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The three-sphere swimmer by Najafi and Golestanian is composed of threespheres connected by two arms. The case in which the swimmer can control thelengths of the two arms has been studied in detail. Here we study a variationof the model in which the swimmer's arms are constructed according to Hill'smodel of muscular contraction. The swimmer is able to control the tensiondeveloped in the active components of the arms. The two shape parameters andthe tensions acting on the two arms are then obtained by solving a system ofordinary differential equations. We study the qualitative properties of thesolutions, compute analytically their leading order approximation and comparethem with numerical simulations. We also formulate and solve some optimisationproblems, aimed at finding the actuation strategies maximising performance, forvarious performance measures. Finally, we discuss the structure of thegoverning equations of our microswimmers from the point of view of controltheory. We show that our systems are control affine systems with drift.

Dynamics and optimal actuation of a three-sphere low-Reynolds-number swimmer with muscle-like arms