  We consider a finite-dimensional model for the motion of microscopic
organisms whose propulsion exploits the action of a layer of cilia covering its
surface. The model couples Newton's laws driving the organism, considered as a
rigid body, with Stokes equations governing the surrounding fluid. The action
of the cilia is described by a set of controlled velocity fields on the surface
of the organism. The first contribution of the paper is the proof that such a
system is generically controllable when the space of controlled velocity fields
is at least three-dimensional. We also provide a complete characterization of
controllable systems in the case in which the organism has a spherical shape.
Finally, we offer a complete picture of controllable and non-controllable
systems under the additional hypothesis that the organism and the fluid have
densities of the same order of magnitude.
