Controllability of a bent 3-link magnetic microswimmer

TL;DR

This paper studies the controllability of a bent 3-link magnetic microswimmer with torsional springs, demonstrating local controllability and proposing a method to steer the swimmer along desired paths using external magnetic fields.

Contribution

It introduces a controllability analysis and a constructive control method for a bent 3-link magnetic microswimmer with torsional springs, advancing microswimmer navigation techniques.

Findings

Local partial controllability around equilibrium states.

Constructive method to determine magnetic fields for prescribed trajectories.

Numerical simulations confirming effective path following.

Abstract

- In this paper, we focus on a variant of a 3-link magnetic microswimmer which consists of three rigid magnetized segments connected by two torsional springs. In particular, we assume that one of the springs is twisted so that the swimmer is not aligned at rest. By acting on it with an external magnetic field, the swimmer twists and moves through the surrounding fluid. By considering the external magnetic field as a control function, we state a local partial controllability result around the equilibrium states. Then, we propose a constructive method to find the magnetic field that allows the swimmer to move along a prescribed trajectory. Finally, we show numerical simulations in which the swimmer moves along a prescribed path.