When the robot moves from the current point to the target point, the environment is often dynamic and unknown, which makes it difficult for the traditional path planning algorithm to establish an accurate mathematical model for the mobile robot obstacle avoidance process. Aiming at the situation that the environment information is completely unknown, a multi-behaviour local path planning method based on fuzzy control is designed for the mobile robot. The method ensures that the robot avoids static and dynamic obstacles safely and promptly by switching various behaviours timely and reasonably. The improved artificial potential field method is used to track the variable speed target point. To deal with the common obstacle avoidance U-trap problem, a trap escaping strategy of the boundary tracking is proposed, which makes the robot successfully lift the deadlock state. In addition, a speed fuzzy controller is designed to realize the robot's intelligent driving. Finally, the simulation results based on the Matlab platform verify the effectiveness and real-time performance of the proposed algorithm. Compared with the A* potential field method, the proposed algorithm is more feasible.