On the extension of the hybrid minimum principle to Riemannian manifolds

This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous hybrid systems on Riemannian manifolds. The analysis is expressed in terms of extremal trajectories on the cotangent bundle of the manifold state space. In the case of autonomous hybrid systems, switching manifolds are defined as smooth embedded submanifolds of the state manifold. The HMP results are obtained in the case of time invariant switching manifolds on Riemannian manifolds.