Control and Nonlinearity
Controllability and Time Optimal Control for Low Reynolds Numbers Swimmers
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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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. To rest on what has been done in Alouges et al. (Discrete Contin. Dyn. Syst., Ser. B 18(5):1189---1215, 2013) for such systems swimming on R3, we demonstrate that a controllable swimmer remains controllable in a half space whereas the reachable set of a non fully controllable one is increased by the presence of a wall.