On motion planning for an underactuated ship: Fundamental limitations and a bearings-only navigation strategy

The problem of guiding an underactuated ship to a particular position and heading is considered. A common approach to motion planning of robots and vehicles involves finding suitable trajectories for the positions of each configuration variable, and then using feedback to regulate the system to these trajectories. However, when the system has less actuators than dynamical degrees of freedom, it is not always possible to do this arbitrarily. In this paper it is shown that such an approach is not feasible for an underactuated ship when the desired path is an arc of circle. An alternative strategy is proposed in which a constraint on velocities is regulated, based on the circular navigation guidance principle previously developed for missile guidance and wheeled robot navigation.