Purcell magneto-elastic swimmer controlled by an external magnetic field

TL;DR

This paper investigates how a magnetized Purcell swimmer can be controlled using an external oscillating magnetic field, analyzing its propulsion mechanism and controllability limitations through asymptotic analysis.

Contribution

It introduces a control strategy for magnetized Purcell swimmers using oscillating magnetic fields and discusses controllability challenges.

Findings

Swimmer can be steered along a desired direction with prescribed oscillating fields.

Asymptotic analysis proves controllability under certain conditions.

Identifies main obstructions to classical controllability.

Abstract

This paper focuses on the mechanism of propulsion of a Purcell swimmer whose segments are magnetized and react to an external magnetic field applied into the fluid. By an asymptotic analysis, we prove that it is possible to steer the swimmer along a chosen direction when the control functions are prescribed as an oscillating field. Moreover, we discuss what are the main obstructions to overcome in order to get classical controllability result for this system.