Objective Automatic berthing path planning for underactuated ships is challenged by low search efficiency, large terminal position and heading errors, and the conflict between obstacle clearance and berth reachability. This study develops an improved bidirectional hybrid A* (IBHA*) algorithm that incorporates the changing maneuverability of a ship throughout the berthing process and generates a safe, smooth, and terminal-state-constrained reference path without dividing the task into separate planning stages.

Method The navigation environment is first rasterized, and ship position and heading are jointly represented in the search state. Then, a bidirectional hybrid A* framework expands paths simultaneously from the initial ship state and the target berth state, reducing unnecessary node expansion and imposing terminal position and ship heading constraints from the beginning of the reverse search. To reflect the progressive reduction in speed and maneuverability during berthing, the maximum steering angle and expansion step are dynamically adjusted according to the Euclidean distance to the berth. Specifically, relatively large values are used in the early stage to preserve search efficiency, whereas smaller values are adopted near the berth to improve path resolution and heading alignment. A rectangular collision-detection boundary enlarged from the ship’s principal dimensions is used to account for hull size, underactuation, maneuvering delay, and path-following errors. In addition, a multi-objective cost function combines adaptively weighted path length, steering variation, and a dynamic safety-distance penalty. The safety threshold decreases as the ship approaches the quay, thereby maintaining sufficient obstacle clearance during transit while preserving access to the target berth. Forward and reverse paths are joined only when both distance and heading consistency criteria are satisfied. Finally, Bezier curves subject to maximum-curvature, positional-continuity, and tangential-continuity constraints smooth the initial path and suppress abrupt heading changes.

Results Simulations using the 167m long underactuated vessel CISNE BLANCO were conducted in two berthing scenarios and compared with A*B and A*QB algorithms. IBHA* achieved zero terminal position error in both scenarios, with terminal heading errors of 0.00° and 0.08° and search times of 3.46s and 2.12s, respectively. Compared with A*B, which also considers obstacle clearance, IBHA* shortened the mean path length by 1.3%. Compared with A*QB, which performs better in terms of search efficiency among the existing methods, IBHA* reduced the mean search time by 19.93%. At the same time, the maximum steering angles of IBHA* remained within reasonable limits.

Conclusion The proposed IBHA* ship berthing path planning method achieves a balance between search efficiency and feasibility. Its generated berthing paths consider both navigation safety and stability, providing reference paths for berthing control.