# Learning to swim in potential flow

arXiv: https://arxiv.org/abs/2009.14280 · HTML: https://mlsanity.com/paper/2009.14280/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2020.

## Built on by (most cited first, 6 of 6)

- [Learning Efficient Navigation in Vortical Flow Fields](https://mlsanity.com/paper/2102.10536/) (2021)
- [Review of Metrics to Measure the Stability, Robustness and Resilience of Reinforcement Learning](https://mlsanity.com/paper/2203.12048/) (2022)
- [Training microrobots to swim by a large language model](https://mlsanity.com/paper/2402.00044/) (2024)
- [Navigation of a Three-Link Microswimmer via Deep Reinforcement Learning](https://mlsanity.com/paper/2506.00084/) (2025)
- [Stabilising viscous extensional flows using Reinforcement Learning](https://mlsanity.com/paper/2110.14677/) (2021)
- [Optimizing Metachronal Paddling with Reinforcement Learning at Low Reynolds Number](https://mlsanity.com/paper/2507.18849/) (2025)

## Abstract (arXiv)

Fish swim by undulating their bodies. These propulsive motions require coordinated shape changes of a body that interacts with its fluid environment, but the specific shape coordination that leads to robust turning and swimming motions remains unclear. To address the problem of underwater motion planning, we propose a simple model of a three-link fish swimming in a potential flow environment and we use model-free reinforcement learning for shape control. We arrive at optimal shape changes for two swimming tasks: swimming in a desired direction and swimming towards a known target. This fish model belongs to a class of problems in geometric mechanics, known as driftless dynamical systems, which allow us to analyze the swimming behavior in terms of geometric phases over the shape space of the fish. These geometric methods are less intuitive in the presence of drift. Here, we use the shape space analysis as a tool for assessing, visualizing, and interpreting the control policies obtained via reinforcement learning in the absence of drift. We then examine the robustness of these policies to drift-related perturbations. Although the fish has no direct control over the drift itself, it learns to take advantage of the presence of moderate drift to reach its target.