Higher-Order Constrained Variational Problems on Principal Bundles with Applications to Optimal Control of Underactuated Systems

This paper explores the relationship between optimal control problems for underactuated mechanical systems with symmetries and the classical calculus of variations problem for constrained higher-order mechanical systems, where the configuration space of both problems are principal bundles. We give necessary optimality conditions for the optimal control problem using the constrained higherorder Lagrange-Poincaré equations which are derived from the constrained higher-order variational problem.