Logic-based switching control for trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty

We address the problem of trajectory-tracking and path-following control design for underactuated autonomous vehicles in the presence of possibly large modeling parametric uncertainty. For a general class of vehicles moving in either two or three-dimensional space, we demonstrate how adaptive switching supervisory control can be combined with a nonlinear Lyapunov-based tracking control law to solve the problem of global boundedness and convergence of the position tracking error to a neighborhood of the origin that can be made arbitrarily small. We also show how these results can be extended to the path-following problem, in which the vehicle is required to converge to and follow a path, without a special temporal specification, and once in the path, to satisfy a desired dynamic behavior. We illustrate our design procedures through two vehicle control applications: a hovercraft (moving on a planar surface) and an underwater vehicle (moving in three-dimensional space). Simulations results are presented and discussed.