The motion and control of differential mobile robots for autonomous position control and obstacle avoidance are analyzed. Two control methods are proposed so that the robot autonomously control its motion and achieves a desired position without colliding with obstacles that could be present in arbitrary positions inside the working area. For both methods, the robot is able to avoid obstacles and achieve the desired position, but the trajectories described by the robot are different for each control method. A trajectory pruning technique is proposed and implemented after the first run of the robot to eliminate the parts of the original trajectory through which the robot passes more than once.