Dynamics-consistent motion planning for underactuated ships using virtual holonomic constraints

Increasing safety and efficiency of autonomous vessels also requires advanced navigation strategies. For the marine systems the task is even more complex than, e.g. for field robots, since hydrodynamic effects should be taken into account also. It is becoming even more challenging for underactuated vessels. Indeed, utilizing the virtual holonomic constraints approach we illustrate that regardless the control law implemented and for any desired geometrical path to follow, velocity profile of the underactuated ship has to satisfy additional constraints imposed as a second order differential equation of the system reduced dynamics. We consider a 4 DOF (surge, sway, roll, yaw) model for a single propeller-twin rudder surface vessel and derive conditions for planning a motion consistent with the system dynamics properties. Straight line and circular path are considered as special cases followed by the practical remarks. This analysis can used as a basis for further orbitally tracking controller design.