Controllability and Optimal Strokes for N-link Micro-swimmer

Abstract : In this paper we focus on the N-link swimmer, a generalization of the classical 3-link Purcell swimmer. We use the Resistive Force Theory to express the equation of motion in a fluid with a low Reynolds number, and prove that the swimmer is controllable in the whole plane for N greater or equal than 3 and for almost every set of stick lengths. As a direct result, there exists an optimal swimming strategy to reach a desired configuration in minimum time. Numerical experiments for N=3 (Purcell swimmer) suggest that the optimal strategy is periodic, namely a sequence of identical strokes. Our results indicate that this candidate for an optimal stroke indeed gives a better displacement speed than the classical Purcell stroke.
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Laetitia Giraldi, Pierre Martinon, Marta Zoppello. Controllability and Optimal Strokes for N-link Micro-swimmer. 52nd IEEE Conference on Decision and Control, Dec 2013, Firenze, Italy. ⟨10.1109/CDC.2013.6760480⟩. ⟨hal-00798363v3⟩



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