A two-stage ship path planning method is proposed, based on the Rapid-exploring Random Tree (RRT) algorithm, which is composed of global path planning and local path planning, addressing the important problem of finding an economical and safe path from start to destination for ships under dynamic environment, especially in waters with multiple obstacles and multiple target ships. The global path planning takes into consideration the ship draft and Under Keel Clearance to find navigable water using RRT, and reduces the path length and waypoints based on elliptic sampling and smoothing. In the local path planning, a dynamic collision risk detection model is constructed by introducing the Quaternion Ship Domain under a dynamic environment, and the restrictions of ship manoeuvrability and COLREGs are also involved. The simulation results show that the proposed model can find a satisfactory path within a few iterations, and keep clear of both static obstacles and dynamic ships. The research can be used to make and verify planned ship routes before sailing and to guide officers to make decisions regarding collision avoidance.

The icebreaker assistance is crucial to the safe navigation of low ice-class ships in ice-covered waters. Nevertheless, the major issues of the icebreaker assistance are the potential accidents due to the uncertain distance between ships. On one side, the close distance between ships could lead to a collision. On the other hand, the following ship may be stuck in the ice due to a large distance, as this distance may cause the broken ice channel to close again. To this end, we propose a new model of the ship navigation risk field for icebreaker convoy operations based on artificial potential field (APF) to describe interactions between ships as well as between ship and ice and to quantify the navigation risk for following ships in the fleet. The proposed model consists of two components: (i) the ship risk field, which describes the ship-ship collision risk; (ii) the sea ice risk field, which describes the ship stuck risk in ice. The risk indicators of ship-ship collision and ship stuck in ice channel for icebreaker convoy operations are established. Finally, a method for obtaining the safety following distance for the fleet is developed based on the proposed model. The proposed model is verified by a case study, has good agreement with safety distance model and empirical data, and its mean absolute percentage error (MAPE) with the minimum safe distance model is less than 1.3% overall and covers the actual maximum safe distance, which can be served as a theoretical guide for icebreaker assistance.