A hybrid dynamical extension of averaging and its application to the analysis of legged gait stability. (February 2018)

• Record Type: Journal Article
• Authors: De, Avik; Burden, Samuel A; Koditschek, Daniel E
• Is Part Of: International journal of robotics research. Volume 37:Number 2/3(2018)
• Page Start: 266
• Page End: 286
• Publication Date: 2018-02
• Subjects: Legged robots -- dynamics -- motion control; Robots -- Periodicals; Robots, Industrial -- Periodicals; 629.89205
• DOI: 10.1177/0278364918756498
• Languages: English
• ISSNs: 0278-3649

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.