By using the pseudo minimum translational distance between convexobjects, this paper presents two algorithms for robot path planning. First, an analytically tractable potential field is defined in the robot configuration space, and the concept of virtual obstacles is introduced and incorporated in the path planner to handle the local minima of the potential function. Second, based on the Lipschitz continuity and differentiability of the pseudo minimum translational distance, the flexible-trajectory approach is implemented. Simulation examples are given to show the effectiveness and efficiency of the path planners for both mobile robots and manipulators.