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.