Controllability and output tracking for an ellipsoidal submarine driven by Kirchhoff´s laws

In this paper, we study the control of an ellipsoid immersed in an infinite volume of ideal fluid with irrotational motion. The dynamics are given by Kirchhoff´s laws. By adopting a backstepping viewpoint, we prove that the position and the attitude of the solid can be forced to approximately follow any given smooth path, using three controls (two controls for the direction and one control for the velocity). Moreover, we prove that the controlled mechanical system (which includes the momenta) is completely controllable in arbitrary small time