Optimal control of slender microswimmers

International audienceWe discuss a reduced model to compute the motion of slender swimmerswhich propel themselves by changing the curvature of their body. Our approach isbased on the use of Resistive Force Theory for the evaluation of the viscous forcesand torques exerted by the surrounding fluid, and on discretizing the kinematicsof the swimmer by representing its body through an articulated chain of N rigidlinks capable of planar deformations. The resulting system of ODEs governing themotion of the swimmer is easy to assemble and to solve, making our reduced modela 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 is greater of equal to 3 and foralmost every set of stick lengths. As a direct result, there exists an optimal swimmingstrategy to reach a desired configuration in minimum time. Numerical experimentsfor N = 3 (Purcell swimmer) suggest that the optimal strategy is periodic, namely asequence of identical strokes. Our results indicate that this candidate for an optimalstroke indeed gives a better displacement speed than the classical Purcell stroke