Enhanced Controllability of Low Reynolds Number Swimmers in the Presence of a Wall

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 R ³, 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.