Abstract: Safety inspection of coal mine shafts is the core link of coal mine safety checks, which is of great significance for achieving safe production in coal mines and ensuring the personal safety of miners. Aiming at the deficiencies of intelligent safety inspection robots in coal mines in terms of positioning accuracy and multi-robot collaboration, a fusion positioning and collaborative operation model for inspection robots based on multi-source positioning information fusion and navigation-following control method is proposed. To address the issues of unstable positioning signals and low positioning accuracy in underground mines, this study adopts three positioning systems, namely inertial navigation system, liDAR positioning system and ultra-wideband positioning system, for underground positioning. The data information of the three positioning systems is fused through the extended Kalman filter and weighted fusion to perform the navigation and positioning of inspection robots. In the long and complex underground environment, the inspection of a single robot is extremely difficult and time-consuming. Safety inspections often need to be carried out through the collaborative operation of multiple robots. To achieve more efficient and coordinated multi-robot collaborative operations, the research adopts the navigation-following control method for multi-robot formation and improves the navigation-following control method by using the graph theory method based on directed graphs, obtaining an improved navigation-following control algorithm based on graph theory for robot collaborative operation formation. In the simulation experiment, it was proposed that the maximum root mean square error value of the trajectory obtained by the model in the x direction was 0.578 m, the average root mean square error value was 0.295 m, and the maximum root mean square error value in the y direction was 0.155 m. Both had relatively small errors, indicating that the proposed model had high positioning accuracy. In the experimental results of different scenarios, the mean maximum value of the x-component position error of the robot using the model proposed in the research in the L-shaped roadway is 0.380 m, and the mean maximum value of the x-component position error in the connecting roadway is 0.442 m. It still has a relatively small error, further verifying that the model has superior positioning performance. Furthermore, the research results indicate that after adding obstacles, the maximum offset of the four follower robots in obstacle avoidance is within 1.025 meters, with a relatively small error. After obstacle avoidance, the follower robot quickly converges to the ideal trajectory. Both the obstacle avoidance and recovery time are approximately 20 seconds, demonstrating a relatively fast convergence speed.