This paper reports a novel path-following method based on error constraints to fulfill formation control with the anti-disturbance for multi-snake robots. A synchronized line-of-sight (SLOS) guidance rule and a high-coupled dynamic frequency compensator are designed to revise the movement speed of each robot, ensuring position consistency among formation members. The equivalent principle of the barrier function restricts the state errors within a set range, eliminating the singularity of virtual variables and enhancing the steady-state performance of path-following. Moreover, this work predicts the model uncertainty and external disturbances to pre-compensate for the joint offset and torque input of the robot. The method further improves the convergence rates and robustness of the following errors. Barrier Lyapunov theory proves the uniform ultimate boundedness (UUB) of the proposed method. Simulation and experimental data indicate that the control strategy reduces oscillations of errors before convergence and achieves fast and smooth formation following effect.