Cascades-Based Leader–Follower Formation Tracking and Stabilization of Multiple Nonholonomic Vehicles

It is known that nonholonomic systems on the plane cannot be stabilized on arbitrary leader's trajectories with piecewise continuous velocities via continuous controllers, even time-varying. In this article, we identify a wide class of smooth bounded reference trajectories (that includes set-points), and we propose a smooth time-varying controller that stabilizes such trajectories, not only for one nonholonomic mobile robot, but also for a network of mobile robots in a leader-follower configuration. We provide new constructions of strict Lyapunov functions with which we establish uniform global asymptotic stability and other strong robustness properties in the formation-error-coordinates space. Thus, our stability statements are unique in the literature and our tools of analysis are original.