Marching control based on the leader-followers scheme and formation graphs

This paper analyzes the case of marching control, where a leader robot follows a desired trajectory, while the whole group reaches a formation pattern established by a formation graph. To guarantee that the group preserves the desired formation and follows the marching path simultaneously, two approaches are given, based on the feedback of the velocity of the desired trajectory or the velocity of some robots. The main result establishes that for both approaches and any well-defined formation graph, there is convergence to the formation and the marching path. The analysis addresses the cases of omnidirectional robots and the extension to unicycle-type robots. The performance of the control strategies is shown some numerical simulations and real-time experiments.