Adaptive shape control for microswimmer navigation in turbulence

TL;DR

A shape-changing spheroidal microswimmer tasked with maximising its displacement from an initial position in two-dimensional stochastic and turbulent flows is investigated and adaptive morphology provides a robust and physically interpretable control paradigm for microswimmer navigation in complex flows.

Abstract

Navigation in turbulent environments is a fundamental challenge for biological and artificial microswimmers. While most existing studies focus on adapting motility or steering, the role of active morphological changes in navigation remains poorly explored. Here, we investigate a shape-changing spheroidal microswimmer tasked with maximising its displacement from an initial position in two-dimensional stochastic and turbulent flows. Using reinforcement learning (RL), the microswimmer learns to adapt its aspect ratio based on its orientation and local velocity-gradient signals. The learned strategies outperform fixed-shape and short-time-optimal baselines across different flow regimes and remain effective when transferred from stochastic flows to fully resolved turbulence. Guided by the learned policies, we propose a minimal analytical model that captures the essential navigation mechanisms and reproduces the performance across flow regimes. These results show that adaptive morphology provides a robust and physically interpretable control paradigm for microswimmer navigation in complex flows.

Figures (10)

• Figure 1: (a) Microswimmer navigation maximizing distance from the initial position $\boldsymbol{x}(t_0)$ (red star). Equidistant black dashed circles denote radial distances. Two example trajectories of microswimmers following Eq. (\ref{['eq:eom']}) with constant shape factor, evolving in a frozen realization of the stochastic model (magenta: $\Lambda=-0.98$; black: $\Lambda=0.98$). (b) Schematic of a spheroidal microswimmer and its reference frame. (c,d) Microswimmers can adjust their aspect ratio, becoming (c) prolate, $\Lambda>0$, or (d) oblate, $\Lambda<0$.
• Figure 2: Comparison across flow regimes of reinforcement-learned smart strategy (orange), naive strategy [$\Lambda=0.98$] (black), and the STO strategy [Eq. (\ref{['eq:sto']})] (green). (a) Normalised performance index $\hat{R}$ [Eq. \ref{['eq:reward2']}] against Kubo number ${\rm Ku}$. Error bars show the standard deviation of $\hat{R}$ over 100 flow realizations with $10^3$ trajectories each. (b) to (e): Final positions of $10^3$ microswimmers starting from the origin (red star) for (b) ${\rm Ku}=0.1$, (c) ${\rm Ku}=1$, (d) ${\rm Ku}=10$, (e) ${\rm Ku}=10^7$.
• Figure 3: (a) Trajectories of microswimmers using different strategies at ${\rm Ku}=0.1$: smart (orange), naive [$\Lambda=0.98$] (black), and STO [Eq. (\ref{['eq:sto']})] (green). (b) Scatter plot of $\Lambda$ against $n_{\theta} S_{np}$ for the smart and STO strategies. Inset: $\Lambda$ against $n_\theta$ and $S_{np}$ for the smart strategy, based on $10^3$ trajectories.
• Figure 4: Shape factor $\Lambda$ (color) for the smart strategy at ${\rm Ku}=10^7$ as a function of (a) $n_r$, $S_{np}$ and $\omega$; (b) $S_{np}$ and $\omega$ conditioned on $n_r\ge 0.8$; (c) $S_{np}$ and $\omega$ with $n_r\le -0.8$. Data is based on $4\times10^4$ trajectories.
• Figure 5: Shape factor $\Lambda$ (color) for the smart strategy as a function of $S_{np}$ and $n_\theta$ (top row), and $S_{np}$ and $\Omega$ (bottom row). (a, e) ${\rm Ku}=0.1$. (b, f) ${\rm Ku}=1$. (c, g) ${\rm Ku}=10$. (d, h) ${\rm Ku}=10^7$. The data are based on $10^3$ trajectories.