Optimal Strokes for Driftless Swimmers: A General Geometric Approach

Thomas Chambrion (1) , Laetitia Giraldi (2) , Alexandre Munnier (1)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

This paper presents a unified geometric approach for the optimiza- tion of the shape deformations of the so-called driftless swimmers. The class of driftless swimmers includes, among other, isolated swimmers in an infinite 3D Stokes flow (case of micro-swimmers in viscous fluids) or isolated swimmers in an infinite 2D or 3D potential flow. A general framework is introduced, in which five usual nonlinear optimization problems related with the maximization of the traveled distance with a constrained energy consumption) are stated. We prove the existence of regular minimizers under generic con- trollability assumptions. The results are illustrated with an in-depth study of the isolated swimmer with two degrees of freedom in a 2D potential flow.

Domaines: Optimisation et contrôle [math.OC]

Thomas Chambrion, Laetitia Giraldi, Alexandre Munnier. Optimal Strokes for Driftless Swimmers: A General Geometric Approach. 2014. ⟨hal-00969259v1⟩