Retraction balancing and formation control

We consider a formation control problem in which a collection of systems is ought to attain a balanced configuration on a submanifold of their state space. The submanifold thus determines the shape and position of the desired formation. We solve the formation control problem by simultaneously balancing the retractions of the systems onto the submanifold and asymptotically stabilizing the submanifold. In doing so, we arrive at a distributed control law.