Gait controllability of length-changing slender microswimmers

TL;DR

This paper investigates the controllability of four models of length-changing microswimmers using geometric control theory, demonstrating total controllability through gait controllability with numerical simulations.

Contribution

It introduces a framework for analyzing controllability of length-changing microswimmers and provides sufficient conditions for gait and total controllability in four different models.

Findings

Total controllability is achieved via gait controllability in all models.

Different mechanisms for length change are analyzed within the framework.

Numerical simulations support the theoretical results.

Abstract

Controllability results of four models of two-link microscale swimmers that are able to change the length of their links are obtained. The problems are formulated in the framework of Geometric Control Theory, within which the notions of fiber, total, and gait controllability are presented, together with sufficient conditions for the latter two. The dynamics of a general two-link swimmer is described by resorting to Resistive Force Theory and different mechanisms to produce a length-change in the links, namely, active deformation, a sliding hinge, growth at the tip, and telescopic links. Total controllability is proved via gait controllability in all four cases, and illustrated with the aid of numerical simulations.