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.

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}, pages = {662--703}, publisher = {EDP-Sciences}, volume = {20}, number = {3}, year = {2014}, doi = {10.1051/cocv/2013079}, mrnumber = {3264219}, zbl = {1301.35098}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2013079/} }

TY - JOUR AU - Lecaros, Rodrigo AU - Rosier, Lionel TI - Control of underwater vehicles in inviscid fluids JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 662 EP - 703 VL - 20 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2013079/ DO - 10.1051/cocv/2013079 LA - en ID - COCV_2014__20_3_662_0 ER -

%0 Journal Article %A Lecaros, Rodrigo %A Rosier, Lionel %T Control of underwater vehicles in inviscid fluids %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 662-703 %V 20 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2013079/ %R 10.1051/cocv/2013079 %G en %F 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://archive.numdam.org/articles/10.1051/cocv/2013079/

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