Stability analysis of a walk of a biped with control of the ZMP

The objective of this study is to analyze the stability of control strategy for a planar biped robot. The avoidance of unexpected rotation of the supporting foot is treated via the control of the zero moment point or ZMP. When the task is a simultaneous control of the joints and of the ZMP, the system becomes under-actuated in the sense that there is less inputs than the number of outputs. The control law is defined in such a way that only the geometric evolution of the biped configuration is controlled, but not the temporal evolution. The temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of a model with one degree of freedom. Simple conditions, which guarantee the existence of a cyclic motion and the convergence towards this motion, are deduced.