A Hybrid Dynamical Extension of Averaging

TL;DR

This paper extends a smooth dynamical systems averaging technique to hybrid systems with limit cycles, aiding the synthesis of stable legged gaits and suggesting potential for broader generalizations.

Contribution

It introduces a hybrid averageability concept that generalizes classical averaging, specifically applied to legged locomotion systems.

Findings

Hybrid averaging technique applicable to legged gait synthesis

Demonstrates stability analysis for hybrid systems with limit cycles

Suggests avenues for further theoretical generalizations

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 provide a simple illustration of its applicability to legged locomotion and conclude with some rather more speculative remarks concerning the prospects for further generalization of these ideas.