CYCLIC-FOLD BIFURCATION AND BOUNDARY CRISIS IN DYNAMIC WALKING OF BIPED ROBOTS

Abstract

The aim of this paper is to show that the onset/destruction of bipedal chaos in the dynamic walking of a passive compass-gait biped robot and a semi-passive torso-driven biped robot walking down a slope can occur via a transition mechanism known as boundary crisis. It is known that such biped robots exhibit a scenario of period-doubling bifurcations route to chaos as one of their geometrical or inertial parameters changes. In this paper, we show that a cyclic-fold bifurcation is the key of the occurrence of a double boundary crisis. We demonstrate through bifurcation diagrams how the same period-three unstable periodic orbit generated from the cyclic-fold bifurcation causes the sudden birth/death of the bipedal chaos in the dynamic walking of the two biped robots. We stress that a double boundary crisis is responsible for the fall of each biped robot while walking down an inclined surface and as some bifurcation parameter varies. Stability of the cyclic-fold bifurcation under small perturbations is also discussed.