We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploitsthe action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, withStokes equations governing the surrounding fluid.The action of thecilia 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 systemis 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 whichthe organism has a spherical shape. Finally, we offer a complete picture of controllable and non-controllable systems under the additional hypothesis thatthe organism and the fluid have densities of the same order of magnitude.
