We present a theoretical study of the coordination of the geometrical movements of one flotilla of autonomous underwater vehicles. We make the assumption that the flotilla must move by respecting geometrical constraints of forming which we indicate by the term of geometrical constellation. Under this hypothesis, every vehicle has to follow a trajectory so that the whole flotilla forms a desired geometrical figure. We make depend this geometrical constellation of the state vector of each vehicle. All the time, if this constellation is not realized, it is then possible to compute the deformation between the real constellation of the flotilla and a desired constellation. From this deformation, we compute the movement that every vehicle should make to obtain a regulation around zero of the deformation. The control of the flotilla should be compatible with the possibility for every vehicle, to realize obstacle avoidance We use an approach called the "deformable virtual zones", and show that all these constraints can be resolved in a homogeneous way and supply a command vector for each vehicle.