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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.
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Generalization of waving‐plate theory to multiple interacting swimmers
Abstract Early research in aerodynamics and biological propulsion was dramatically advanced by the analytical solutions of Theodorsen, von Kármán, Wu and others. While these classical solutions apply only to isolated swimmers, the flow interactions between multiple swimmers are relevant to many practical applications, including the schooling and flocking of animal collectives. In this work, we derive a class of solutions that describe the hydrodynamic interactions between an arbitrary number of swimmers in a two‐dimensional inviscid fluid. Our approach is rooted in multiply‐connected complex analysis and exploits several recent results. Specifically, the transcendental (Schottky–Klein) prime function serves as the basic building block to construct the appropriate conformal maps and leading‐edge‐suction functions, which allows us to solve the modified Schwarz problem that arises. As such, our solutions generalize classical thin aerofoil theory, specifically Wu's waving‐plate analysis, to the case of multiple swimmers. For the case of a pair of interacting swimmers, we develop an efficient numerical implementation that allows rapid computations of the forces on each swimmer. We investigate flow‐mediated equilibria and find excellent agreement between our new solutions and previously reported experimental results. Our solutions recover and unify disparate results in the literature, thereby opening the door for future studies into the interactions between multiple swimmers.
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- Award ID(s):
- 2108839
- PAR ID:
- 10442131
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Communications on Pure and Applied Mathematics
- ISSN:
- 0010-3640
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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