Non-Locally Controllable but Trackable Magnetic Head Flagellated Swimmer

TL;DR

This paper studies the controllability of a magnetic microswimmer with a spherical head and elastic tail, showing it is not fully controllable but can still track trajectories using optimization techniques.

Contribution

It demonstrates the non-controllability of the swimmer under planar motion and proposes a Bayesian optimization approach for trajectory tracking.

Findings

System is not small-time locally controllable in planar motion.

Trajectory tracking is achievable through Bayesian optimization.

Large-amplitude deformations are necessary for effective control.

Abstract

Unlike macroscopic swimmers, microswimmers operate in a low-Reynolds-number regime dominated by viscous forces. This paper investigates the controllability of a magnetic microswimmer composed of a spherical magnetic head and an elastic, non-magnetic flagellum. The swimmer evolves in a Stokes flow and is modeled using the resistive force theory. We prove that, under planar motion, the system is not small-time locally controllable and numerically identify regions that remain inaccessible. Nevertheless, simulations show that trajectory tracking can still be achieved via Bayesian optimization, though it requires large-amplitude transverse deformations.