Optimal Control of Microswimmers for Trajectory Tracking Using Bayesian Optimization

TL;DR

This paper introduces a Bayesian optimization-based method for optimal control of microswimmers, enabling effective trajectory tracking across various models and complex fluid interactions without requiring gradient computations.

Contribution

It presents a novel approach combining B-spline parametrization with Bayesian optimization for microswimmer control, handling high computational costs and model variability.

Findings

Successfully tracks complex trajectories in experiments

Adapts to wall-induced hydrodynamic effects

Works across different model fidelities

Abstract

Trajectory tracking for microswimmers remains a key challenge in microrobotics, where low-Reynolds-number dynamics make control design particularly complex. In this work, we formulate the trajectory tracking problem as an optimal control problem and solve it using a combination of B-spline parametrization with Bayesian optimization, allowing the treatment of high computational costs without requiring complex gradient computations. Applied to a flagellated magnetic swimmer, the proposed method reproduces a variety of target trajectories, including biologically inspired paths observed in experimental studies. We further evaluate the approach on a three-sphere swimmer model, demonstrating that it can adapt to and partially compensate for wall-induced hydrodynamic effects. The proposed optimization strategy can be applied consistently across models of different fidelity, from low-dimensional ODE-based models to high-fidelity PDE-based simulations, showing its robustness and generality. These results highlight the potential of Bayesian optimization as a versatile tool for optimal control strategies in microscale locomotion under complex fluid-structure interactions.