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Abstract - In this paper, an optimal trajectory planning method is presented for robot manipulators with multiple degrees of freedom in 3D space using a new analytical technique for collision avoidance in the presence of ellipsoidal obstacles. To generate the robot’s trajectory, a genetic algorithm with a fuzzy mutation rate is introduced to have a quick access to optimal solutions in a complex workspace. A cubic spline interpolation polynomial is applied to approximate trajectories in the joint space. In order to optimize the objective function, the genetic algorithm determines a number of interior points for curve fitting using interpolation polynomials. The performance of the proposed technique is demonstrated by simulations.