Optimally swimming Stokesian robots

Details Optimally swimming Stokesian robots Optimally swimming Stokesian robots

2010-07-28

arxiv.org/abs/1007.4920v2

Mathematics

Optimization and Control

32 pages, 9 figures

Scientific paper

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.

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