Path planning in narrow passages is a challenging problem in various applications. Traditional planning algorithms often face challenges in complex environments like mazes and traps, where narrow entrances require special orientation control for successful navigation. In this work, we present a novel approach that combines superquadrics (SQ) representation and Voronoi diagrams to solve the narrow passage problem in both 2D and 3D environment. Our method utilizes the SQ formulation to expand obstacles, eliminating impassable passages, while Voronoi hyperplane ensures maximum clearance path. Additionally, the hyperplane provides a natural reference for robot orientation, aligning its long axis with the passage direction. We validate our framework through a 2D object retrieval task and 3D drone simulation, demonstrating that our approach outperforms classical planners and a cutting-edge drone planner by ensuring passable trajectories with maximum clearance.

翻译：狭窄通道中的路径规划是各类应用中的关键难题。传统规划算法在迷宫、陷阱等复杂环境中常面临挑战，狭窄入口处需要特殊的方向控制才能实现成功导航。本研究提出一种融合超二次曲面表示与Voronoi图的新方法，用于解决二维与三维环境中的狭窄通道问题。该方法利用超二次曲面公式扩展障碍物以消除不可通行通道，同时通过Voronoi超平面确保最大间隙路径。此外，该超平面为机器人方向控制提供自然参考基准，使其长轴与通道方向自动对齐。我们通过二维物体抓取任务与三维无人机仿真验证了本框架的有效性，实验表明该方法能确保生成具有最大间隙的可通行轨迹，其性能优于经典规划器及前沿无人机规划器。