Universal practical tracking control of a planar underactuated vehicle

In this article, a universal controller is proposed for a planar underactuated vehicle to track arbitrary trajectories including feasible/non-feasible ones and fixed points. The controller design relies on several coordinate/input transformations, auxiliary trajectory design and the back-stepping technique. The stability analysis shows that the position and orientation tracking errors are uniformly globally practically asymptotically convergent (UGPAC), and the velocity tracking errors are uniformly globally asymptotically convergent (UGAC) to a ball of origin. Moreover, if the tracked target is in uniform rectilinear motion or motionless, the whole closed-loop tracking error system is uniformly globally practically asymptotically stable (UGPAS). The effectiveness of proposed control law is verified by simulation examples.