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

Citation:

A. De, S. A. Burden, and D. E. Koditschek, “A hybrid dynamical extension of averaging and its application to the analysis of legged gait stability,” The International Journal of Robotics Research, vol. 37, no. 2-3, pp. 266-286, 2018. Copy at http://j.mp/2ChHE6J

Date Published:

2018

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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