New bifurcations in the simplest passive walking model

Abstract

This paper uncovers several new stable periodic gaits in the simplest passive walking bipedal model proposed in the literature. It is demonstrated that the model has period-3 to period-7 gaits beside the period-1 gaits found by Garcia et al. By simulations, this paper shows that each of these new gaits leads to chaos via period-doubling bifurcation and loses its stability by cyclic-fold bifurcation. This interesting phenomenon suggests a series of new bifurcation scenarios that have not been observed before. To confirm the new gaits and their bifurcations, this paper presents computer assisted proofs on the existence and stability of each periodic gait and its period-doubling gaits with the interval Newton method. To verify that the routes indeed lead to chaos, computer-assisted proofs are also given by means of topological horseshoes theory.