Optimal Control of Slender Microswimmers

摘要

In this chapter we study the /V-link swimmer, and use the Resistive Force Theory to derive its dynamics. In this context, we prove that for N greater than 3 and for almost any N-uplet of sticks lengths, the swimmer is globally controllable in the whole plane. Then, we focus on finding a swimming strategy that leads the /V-link swimmer from an fixed initial position to a given final position, in minimum time. As a consequence of the controllability result, we show that there exists a shape change function which allows to reach the final state in a minimal time. We formulate this optimal control problem and solve it with a direct approach (BOCOP) for the case N = 3 (Purcell swimmer). Without any assumption on the structure of the trajectory, we obtain a periodic solution, from which we identify an optimal stroke. Comparing this optimal stroke with the Purcell one confirms that it is better, actually giving a greater displacement speed.