Mobile robots can enhance the level of automation and intelligence in industrial production. The implementation of multiple mobile robot systems (MMRSs) for transporting large components not only enhances transport efficiency but also improves manufacturing flexibility. Most current research on MMRS focuses on algorithms, with less attention paid to the control effects in practical applications, which are not conducive to the promotion of engineering applications. This article proposes a control method based on the leader-follower principle to achieve higher precision in formation control. Three laser distance sensors are utilized to accurately measure the relative positions between a leader and a follower. By considering the variations in input and the error propagation related to relative position solutions, a back propagation neural network (BPNN) is utilized to compute speed control parameters effectively. This approach also contributes to reducing debugging time. A trajectory planning method is proposed that enables precise localization of the robot at target points. In addition, considering the unfavorable factors such as the "a relative leader" and the approximate solution of relative positioning, simulation analysis is implemented on the transportation system. Tests are conducted on the precise localization of a robot under different conditions. Experimental results show that the trajectory planning method can achieve a position deviation of within 5 mm and an attitude deviation of within 1°. Four mobile robots are deployed to test cooperative transportation performance under a load of 3 tons. Experimental results indicate that the relative position deviation between any two robots is within 15 mm, and the attitude deviations do not exceed 1°.