Energy–Time Co-Optimization for Autonomous Ship Berthing in Complex Ocean Currents Using an Improved hp-Pseudospectral Optimal Method

Berthing path planning for ships in the presence of ocean currents is a challenging task. Several relevant methods have been proposed, but they all assume a constant surge velocity for the whole path. This hypothesis makes it impossible to achieve the simultaneous optimization of speed and energy consumption. To deal with this issue, in this paper an optimal control path planning method that considers the characteristics of currents is proposed. Unlike traditional algorithms such as the A* algorithm and genetic algorithm, the proposed improved hp-pseudospectral (IHP) method does not require a constant thrust assumption. In addition, it can obtain the Pareto optimal path under various current environments and optimize the sailing parameters. Specifically, first a multi-objective optimal control path planning model considering the kinematic characteristics of autonomous ships is established. Second, the IHP method is proposed to solve it, which includes dividing the time interval, subdomain collocation, and transformation optimization. Last, the optimality and high efficiency of the proposed method are proved theoretically. Simulation experiments show that the proposed method can provide solutions to this problem where existing algorithms fail and it has strong robustness and high efficiency. Furthermore, the obtained path is superior to those obtained using the existing algorithms in various scenarios; the results show that the proposed method outperforms A* and genetic algorithms in terms of path smoothness, energy efficiency, and computational economy, achieving reductions in travel distance, sailing time, and energy consumption by up to 6.0%, 6.9%, and 4.0%, respectively, compared with A, and by 3.3%, 4.4%, and 1.8%, respectively, compared with the genetic algorithm.