Control of underwater vehicles in inviscid fluids

I. Irrotational flows

¹ Centro de Modelamiento Matemático (CMM) and Departamento de Ingeniería Matemática, Universidad de Chile (UMI CNRS 2807), Avenida Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile
rlecaros@dim.uchile.cl
² Basque Center for Applied Mathematics – BCAM, Mazarredo 14, 48009 Bilbao, Basque Country, Spain
rlecaros@bcamath.org
³ Institut Elie Cartan, UMR 7502 UdL/CNRS/INRIA, B.P. 70239, 54506 Vandœuvre-lès-Nancy Cedex, France
Lionel.Rosier@univ-lorraine.fr

Received: 7 March 2013
Revised: 1 August 2013

Abstract

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 vehicle with an ellipsoidal shape.