Exponentially Stabilizing Continuous-Time Controllers for multi-domain hybrid systems with application to 3D bipdeal walking

TL;DR

This paper develops a systematic control approach to exponentially stabilize periodic orbits in multi-domain hybrid systems, specifically applied to 3D bipdeal walking, including asymmetric gait scenarios.

Contribution

It extends Poincare section methods to multi-domain hybrid systems and introduces a piecewise feedback control strategy with independent parameter design.

Findings

Successfully stabilizes 3D bipdeal walking with asymmetric gait.

Demonstrates controller effectiveness through simulation examples.

Provides a flexible design method applicable to complex hybrid systems.

Abstract

This paper presents a systematic approach to exponentially stabilize the periodic orbits of multi-domain hybrid systems arising from 3D bipedal walking. Firstly, the method of Poincare sections is extended to the hybrid systems with multiple domains. Then, based on the properties of the Poincare maps, a continuous piecewise feedback control strategy is presented, and three methods are furthermore given to design the controller parameters based on the developed theorems. By those design methods, the controller parameters in each continuous phase can be designed independently, which allows the strategy to be applied to hybrid systems with multiple domains. Finally, the proposed strategy is illustrated by a simulation example. To show that the proposed strategy is not limited to bipedal robots with left-right symmetry property which is assumed in some previous works, an underactuated 3D bipedal robot with asymmetric walking gait is considered.