Trajectory Tracking Control of the Compass-Type Bipedal Robot Gait via an Improved PD+ Controller

This work focuses on the stabilization of the passive dynamic walking gait of the compass-type bipedal robot. Such walker robot is a 2-DOF biped that descends an inclined surface without any actuators. Its bipedal walking is modeled by a complex system, which is characterized by a nonlinear dynamics with impulse effects. We show the complexity of the bipedal walk by analyzing the bifurcation diagrams which reveal the existence of undesirable phenomena such as different bifurcation types and chaos. In order to properly imitate human locomotion, the chaotic bipedal walking of the compass robots walkers should be transformed into a one-periodic stable behavior. Hence, to achieve this goal, we propose an improved PD+ control law, which is based on the PD controller and the gravity compensation. Finally, and via some simulations, we demonstrate that the bipedal walking is controlled and hence chaos is suppressed.