Optimally swimming Stokesian robots

TL;DR

This paper proves controllability of self-propelled Stokesian robots made of ball assemblies in 2D and 3D, simplifies existing analyticity proofs, and computes their energetically optimal swimming strokes.

Contribution

It introduces a simplified analyticity framework for controlling complex Stokesian swimmers and numerically determines their optimal swimming strokes.

Findings

Robots can control position and orientation in 2D and 3D.

Simplified proof of controllability using Chow's theorem.

Numerical computation of optimal swimming strokes.

Abstract

We study self propelled stokesian robots composed of assemblies of balls, in dimensions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow's theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically the analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.