This paper introduces a novel leader–follower formation control strategy for autonomous vehicles, aimed at achieving precise trajectory tracking in uncertain environments. The approach is based on a graph guidance law that calculates the desired yaw angles and velocities for follower vehicles using the leader’s reference trajectory, improving system stability and predictability. A key innovation is the development of a Neural Adaptive Prescribed Performance Controller (NA-PPC), which incorporates a Radial Basis Function Neural Network (RBFNN) to approximate nonlinear system dynamics and enhances disturbance estimation accuracy. The proposed method enables high-precision trajectory tracking and formation maintenance under random disturbances, which are vital for autonomous vehicle logistics and detection technologies. Leveraging a graph-based guidance law reduces control complexity and improves robustness against external disturbances. The inclusion of second-order filters and adaptive RBFNNs further enhances nonlinear error handling, improving control performance, stability, and accuracy. The integration of guidance laws, leader–follower control strategies, backstepping techniques, and RBFNNs creates a robust formation control system capable of maintaining performance under dynamic conditions. Comprehensive computer simulations validate the effectiveness of this controller, highlighting its potential to advance autonomous vehicle formation control.