This paper presents a geometrical path planning method, and it can help unmanned aerial vehicle to find a collision-free path in two-dimensional and three-dimensional (2D and 3D) complex environment quickly. First, a list of tree is designed to describe obstacles, and it is used to query the obstacles which block the line from starting point to finishing point (blocking obstacle). Specially, the list also stores the edge information of blocking obstacle. For the obstacles with short distance, a reasonable way to fly over is studied. Then, a shortest path planning method based on geometrical computation is proposed according to different shapes of obstacles. The obstacles are convex and divided into two cases of 2D and 3D. 2D environment includes rectangular obstacle, trapezoidal obstacle, triangular obstacle, circular obstacle and elliptic obstacle. In 3D, it includes cuboid, sphere and ellipsoid. To compare with other methods, the simulation is made in different environments. In 2D environment with circular obstacles, the method is similar to the artificial potential field. In 2D environment with rectangular obstacles, the performance of the proposed method is better than A-star. Compared with genetic algorithm, the proposed method gives a better result in 3D environment with cuboid obstacles. In 3D environment with hybrid obstacles, it is similar to interfered fluid dynamical system. Through comprehensive comparison and analysis, the conclusion is that the method has good adaptability and does not require grid modeling. It can find a shorter path in 2D/3D complex environment within a short time, so it has the ability of real-time path planning. Keywords Unmanned aerial vehicle (UAV) • Path planning • Geometrical shortest path • 2D/3D complex environment • Convex obstacles • Optimal and real-time planning B Xiao Liang

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