Generic Controllability of 3D Swimmers in a Perfect Fluid

Thomas Chambrion (1) , Alexandre Munnier (1)

1 CORIDA - Robust control of infinite dimensional systems and applications

We address the problem of controlling a dynamical system governing the motion of a 3D weighted shape changing body swimming in a perfect fluid. The rigid displacement of the swimmer results from the exchange of momentum between prescribed shape changes and the flow, the total impulse of the fluid-swimmer system being constant for all times. We prove the following tracking results: (i) Synchronized swimming: Maybe up to an arbitrarily small change of its density, any swimmer can approximately follow any given trajectory while, in addition, undergoing approximately any given shape changes. In this statement, the control consists in arbitrarily small superimposed deformations; (ii) Freestyle swimming: Maybe up to an arbitrarily small change of its density, any swimmer can approximately tracks any given trajectory by combining suitably at most five basic movements that can be generically chosen (no macro shape changes are prescribed in this statement).

Mots clés: Locomotion; Geometric control theory; Biomechanics; Ideal fluid

Domaines: Optimisation et contrôle [math.OC]; Biomécanique [physics.med-ph]; Biomécanique [physics.med-ph]

Thomas Chambrion, Alexandre Munnier. Generic Controllability of 3D Swimmers in a Perfect Fluid. SIAM Journal on Control and Optimization, 2012, 50 (5), pp.2814--2835. ⟨10.1137/110828654⟩. ⟨hal-00579986⟩