Tracking and regulation control of an underactuated surface vessel with nonintegrable dynamics

Abstract—In this note, a continuous, time-varying tracking controller is designed that globally exponentially forces the position/orientation tracking error of an underactuated surface vessel to a neighborhood about zero that can be made arbitrarily small [i.e., global uniformly ultimately boundedness (GUUB)]. The result is facilitated by fusing a filtered tracking error transformation with the dynamic oscillator design presented in [6]. We also illustrate that the proposed tracking controller yields a GUUB result for the regulation problem. Index Terms—Lyapunov, nonlinear, surface vessels, tracking, underac-tuated. I