Generation of and Switching among Limit-Cycle Bipedal Walking Gaits

Abstract

In this paper we provide a method to generate a continuum of limit cycles using a single precomputed exponentially stable limit cycle designed within the Hybrid Zero Dynamics framework. Guarantees for existence and stability of these limit cycles are provided. We derive analytical constraints that ensure boundedness of the state under arbitrary switching among a finite set of limit cycles extracted from the continuum. These limit cycles are used for changing the speeds of an underactuated planar bipedal model while satisfying all modeling constraints such as saturation torque and coefficient of friction in a provably correct manner. A strongly connected directed graph of allowable limit cycle switches is built to obtain valid limit cycle transitions for speed changes within 0.42-0.81 m/s.