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

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 bounded, GUUB). The result is facilitated by fusing a filtered tracking error transformation with the dynamic oscillator design presented in Dixon et al. (1999). We also illustrate that the proposed tracking controller yields a GUUB result for the regulation problem. In addition, an extension is provided that illustrates that the proposed unified tracking/regulation controller can be applied to a twin rotor helicopter model