Enhanced controllability of low Reynolds number swimmers in the presence of a wall

TL;DR

This paper investigates how the presence of a wall influences the controllability of low Reynolds number swimmers, showing that controllable swimmers remain controllable near walls, while non-controllable ones are affected.

Contribution

It provides a mathematical proof that walls can enhance controllability of certain micro-swimmers, extending understanding of their motility in confined environments.

Findings

Controllable swimmers remain controllable near walls.

Non-controllable swimmers have restricted reachable sets near walls.

Wall presence affects swimmer motility depending on controllability status.

Abstract

Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers which is the regime of interest for micro-organisms and micro-robots. We focus on self-propelled stokesian robots composed of assemblies of balls and we prove that the presence of a wall has an effect on their motility. More precisely, we demonstrate that a controllable swimmer remains controllable in a half space whereas the reachable set of a non fully controllable one is affected by the presence of a wall.