Optimal control of slender microswimmers

Abstract

We discuss a reduced model to compute the motion of slender swimmers which propel themselves by changing the curvature of their body. Our approach is based on the use of Resistive Force Theory for the evaluation of the viscous forces and torques exerted by the surrounding fluid, and on discretizing the kinematics of the swimmer by representing its body through an articulated chain of N rigid links capable of planar deformations. The resulting system of ODEs, governing the motion of the swimmer, is easy to assemble and to solve, making our reduced model a valuable tool in the design and optimization of bio-inspired artificial microdevices. 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.