Nonlinear tracking of underactuated surface vessels

In this paper a control law for tracking of underactuated surface vessels is presented. Optimal trajectories for surface vessels are given as combinations of arcs of circles and line segments. It is shown how optimal trajectories can be made smooth by a technique called splines, and how these trajectories can be stabilized by backstepping. The control law depends on that the forward velocity of the surface vessel always is positive, which is not a major limitation for tracking purposes. It is also shown how this work can be parts of a hierarchical hybrid system for control of surface vessels.