A Practical and Online Trajectory Planner for Autonomous Ships' Berthing, Incorporating Speed Control

Autonomous ships are essentially designed and equipped to perceive their internal and external environment and subsequently perform appropriate actions depending on the predetermined objective(s) without human intervention. Consequently, trajectory planning algorithms for autonomous berthing must consider factors such as system dynamics, ship actuators, environmental disturbances, and the safety of the ship, other ships, and port structures, among others. In this study, basing the ship dynamics on the low-speed MMG model, trajectory planning for an autonomous ship is modeled as an optimal control problem (OCP) that is transcribed into a nonlinear programming problem (NLP) using the direct multiple shooting technique. To enhance berthing safety, besides considering wind disturbances, speed control, actuators' limitations, and collision avoidance features are incorporated as constraints in the NLP, which is then solved using the Sequential Quadratic Programming (SQP) algorithm in MATLAB. Finally, the performance of the proposed planner is evaluated through (i) comparison with solutions obtained using CMA-ES for two different model ships, (ii) trajectory planning for different harbor entry and berth approach scenarios, and (iii) feasibility study using stochastically generated initial conditions and positions within the port boundaries. Simulation results indicate enhanced berthing safety as well as practical and computational feasibility making the planner suitable for real-time applications.