In this paper we present a leader-follower control law that enables a mobile robot to track a desired trajectory, and allows us to specify the position in the plane of the follower robot with respect to the leader robot. We first describe the dynamic model of the plant, including input torques, and friction forces. Then the control law is developed using backstepping, and it is proved to asymptotically stabilize the tracking error to the origin. Simulation and experimental results of the closed loop system are presented, highlighting its potential application to formation control. The special case of pure tracking (without bi-dimensional position information use) is analyzed, showing that it can be applied to particular classes of non-feasible trajectories. Finally, motivated by some observations on the experiments, the effects of odometry errors are analyzed, revealing that boundedness of the tracking errors can be guaranteed if absolute position information becomes available periodically.
Piovesan, Jorge; Chaouki Abdallah; and Herbert Tanner. "Leader-Follower Control with Odometry Error Analysis." (2007). https://digitalrepository.unm.edu/ece_rpts/19