In this article, the artificial potential field is computed for the obstacle avoidance problem of a mobile robot, using harmonic-functions. Given the maximum linear attainable velocity of the robot, equidistant points on the robot's resulting path are selected. A third-order Bézier-curve is used for time and space parameterization of each segment of the path between neighbouring points. This curve is optimized so as the robot to be capable of moving along these segments given the maximum constraints on its linear and angular velocity. A simple non-linear feedback controller is used for tracking control of the trajectory. Simulation studies indicate the efficiency of the proposed method in optimizing the robot's trajectory.