Non-rigid formations of nonholonomic robots

The paper deals with a general class of leader-follower formations of unicycle robots induced by a constraint function that depends on the position and the orientation of the vehicles. We study the flexibility of such formations by introducing the notion of formation internal dynamics, characterize its equilibria and give sufficient geometric conditions for their existence. In particular, we show that the displacement and the relative orientation of each follower with respect to the leader´s reference frame are fixed if and only if the robots either move along circular paths or parallel straight lines. These equilibrium configurations always exist if the trajectory of the leader is a circle of sufficiently small curvature or a straight line.