Path Following for Underactuated Marine Vessels

This paper investigates the problem of making an under actuated marine vessel follow an arbitrary differentiable Jordan curve. A solution is proposed which relies on a hierarchical control methodology involving the simultaneous stabilization of two nested sets, and results in a smooth, static, and time-invariant feedback. The methodology in question effectively reduces the control problem to one of path following for a kinematic point-mass. It is shown that as long as the curvature of the path is smaller than a quantity dependent on the mass and damping parameters of the ship, path following is achieved with uniformly bounded sway speed.