Controllability and optimal strokes for N-link microswimmer

In this paper we focus on the N-link swimmer [1], a generalization of the classical 3-link Purcell swimmer [18]. We use the Resistive Force Theory to express the equation of motion in a fluid with a low Reynolds number, see for instance [12]. We prove that the swimmer is controllable in the whole plane for N ≥ 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.