The paper demonstrates a following robot with omni-directional wheels, which is able to take action to avoid obstacles. The robot design is based on both fuzzy and extension theory. Fuzzy theory was applied to tune the PMW signal of the motor revolution, and correct path deviation issues encountered when the robot is moving. Extension theory was used to build a robot obstacle-avoidance model. Various mobile models were developed to handle different types of obstacles. The ultrasonic distance sensors mounted on the robot were used to estimate the distance to obstacles. If an obstacle is encountered, the correlation function is evaluated and the robot avoids the obstacle autonomously using the most appropriate mode. The effectiveness of the proposed approach was verified through several tracking experiments, which demonstrates the feasibility of a fuzzy path tracker as well as the extensible collision avoidance system.