In　this　article,　an　adaptive　path　following　the　controller　of　a　multijoint　snake　robot　(MSR)　based　on　the　improved　Serpenoid　curve　is　proposed.　The　proposed　controller　can　make　the　MSR　follow　the　desired　path.　Compared　with　the　traditional　controller,　this　controller　can　make　the　position　error　possess　fast　convergence　speed　and　high　stability.　The　swing,　the　controller　can　estimate　unknown　friction　coefficients,　which　improves　the　adaptive　path　following　the　ability　of　the　MSR　in　an　environment　with　unknown　friction　coefficients.　First,　the　dynamic　model　without　lateral　force　is　established.　Then,　the　control　objectives　of　the　controller　are　formulated.　Third,　the　Serpenoid　gait　equation　is　improved,　and　the　state-dependent　time-varying　amplitude　is　obtained.　Fourth,　the　input-output　control　function　of　the　system　and　the　tracking　function　of　the　swing　amplitude　compensation　are　designed　by　the　adaptive　control　method.　The　stability　of　the　motion　attitude　angle　variable　errors　and　uniformly　ultimately　bounded　stability　of　the　tracking　position　are　verified,　respectively.　Finally,　the　effectiveness　and　superiority　of　the　proposed　controller　are　verified　by　experiments.