Lecaros, Rodrigo; Rosier, Lionel Control of underwater vehicles in inviscid fluids. (English) Zbl 1301.35098 ESAIM, Control Optim. Calc. Var. 20, No. 3, 662-703 (2014). The authors investigate the controllability of a vehicle in a 3D inviscid incompressible and irrotational fluid. They consider a neutrally buoyant underwater vehicle without rudder, and actuated by a few number of propellers located into some tunnels inside the rigid body. The motion of such a 3D rigid body is described by twelve functions: the three dimensional position, the attitude, the linear velocity, and the angular velocity of the vehicle. The authors give a rigorous analysis of the control of these functions.Considering the Euler equations, they derive an initial-boundary value problem for the corresponding functions, and apply the return method of Coron. They prove that if the rigid body of the vehicle is symmetric in some sense, and a rank condition is satisfied, then the system is locally controllable around the origin in a finite time.They give examples with six, four, or only three control inputs for a vehicle with an ellipsoidal shape. Reviewer: Keisuke Uchikoshi (Yokosuka) Cited in 1 ReviewCited in 3 Documents MSC: 35Q31 Euler equations 76B75 Flow control and optimization for incompressible inviscid fluids 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids Keywords:underwater vehicle; controllability; Euler equations; return method PDFBibTeX XMLCite \textit{R. Lecaros} and \textit{L. Rosier}, ESAIM, Control Optim. Calc. Var. 20, No. 3, 662--703 (2014; Zbl 1301.35098) Full Text: DOI arXiv