Applied trajectory generation to dock a feeder vessel

Autonomous sailing is seen as one of the possible solutions to cope with the decrease in qualified officers, to minimise the risk to humans and ships at challenging conditions, and to decrease the environmental impact of the transport sector. Autonomous sailing is not limited to moving the vessel safely through the seas, but it also includes docking the vessel. Docking is considered a difficult and critical manoeuvre in autonomous sailing.
The objective of this work is to construct a trajectory including its time derivatives for our newly designed 71m long underactuated feeder vessel to approach a dock. The trajectory can be used by a feedback controller to steer the vessel to the dock, and the time derivatives can be used to construct a feed forward signal to improve the tracking performance.
An optimal control problem is formulated to answer i) what the best pose is to start an approach to the dock, and ii) what trajectory is optimal from an arbitrary initial pose. The resulting trajectory gives an optimal minimal-time solution, but the computational time was too large to employ real-time. A second trajectory was constructed based on Bézier curves. The computational load of this trajectory is negligible. The trajectory can be used for a subset of initial states. It does provide a smooth trajectory with all the derivatives, and is seen as a good option when the vessel starts the docking manoeuvre from a not too challenging pose.