Nahla Khraief

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

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.

Dynamic walking control by using the liquid level model and the preview of zero-moment-point

This electronic document presents the application of a novel method of bipedal walking pattern generation assured by “the liquid level model” and the preview control of zero-moment-point (ZMP). In this method, the trajectory of the center of mass (CoM) of the robot is generated assured by the preview controller to maintain the ZMP at the desired location knowing that the robot is modeled as a running liquid level model on a tank. The proposed approach combines the preview control theory with simple model “the liquid level model”, to assure a stable dynamic walking. Simulations results show that the proposed pattern generator guarantee not only to walk dynamically stable but also good performance.