Abstract: A method of planning paths for autonomous carrier vehicles, such as a mobile robots, capable of planning curved paths consisting of cubic spirals smoother than those planned by conventional path planning methods. The path planned by the method of the invention is defined by one or two of cubic spirals with curvature expressed by a quadratic function of distance measured along the cubic spiral with zero curvatures at its opposite ends. The path is designed so that curvatures at the junctions are zero and the integral of the square of the derivative of curvature function between the opposite ends of the path is minimized. The mobile robot is able to travel very smoothly across the junctions when the integral of the square of the derivative of curvature is minimized.