Semi-passive control of a torso-driven compass-gait biped robot: bifurcation and chaos

In this paper we study the problem of semi-passive bipedal walking for a compass-gait biped robot with torso down a sloped surface. We use a novel control law based on a PD controller. Suc law acts only between the torso and the stance leg, and hence the swing leg is considered entirely passive. We show that such robotic system exhibits some kind of period-doubling bifurcation route to chaos in response to a change in the ground slope and the desired torso angle. The analysis via bifurcation diagrams shows that the torso can perform a stable periodic dynamic walking down steeper slopes. We also show that the backward position of the torso can be used to control chaos.