Robust smooth control for global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters

This paper investigates how to design controllers to stabilize the underactuated surface vessel to desired constant location and orientation with vanishing velocities. The first control law is designed as a smooth function of position and orientation errors without using model parameters, where a gain is made time-varying to get over the nonholonomic constraint on model. Skew-symmetric and damping terms in model are exploited to help construct two particular Lyapunov functions, and Barbalat's lemma are combined to verify the global uniform asymptotic convergence of errors and velocities. Then, the second and the third control laws are devised as the forms of the first controller plus velocity feedbacks and can achieve the same stability as the first one but have a weaker gain condition. All the three controllers are robust to model parameters due to their absence in controllers and only require three model parameters' upper/lower bounds, decreasing the identification workload greatly. Moreover, they are the first smooth ones capable of achieving global uniform asymptotic full-state stabilization control of vessel with unknown model parameters. Effectiveness of the proposed controllers is demonstrated by numerical simulations.