Compared with the ground environment， the robot system exposed to cosmic rays in space environment is more susceptible to external interference， and the system parameter changes such as mass and inertia caused by difficult maintenance and fuel consumption make it more prone to system uncertainty. Aiming at the problems of system uncertainty and external interference in a floating space robot system with uncontrolled carrier position， a trajectory tracking control method based on variable universe fuzzy control is proposed. On the basis of calculating torque controller to solve the nominal system control torque， the variable universe adaptive fuzzy controller is used to compensate the errors caused by the system uncertainty and external interference. The real-time change of the scope of the variable domain makes the fuzzy controller applicable to different error ranges at different time， thus effectively improving the response speed of the system and reducing the steady-state tracking error of the system. Finally， the stability of the control scheme is proved by Lyapunov method， and the effectiveness of the control method is proved by numerical simulation.