Position tracking of underactuated vehicles

This paper addresses the problem of position tracking for underactuated autonomous vehicles moving in either two or three-dimensional space. A nonlinear tracking controller is proposed for a general class of vehicles that yields global stability and exponential convergence of the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be of a particular type (e.g., trimming trajectories) and in fact can be any sufficiently smooth bounded curve parameterized by time. The control algorithm proposed builds upon Lyapunov techniques. To illustrate its potential, we describe two vehicle control applications: an hovercraft (moving on a planar surface) and an underwater vehicle (moving in three-dimensional space). Simulation results are presented and discussed.