Artificial potential fields and artificial force fields are widely used in robotics for path planning and collision avoidance, both for robot manipulators and for mobile robots. Despite intensive research in designing suitable artificial potential fields, little attention has been devoted to tracking control for following the gradient of an artificial potential field. However, good tracking control is vital for successful application of the artificial potential field method in order to guarantee safe operation of the robot. In this paper, we extend previous results on a sliding mode control strategy to include actuator dynamics and non-holonomic motion constraints of mobile robots into the gradient tracking control algorithm.