Geodesic
Control of underwater vehicles in inviscid fluids
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 3, pp. 662-703

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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.

DOI : 10.1051/cocv/2013079
Classification : 35Q35, 76B03, 76B99
Keywords: underactuated underwater vehicle, submarine, controllability, Euler equations, return method, quaternion 
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     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},
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     zbl = {1301.35098},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013079/}
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Lecaros, Rodrigo; Rosier, Lionel. Control of underwater vehicles in inviscid fluids. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 3, pp. 662-703. doi: 10.1051/cocv/2013079

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