On the control of the underactuated ship: a trajectory planning approach

A trajectory planning approach is proposed for controlled path tracking maneuvers in an underactuated ship model. The trajectories of the position coordinates are planned in an off-line manner exploiting the partial differential flatness of the non-linear model and its Liouvillian character. The nominal state and control inputs trajectories are then used, in the traditional manner, to obtain an incremental feedback control law, computed on the basis of the controllable, time-varying, Jacobian linearization model