Minimization of cross-track and along-track errors for path tracking of marine underactuated vehicles

This paper deals with developing a guidance scheme for minimizing the position error of a marine underactuated vehicle during a path-tracking scenario. The desired position is determined by a virtual vehicle, which is assumed to navigate on the desired path, and the position error is analyzed in two components: a) the along-track error, and b) the cross-track error. Initially, perfect heading tracking is assumed and the well-known Line-of-Sight (LOS) guidance is used to minimize the cross-track error. Moreover, by using the vehicle kinematics and assuming perfect velocity tracking, a surge velocity guidance law for minimizing the along-track error is proposed. Then, the perfect velocity and heading tracking assumptions are relaxed and the stability of the total system, including the heading and velocity controllers, is studied and the system is shown to be globally κ-exponentially stable. The results are supported by computer simulations.