Separable Control Lyapunov Functions with Application to Prostheses

This letter extends bipedal trajectory tracking methods to prostheses to enable construction of a class of model-dependent prosthesis controllers using locally available sensor information. The rapidly exponentially stabilizing control Lyapunov functions (RES-CLFs) developed for bipedal robots guarantee stability of the hybrid zero dynamics in the presence of impacts that occur in walking. These methods cannot be directly applied to prostheses because of the unknown human dynamics. We overcome this challenge with two RES-CLFs, one for the prosthesis subsystem and another for the remaining human system. Further, we outline a method to construct these RES-CLFs for this type of separable system by first constructing separable CLFs for partially feedback linearizable systems. This letter develops a class of separable subsystem controllers that rely only on local information but provide formal guarantees of stability for the full hybrid system with zero dynamics.