A practical and online trajectory planner for autonomous ships’ berthing, incorporating speed control

Abstract Autonomous ships are designed and equipped to perceive their internal and external environments and subsequently take appropriate actions based on predefined objective(s) without human intervention. Consequently, trajectory-planning algorithms for autonomous berthing must consider factors such as system dynamics, ship actuators, environmental disturbances, and operational safety. In this study, trajectory planning for an autonomous ship was modeled as an optimal control problem (OCP), which was transcribed into a nonlinear programming problem (NLP) using direct multiple shooting. To enhance berthing safety, wind disturbances, speed control guidelines, actuator limitations, and collision avoidance features were incorporated as constraints in the NLP, which was then solved using the sequential quadratic programming (SQP) algorithm in MATLAB. Finally, the performance of the proposed planner was evaluated through (i) comparison with an existing method, (ii) trajectory planning for different harbor entry and berth approach scenarios, and (iii) a feasibility study using predefined as well as stochastically generated initial conditions. The simulation results indicate improved berthing safety as well as practical and computational feasibility.