A　second-order　sliding　mode　fixed-time　trajectory　tracking　controller　is　designed　for　the　rigid　free-floating　space　robot.　The　dynamic　model　of　the　free-floating　space　robot　system　is　established　by　the　use　of　Lagrange　method,　and　a　second-order　sliding　mode　fixed-time　trajectory　tracking　controller　is　designed　for　the　system　with　the　help　of　the　power-addition　integral　method　and　the　virtual　variable　strategy.　It　has　been　proven　through　the　Lyapunov　function　method　that　the　controller　can　ensure　the　global　fixed-time　convergence　of　the　system　tracking　error,　and　the　convergence　time　is　independent　of　the　initial　state　of　the　space　robot　system.　The　presented　method　can　estimate　the　upper　bound　of　the　minimum　convergence　time　of　the　system　tracking　error,　which　implies　that　the　issue　of　the　overestimation　of　the　convergence　time　existing　in　traditional　fixed-time　control　methods　has　been　solved,　and　it　can　also　effectively　weaken　the　chattering　phenomenon　of　the　control　torque.　The　simulation　results　are　in　accord　with　the　theoretical　analysis,　which　verifies　the　feasibility　and　the　superiority　of　the　formulated　method.　©　2024　Northeast　University.　All　rights　reserved.