针对欠驱动水面无人艇的自主靠泊问题，提出一种基于构造可规划域和优化求解三次Bezier曲线的自主靠泊末端轨迹规划方法。以常见的欠驱动双体水面艇为研究对象，对常见的泊位——平行泊位进行可规划域分析构造，得到一个三次Bezier曲线的可规划域。通过在可规划域内增加一个引力势场点或者辅助目标点，引导无人艇基于前端路径规划方法达到可规划域，再基于三次Bezier曲线的原理提出一个最优求解问题，将规划轨迹的距离作为目标函数，将障碍物的位置、最大曲率、无人艇的初始以及终点位姿作为最优化问题的约束，通过求解最优化问题得到一条满足约束的最短三次Bezier曲线作为末端目标轨迹。在可规划域内利用蒙特卡洛方法验证了在可规划域的边界进入可规划区域可以通过优化求解三次Bezier曲线的方法完成末端轨迹规划，并通过仿真实验来验证了无人艇能够跟踪目标轨迹完成避障以及精准靠泊，靠泊的位置精度小于0.2 m，航向角精度小于8°。相较于经典的混合A*算法，所提规划方案的规划效率提升了18.46%，规划的轨迹更加平滑易跟踪，验证了提出的算法具有一定的优越性。
To address the autonomous berthing of underactuated unmanned surface vehicles (USVs), this paper proposes an end-phase trajectory planning method based on constructing a plannable domain and optimizing cubic Bézier curves. Focusing on a common underactuated catamaran USV, we construct a plannable domain for a typical parallel berth scenario, establishing a feasible region for cubic Bézier curve generation. By introducing an attractive potential field point or auxiliary target point within this domain, the USV is guided to enter the plannable region using a front-end path planner. Subsequently, leveraging the principles of cubic Bézier curves, we formulate an optimal control problem. This problem minimizes the trajectory length as the objective function, subject to constraints including obstacle positions, maximum curvature, and the USV's initial and terminal poses. Solving this optimization yields the shortest feasible cubic Bézier curve as the end-phase target trajectory. Monte Carlo simulations within the plannable domain validate that entry from its boundary enables successful end-phase trajectory planning via the proposed cubic Bézier optimization method. Furthermore, simulation experiments demonstrate the USV's ability to track the target trajectory for obstacle avoidance and precise berthing. The achieved berthing position accuracy is less than 0.2 m, with a heading angle error below 8°. Compared to the classical hybrid A* algorithm, the proposed method improves planning efficiency by 18.46%, generates smoother trajectories that are easier to track, and exhibits superior overall performance.
2026,48(3): 162-168 收稿日期：2025-4-25
DOI：10.3404/j.issn.1672-7649.2026.03.025
分类号：U675
基金项目：航空科学基金项目资助（20220056060001）；国家自然科学基金重大科研仪器研制项目（61527810）；中央高校基本科研业务费专项资金资助（x2zdD2250080）；中国高校产学研创新基金新一代信息技术创新项目（2022IT046）
作者简介：邱秋彪(2001-),男,硕士研究生,研究方向为无人艇自主导航技术
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