Wind Affected Maneuverability of Tugboat-Controlled Ships

The development of maritime transportation, in terms of the size and traffic volume of container ships, is increasingly posing technical challenges especially in crowded harbors and narrow canals. To ensure safe and efficient operation, tugboats are used for assisting large ships in such critical areas under the supervision of the responsible pilots. However, the mis-assessment of risk, especially under bad weather conditions, can lead to accidents, economic losses, and even casualties. Accordingly, the need for automated assistant systems is strong. In this paper, we investigate the maneuverability of tugboat-controlled ships under the influence of wind. We provide a characterization of the admissible set of safe wind situations for the execution of a given maneuver in terms of a constrained system of differential equations. Under some restrictions over the type of maneuvers, we prove the star-convexity of the admissible set. For this purpose, the dynamical model of the ship motion is derived, which takes tugboat and wind forces into account. The star-convexity of the sought-after set and the ship model allow for an efficient approximation of this set by optimal control methods. As an application, we propose a visual aid that allows the tugboat pilots to clearly distinguish between safe and hazardous wind situations during maneuver planning.