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This paper presents a method for curvature continuous (G2 continuous) path generation for a UAV flying in a cluttered environment in real-time. First we generate a collision free path using a rapidly-exploring random tree (RRT). However a UAV cannot fly this path since it consists of piecewise linear segments. G2 continuous path algorithm using cubic Bezier spiral curves is presented in this paper. Simulation results show the superiority of cubic Bezier spiral curves to Dubins path and C1 continuous cubic Bezier curves.