Path planning for ships assisted by the icebreaker in ice-covered waters in the Northern Sea Route based on optimal control

This paper aims to develop an innovative model based on optimal control to optimize the shipping path of the fleet, including icebreakers and following ships in continuous time and space in the Northern Sea Route (NSR) waters, considering the influence of breakable and unbreakable ice. Path planning assumptions of ship navi-gation in ice-covered waters are summarized by considering navigation efficiency, navigation cost, icebreaking cost, and safety. The objective function of the model based on optimal control is formulated to convert the path planning problem into a multi-objective optimization problem. The cost functions based on path planning as-sumptions are specified in the objective function. Finally, dynamic programming and numerical simulation are used to solve the multi-objective optimization functions. Then, the optimal path in continuous time and space in ice-covered waters in the NSR is obtained. A case study of four scenarios, considering breakable and unbreakable sea ice conditions in the NSR, is conducted to verify the strength of the proposed model. The case study results show that the proposed model can optimize the path of ships in ice-covered waters. The method proposed in this research could guide ship fleet path planning for the bridge team and improve icebreaker management in the NSR.