Optimally swimming stokesian robots

François Alouges; Antonio DeSimone; Luca Heltai; Aline Lefebvre-Lepot; Benoît Merlet

doi:10.3934/dcdsb.2013.18.1189

Article Contents

2013, Volume 18, Issue 5: 1189-1215. Doi: 10.3934/dcdsb.2013.18.1189

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Optimally swimming stokesian robots

1.
CMAP UMR 7641, CNRS, École Polytechnique, Route de Saclay, 91128 Palaiseau Cedex
2.
SISSA, International School of Advanced Studies, Via Bonomea 265, 34136 Trieste

Received: October 31, 2011

Revised: September 30, 2012

Published: June 2013

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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, similar to what has been done in [4] for an axisymmetric system swimming along the axis of symmetry. We generalize the analyticity result given in [4] to the situation where the swimmers can 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.

Keywords:

Biological and artificial micro-swimmers,
optimal control,
propulsion efficiency,
movement and locomotion,
low-Reynolds-number (creeping) flow.

Mathematics Subject Classification: 76Z10, 74F10, 49J20, 93B05.

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