This paper describes a robotic application that tracks a moving object by utilizing a mobile robot with multiple sensors. The robotic platform uses a visual camera to sense the movement of the desired object and a range sensor to help the robot detect and then avoid obstacles in real time while continuing to track and follow the desired object. In terms of real-time obstacle avoidance capacity, this paper also presents a modified potential field algorithm called Dynamic Goal Potential Field algorithm (DGPF) for this robotic application specifically. Experimental results show that the robotic and intelligent system can fulfill the requirements of tracking an object and avoiding obstacles simultaneously when the object is moving.