Bifurcation of Periodic Gait and Chaos in a Bipedal Model with Asymmetric Leg Motion

This paper presents a bipedal model with asymmetric leg motion under a two-parameter pulse thrust, represented by an impulsive hybrid system. By exploring the successive and immediate transitions in motion states, a Poincaré map with explicit form is designed to reveal the dynamic characteristics of walking. The stability of periodic orbits during bipedal walking under two-parameter regulation, as well as the bifurcation mechanism of locomotion, is discussed. The simulation results about periodic gait, flip bifurcation, chaotic gait, and bifurcation control are in agreement with the theoretical analysis. The reliability of bipedal walking for collision angle is demonstrated through an error analysis comparing the nonlinear impulsive hybrid system and its linearized system. The research findings may help to predict and control the motion behavior of bipedal robots. Furthermore, it constitutes part of a theoretical analysis for the pulse propulsion method.