A δ-Persistently-Exciting Formation Controller for Non-Holonomic Systems Over Directed Graphs

We study a formation control problem of nonholonomic vehicles which consists in making a group of them gather around a given rendezvous set-point and acquire a common orientation. This task may be regarded as part of a more complex maneuver, e.g., requiring the robots to advance in a scouting mission on a path composed of straight lines and occasional turns. The control approach relies on addressing separately the problems of stabilization (on the plane) and of orientation consensus. For the former we use individual controllers involving smooth time-varying terms and for the latter we use distributed consensus control, under the assumption that the robots form a directed graph that contains a spanning tree.