Falling of a Passive Compass-Gait Biped Robot Caused by a Boundary Crisis

The planar passive compass-gait biped robot on sloped surfaces is the simplest model of legged walkers. It is a two-degrees-of-freedom impulsive mechanical system known to exhibit, in response to an increase in the slope angle of the walking surface, a sequence of period-doubling bifurcations leading to chaos before falling down at some critical slope without any explanation. The fall is found to be occured with the abrupt destruction of chaos. We showed recently that a cyclicfold bifurcation is also generated in the passive walking patterns of the compass robot. The aim of this paper is to show that the fall of the passive compass-gait biped robot occurs via a global bifurcation known as boundary crisis. We show that the cyclic-fold bifurcation is the key of the occurrence of such boundary crisis. We demonstrate how the same period-three unstable periodic orbit generated from the cyclic-fold bifurcation causes the abrupt death of chaos in the passive dynamic walking and hence the fall of the compass-gait biped robot.