Control of underwater vehicles in inviscid fluids. I: Irrotational flows.

Rodrigo Lecaros (1, 2) , Lionel Rosier (3, 4)

1 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
2 BCAM - Basque Center for Applied Mathematics
3 CAS - Centre Automatique et Systèmes
4 IECL - Institut Élie Cartan de Lorraine

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron's return method, we establish some local controllability results for the position and velocities of the underwater vehicle. Examples with six, four, or only three controls inputs are given for a vehicule with an ellipsoidal shape.

Mots clés: controllability; submarine; Euler equations; quaternion; return method; Underactuated underwater vehicle

Domaines: Equations aux dérivées partielles [math.AP]; Automatique / Robotique

Rodrigo Lecaros, Lionel Rosier. Control of underwater vehicles in inviscid fluids. I: Irrotational flows.. ESAIM: Control, Optimisation and Calculus of Variations, 2014, 20 (3), pp.662-703. ⟨10.1051/cocv/2013079⟩. ⟨hal-00797991⟩