Stable Bipedal Walking With Foot Rotation Through Direct Regulation of the Zero Moment Point

Consider a biped evolving in the sagittal plane. The unexpected rotation of the supporting foot can be avoided by controlling the zero moment point (ZMP). The objective of this study is to propose and analyze a control strategy for simultaneously regulating the position of the ZMP and the joints of the robot. If the tracking requirements were posed in the time domain, the problem would be underactuated in the sense that the number of inputs would be less than the number of outputs. To get around this issue, the proposed controller is based on a path-following control strategy, previously developed for dealing with the underactuation present in planar robots without actuated ankles. In particular, the control law is defined in such a way that only the kinematic evolution of the robot's state is regulated, but not its temporal evolution. The asymptotic temporal evolution of the robot is completely defined through a one degree-of-freedom subsystem of the closed-loop model. Since the ZMP is controlled, bipedal walking that includes a prescribed rotation of the foot about the toe can also be considered. Simple analytical conditions are deduced that guarantee the existence of a periodic motion and the convergence toward this motion.