This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous hybrid systems whose state manifolds constitute a Lie group (G,*) which is left invariant under the controlled dynamics of the system, and whose switching manifolds are defined as smooth embedded time invariant submanifolds of G. The analysis is expressed in terms of extremal (i.e. optimal) trajectories on the cotangent bundle of the state manifold G.
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