Enhanced controllability of low Reynolds number swimmers in the presence of a wall

François Alouges (1) , Laetitia Giraldi (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Mots clés: low Reynolds motion; control theory; Lie brackets.; Lie brackets

Domaines: Optimisation et contrôle [math.OC]

François Alouges, Laetitia Giraldi. Enhanced controllability of low Reynolds number swimmers in the presence of a wall. 2012. ⟨hal-00735919⟩