Reinforcement learning of a multi-link swimmer at low Reynolds numbers

The use of machine learning techniques in the development of microscopic swimmers has drawn considerable attention in recent years. In particular, reinforcement learning has been shown useful in enabling swimmers to learn effective propulsion strategies through its interactions with the surroundings. In this work, we apply a reinforcement learning approach to identify swimming gaits of a multi-link model swimmer. The swimmer consists of multiple rigid links connected serially with hinges, which can rotate freely to change the relative angles between neighboring links. Purcell [ "Life at low Reynolds number, " Am. J. Phys. 45, 3 (1977)] demonstrated how the particular case of a three-link swimmer (now known as Purcell's swimmer) can perform a prescribed sequence of hinge rotation to generate self-propulsion in the absence of inertia. Here, without relying on any prior knowledge of low-Reynolds-number locomotion, we first demonstrate the use of reinforcement learning in identifying the classical swimming gaits of Purcell's swimmer for case of three links. We next examine the new swimming gaits acquired by the learning process as the number of links increases. We also consider the scenarios when only a single hinge is allowed to rotate at a time and when simultaneous rotation of multiple hinges is allowed. We contrast the difference in the locomotory gaits learned by the swimmers in these scenarios and discuss their propulsion performance. Taken together, our results demonstrate how a simple reinforcement learning technique can be applied to identify both classical and new swimming gaits at low Reynolds numbers.