Preservation of Formation Tracking under Incomplete Information and Chaotic Path-following*

This paper presents a formation tracking strategy based on local potential functions and the leader-followers scheme for a group of point robots moving in the space. A leader robot is chosen to follow a prescribed trajectory whilst the rest, considered as followers, are formed in an open chain configuration. The formation convergence and the path following, including chaotic trajectories, are guaranteed if every follower robot measures exactly the velocity of the next robot and the leader knows the velocity of the marching path. Then, we analyze the preservation of the formation using approximations of the velocities of robots and the chaotic path. These restrictions appear in real implementations in robots equipped by position sensors only and where the velocities functions are approximated by online numerical methods.