Adaptive tracking control of underactuated surface vessels

We design a continuous, time-varying tracking controller for an underactuated surface vessel in the presence of uncertainty associated with the hydrodynamic damping coefficients. A Lyapunov-based approach is used to ensure that the position/orientation tracking error is ultimately confined to a ball that can be made arbitrarily small. The result is achieved via the judicious design of a dynamic oscillator in conjunction with two state transformations. We also illustrate how the proposed tracking controller yields the same stability result for the stabilization problem