Energy Shaping of Hybrid Systems via Control Lyapunov Functions

This paper presents a method for adding robustness to periodic orbits in hybrid dynamical systems by shaping the energy. This energy shaping method is similar to existing methods but improves upon them by utilizing control Lyapunov functions which allow for formal results on stability. The main theoretical result, Theorem 1, states that, given an exponentially-stable limit cycle in a hybrid dynamical system, application of the presented energy shaping controller results in a closed-loop system which is exponentially stable. As illustrated through simulation on the compass gait biped, this method turns out to be useful in practice, providing an improvement in robustness and convergence properties while maintaining existing stability.