The　multi-joint　snake　robot　is　poised　to　become　a　crucial　asset　for　investigation,　surveillance,　and　attack　in　national　defense　and　military　applications.　This　paper　addresses　the　trajectory　tracking　challenge　of　a　multi-joint　snake　robot　characterized　by　high　redundancy　and　multiple　degrees　of　freedom　in　the　plane.　We　propose　an　adaptive　trajectory　tracking　controller　that　accounts　for　non-holonomic　constraints.　This　controller　estimates　unknown　environmental　parameters,　effectively　mitigating　the　negative　impacts　of　uncertain　and　time-varying　conditions　during　robot　movement,　thereby　ensuring　stability.　A　suitable　Lyapunov　function　is　identified　to　confirm　the　controller’s　stability.　The　trajectory　tracking　performance　of　the　robot　is　thoroughly　analyzed　through　simulations　and　experiments,　demonstrating　the　effectiveness　of　the　proposed　adaptive　controller.　©　The　Author(s)　2024.