Departmental Papers (ESE)

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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.

Sponsor Acknowledgements

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.

Document Type

Journal Article

Subject Area

GRASP, Kodlab

Date of this Version

3-8-2018

Publication Source

The International Journal of Robotics Research

Volume

37

Issue

2-3

Start Page

266

Last Page

286

DOI

10.1177/0278364918756498

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Bib Tex

@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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Date Posted: 12 March 2018

This document has been peer reviewed.