Time-Optimal Control for Underwater Vehicles

Abstract This paper addresses time-optimal control problems for a special class of controlled mechanical systems, underwater vehicles. Lie algebras associated to mechanical systems enjoy certain very special properties, which, together with the maximum principle, allow the deduction of information regarding the structure of singular extremals, and in particular of time-optimal trajectories. We apply the general theory to a model of an underwater vehicle and illustrate our results with some simulations. We consider the fully actuated and the underactuated situations.

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