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.

Classification: 35Q35, 76B03, 76B99

Keywords: underactuated underwater vehicle, submarine, controllability, Euler equations, return method, quaternion

@article{COCV_2014__20_3_662_0, author = {Lecaros, Rodrigo and Rosier, Lionel}, title = {Control of underwater vehicles in inviscid fluids}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {20}, number = {3}, year = {2014}, pages = {662-703}, doi = {10.1051/cocv/2013079}, zbl = {1301.35098}, mrnumber = {3264219}, language = {en}, url = {http://www.numdam.org/item/COCV_2014__20_3_662_0} }

Lecaros, Rodrigo; Rosier, Lionel. Control of underwater vehicles in inviscid fluids. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 3, pp. 662-703. doi : 10.1051/cocv/2013079. http://www.numdam.org/item/COCV_2014__20_3_662_0/

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