# Optimizing metachronal paddling with reinforcement learning at low Reynolds number

## TL;DR

This paper uses reinforcement learning to study how organisms might optimize their swimming motion using metachronal paddling at low Reynolds numbers.

## Contribution

The novel contribution is applying reinforcement learning to discover optimal limb coordination patterns in a zero Reynolds number swimmer model.

## Key findings

- At tight paddle spacings, a back-to-front metachronal wave-like stroke emerges, resembling biological rhythms.
- At wide spacings, different limb coordination patterns are selected by the reinforcement learning algorithm.
- The most efficient stroke is consistently a back-to-front wave-like stroke, regardless of paddle count.

## Abstract

Metachronal paddling is a swimming strategy in which an organism oscillates sets of adjacent limbs with a constant phase lag, propagating a metachronal wave through its limbs and propelling it forward. This limb coordination strategy is utilized by swimmers across a wide range of Reynolds numbers, which suggests that this metachronal rhythm was selected for its optimality of swimming performance. In this study, we apply reinforcement learning to a swimmer at zero Reynolds number and investigate whether the learning algorithm selects this metachronal rhythm, or if other coordination patterns emerge. We design the swimmer agent with an elongated body and pairs of straight, inflexible paddles placed along the body for various fixed paddle spacings. Based on paddle spacing, the swimmer agent learns qualitatively different coordination patterns. At tight spacings, a back-to-front metachronal wave-like stroke emerges which resembles the commonly observed biological rhythm, but at wide spacings, different limb coordinations are selected. Across all resulting strokes, the fastest stroke is dependent on the number of paddles; however, the most efficient stroke is a back-to-front wave-like stroke regardless of the number of paddles.

The online version contains supplementary material available at 10.1140/epje/s10189-025-00511-5.