U. S. Army Research Laboratory and the U. S. Army Research Office under contract/grant number W911NF-16-1-0158 awarded to the second author, and in part by ONR grant #N00014- 16-1-2817, a Vannevar Bush Fellowship held by the last author, sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering.
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Abstract

We extend a smooth dynamical systems averaging technique to a class of hybrid systems with a limit cycle that is particularly relevant to the synthesis of stable legged gaits. After introducing a definition of hybrid averageability sufficient to recover the classical result, we illustrate its applicability by analysis of first a one-legged and then a two-legged hopping model. These abstract systems prepare the ground for the analysis of a significantly more complicated two legged model—a new template for quadrupedal running to be analyzed and implemented on a physical robot in a companion paper. We conclude with some rather more speculative remarks concerning the prospects for further extension and generalization of these ideas.

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2018-03-08
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The International Journal of Robotics Research
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@article{de_hybrid_2018, title = {A hybrid dynamical extension of averaging and its application to the analysis of legged gait stability}, volume = {37}, url = {https://doi.org/10.1177/0278364918756498}, doi = {10.1177/0278364918756498}, abstract = {We extend a smooth dynamical systems averaging technique to a class of hybrid systems with a limit cycle that is particularly relevant to the synthesis of stable legged gaits. After introducing a definition of hybrid averageability sufficient to recover the classical result, we illustrate its applicability by analysis of first a one-legged and then a two-legged hopping model. These abstract systems prepare the ground for the analysis of a significantly more complicated two legged model: a new template for quadrupedal running to be analyzed and implemented on a physical robot in a companion paper. We conclude with some rather more speculative remarks concerning the prospects for further extension and generalization of these ideas.}, number = {2-3}, journal = {The International Journal of Robotics Research}, author = {De, Avik and Burden, Samuel A. and Koditschek, Daniel E.}, year = {2018}, pages = {266--286} }
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