The equations of motion of a controlled mechanical system subject to holonomic constraints may be formulated in termsudof the states and controls by applying a constrained version of the Lagrange-d’Alembert principle. This paper derives audstructure-preserving scheme for the optimal control of such systems using, as one of the key ingredients, a discrete analogueudof that principle. This property is inherited when the system is reduced to its minimal dimension by the discrete nulludspace method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced discreteudequations serve as nonlinear equality constraints for the minimization of a given objective functional. The algorithm yieldsuda sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from theudinitial to the desired final state. In particular, for the optimal control of multibody systems, a force formulation consistentudwith the joint constraints is introduced. This enables one to prove the consistency of the evolution of momentum maps.udUsing a two-link pendulum, the method is compared with existing methods. Further, it is applied to a satellite reorientationudmaneuver and a biomotion problem.
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