Underwater vehicles: a surprising non time-optimal path

This paper deals with the time-optimal problem for a class of underwater vehicles. We prove that if two configurations at rest can be joined by a horizontal or a vertical translation in the body frame coordinates, then there exists a shorter path. Our computations are based on the maximum principle and use that translations in the body frame coordinates are time-equivalent to paths formed by concatenations of 2-singular extremals that are proved to be non time-optimal.