Navigation of micro-swimmers in steady flow: the importance of symmetries

TL;DR

This study investigates how micro-swimmers can optimally navigate complex flow environments using reinforcement learning, emphasizing the role of symmetries and local cues in their strategies for vertical migration.

Contribution

It introduces a framework for analyzing micro-swimmer navigation based on local flow cues and demonstrates the necessity of symmetry-breaking for effective vertical movement.

Findings

Symmetry-breaking is essential for meaningful vertical migration strategies.

Local flow measurements suffice for navigation without global information.

Reinforcement learning reveals diverse strategies based on environmental cues.

Abstract

Marine microorganisms must cope with complex flow patterns and even turbulence as they navigate the ocean. To survive they must avoid predation and find efficient energy sources. A major difficulty in analysing possible survival strategies is that the time series of environmental cues in non-linear flow is complex, and that it depends on the decisions taken by the organism. One way of determining and evaluating optimal strategies is reinforcement learning. In a proof-of-principle study, Colabrese et al. [Phys. Rev. Lett. (2017)] used this method to find out how a micro-swimmer in a vortex flow can navigate towards the surface as quickly as possible, given a fixed swimming speed. The swimmer measured its instantaneous swimming direction and the local flow vorticity in the laboratory frame, and reacted to these cues by swimming either left, right, up, or down. However, usually a motile microorganism measures the local flow rather than global information, and it can only react in relation to the local flow, because in general it cannot access global information (such as up or down in the laboratory frame). Here we analyse optimal strategies with local signals and actions that do not refer to the laboratory frame. We demonstrate that symmetry-breaking is required in order to learn vertical migration in a meaningful way. Using reinforcement learning we analyse the emerging strategies for different sets of environmental cues that microorganisms are known to measure.