In the emergency rescue and disposal of social public emergencies, supply transportation effectively provides a strong supply foundation and realistic conditions. The trajectory tracking control of emergency supplies transportation robot is the key technology to ensure the timeliness of transportation. In this paper, the emergency supplies transportation robot is taken as the research object, based on Koopman operator theory, combined with radial basis function (RBF) neural network disturbance observer and adaptive prediction horizon event-triggered model predictive control (APET-MPC) algorithm to investigate the purely data-driven trajectory tracking control problem of emergency supplies transportation robot when the model parameters and models are unknown. Firstly, the Koopman operator is used to establish a high-dimensional linear model of the robot. Secondly, the RBF neural network disturbance observer is designed to estimate the disturbance during the robot operation and compensate it to the controller. Thirdly, APET-MPC is used to optimize the trajectory tracking control of the emergency supplies transportation robot to reduce computational complexity. Finally, the performance of the proposed trajectory tracking controller is verified by Carsim/ Simulink joint simulation. The simulation results show that the model established by Koopman operator theory can achieve the high accuracy approximation of the robot. Compared with the MPC trajectory tracking controller, the APET-MPC trajectory tracking controller based on RBF neural network disturbance observer (RBF-APET-MPC) improves the tracking accuracy of the robot and reduces the total triggering times of the system by more than 50%.