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.　IEEE