Time-optimal path planning and tracking based on nonlinear model predictive control and its application on automatic berthing

Ming Zhang, Shuang-Rui Yu, Kwang Sic Chung, Ming-Lu Chen, Zhi-Ming Yuan

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Autonomous shipping has been identified as the way forward in maritime transport. There are numerous technologies being developed over the past decades for maritime autonomous surface ships, including advanced automatic manoeuvring control. As one of the essential indices to evaluate ships’ manoeuvrability, the time-optimal problem remains a challenging issue in the process of path planning and path tracking, which has not been properly addressed for the maritime autonomous surface ships. To fill this knowledge gap, we propose a novel time-optimal path planning and tracking control method based on nonlinear model predictive control (MPC) and spatial reformulation. The proposed time-optimal controller is designed as a two-level hierarchical controller to plan the time-optimal path in spatial coordinates and track it in temporal coordinates when considering the low-speed manoeuvring model. At the high level, the nonlinear MPC based on a spatial formulation is used to generate a planned path of minimum manoeuvring time for a manoeuvring ship. At the low level, the optimal planning trajectory is interpolated by a constant time iteration and the vessel tracks the time-optimal planning trajectory by implementing the nonlinear MPC based on a temporal formulation. As an advanced predictive controller, the nonlinear MPC optimises the berthing path to a minimum time mathematically at the planning stage and compensates for the uncertain disturbance during the tracking process. To validate the time-optimal control method, a typical scenario of low-speed berthing operation is analysed. The results of the case study show that the proposed control method can be successfully applied to time-optimal manoeuvring problems.
Original languageEnglish
Article number115228
Number of pages16
JournalOcean Engineering
Issue numberPt. 1
Early online date16 Aug 2023
Publication statusPublished - 15 Oct 2023


  • low-speed manoeuvre
  • model predictive control
  • trajectory optimisation
  • time-optimal control


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