  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. More
precisely, we demonstrate that a controllable swimmer remains controllable in a
half space whereas the reachable set of a non fully controllable one is
affected by the presence of a wall.

Optimization and Control