A　time　delay　estimation　based　terminal　sliding　mode　adaptive　fuzzy　control　for　trajectory　tracking　control　of　free-floating　robot　manipulators　is　presented.　This　controller　consisted　of　a　time　delay　estimation　element,　a　terminal　sliding　mode　and　an　adaptive　fuzzy　system.　Based　on　time　delay　estimation　technology,　which　can　estimate　most　unknowns　of　the　system　for　reducing　the　negative　impact　of　uncertainty　on　stability　caused　by　system　inertia　parameter,　a　terminal　sliding　mode　adaptive　fuzzy　controller　is　designed.　A　nonlinear　error　dynamic　model　is　established　by　terminal　sliding　mode,　which　can　also　make　actual　trajectory　track　the　desired　trajectory　well　in　a　short　time.　The　adaptive　fuzzy　system　would　compensate　for　the　error　caused　by　the　delay　estimation　technique　and　suppresses　the　chattering　problem　caused　by　the　terminal　sliding　mode.　It　is　proved　that　the　tracking　errors　converge　into　zero　asymptotically　by　using　Lyapunov　stability　theory.　Last　numerical　simulation　shows　that　the　controller　has　good　tracking　performance.　©　2020,　Springer　Nature　Singapore　Pte　Ltd.