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Optimal control of underactuated mechanical systems with symmetries
The aim of this paper is to study optimal control problems for
underactuated mechanical systems with symmetries using higher-order Lagrangian mechanics. We variationally derive the corresponding Lagrange -Poincaré equations for second-order Lagrangians with constraints
defined on trivial principal bundles and apply them to study an
optimal control problem for an underactuated vehicle.