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This paper proposes an innovative and efficient three-dimensional (3D) autonomous obstacle algorithm for unmanned aerial vehicles (UAVs) which works by generating circular arc trajectories to avoid obstacles. Firstly, information on irregular obstacles is obtained by an onboard detection system; this information is then transformed into standard convex bodies, which are used to generate circular arc avoidance trajectories, and the obstacle avoidance problem is turned into a trajectory tracking strategy. Then, on the basis of the geometric relationship between a UAV and obstacle modeling, the working mechanism of the avoidance algorithm is developed. The rules of obstacle detection, avoidance direction, and the criterion of avoidance success are defined for different obstacle types. Finally, numerical simulations of different obstacle scenarios show that the proposed algorithm can avoid static and dynamic obstacles effectively and can implement obstacle avoidance missions for UAVs well.