Feet can improve the stability property of a control law for a walking robot

This study proposes the analysis of two control strategies for a planar biped. One control makes it possible to find and study the existence of a cyclic motion and its stability, in this approach the avoidance of unexpected rotation of the supporting foot is treated via the control of the center of pressure or CoP. When the task is a simultaneous control of the joints and of the CoP, the system becomes under-actuated in the sense that we have fewer inputs than outputs. This control law is designed to track a desired geometric evolution of the biped configuration, and not the temporal evolution. But the temporal evolution is completely defined and can be analyzed through the study of a model with one degree of freedom. The influence of the desired geometric evolution of CoP on the stability properties of the control law is studied. The second control law improve the performances of the first one by increasing the rate of convergence towards the cyclic motion and enlarging the basin of attraction of the control. This improvement of the performances is possible by forcing the convergence by the control and relaxing the CoP evolution to be within the foot limits