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

TL;DR

This work tackles autonomous berthing by formulating a local trajectory planning problem for ships under MMG harbor dynamics as a minimum-time optimal control problem, transcribed to an NLP via direct multiple shooting and solved online with Sequential Quadratic Programming in MATLAB. It integrates speed-reduction guidelines, actuator-rate limits, and a ship-domain collision-avoidance constraint within a wind-disturbed environment, and validates the approach against CMA-ES on two model ships. Results show close agreement with CMA-ES trajectories but with substantially lower computation times and improved berthing safety due to speed control and actuation limits, supporting real-time applicability. The findings demonstrate robust performance across diverse harbor-entry scenarios and underline the method's potential for practical deployment in autonomous port operations, while identifying feasibility and computation-time challenges in stochastic, complex environments.

Abstract

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.

Figures (21)

• Figure 1: Model Ship A at Inukai Pond, Osaka University
• Figure 2: Coordinate systems
• Figure 3: Direct Multiple Shooting Technique
• Figure 4: This schematic image can be regarded as a summary of the speed reduction guidelines proposed by inouespeedreduction2002. It depicts two berthing scenarios: (1) The ship approaches the berth with reduced speed (blue path) and reaches the berth safely. Along this path, the braking force may be as low as Dead Slow Astern or as high as Full Astern. (2) The ship approaches the berth with high speed (red path), and even with Full Astern as the braking force, the ship cannot stop at the desired berthing point and consequently collides with the pier, jetty, or wall.
• Figure 5: Speed Reduction criterion proposed by inouespeedreduction2002