Tracking control for an ellipsoidal submarine driven by Kirchhoff's laws

Thomas Chambrion (1, 2) , Mario Sigalotti (1, 2, 3)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECN - Institut Élie Cartan de Nancy
3 INRIA Lorraine

In this paper, we study the control of an ellipsoid immersed in an infinite volume of ideal fluid. The dynamics of the uncontrolled body 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 approximatively follow any given 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.

Mots clés: inviscid fluid; underactuated underwater vehicles; Kirchhoff's equations; output tracking; exact controllability; fast oscillating controls

Domaines: Optimisation et contrôle [math.OC]

Thomas Chambrion, Mario Sigalotti. Tracking control for an ellipsoidal submarine driven by Kirchhoff's laws. IEEE Transactions on Automatic Control, 2008, 53 (1), pp.339-349. ⟨10.1109/TAC.2007.914958⟩. ⟨hal-00097159⟩