In this paper, when the case of the attitude of base controlled and its location uncontrolled, we discuss the control for free-floating space manipulator to track desired trajectory in joint space. Combined the relationship of the linear conversation of the system and the Lagrange approach, the full-controlled dynamic equation of free-floating space manipulator are established. Base on above results proposed, aiming at the case of free-floating space manipulator system with uncertain payload parameters, a composite scheme of a computed torque controller plus a fuzzy compensator is proposed to track desired trajectories in joint space. Namely, it will transfer the impact of system's unknown parameters to computed torque controller through fuzzy adaptive compensation system controller, to
ensure the whole closed-loop control system's asymptotic stability with the existence of unknown parameters. The mentioned control scheme can effectively control two joint of space manipulator to stably track the desired trajectory in joint space. It has obvious advantages that with needless feedback and measured the position, velocity, acceleration, attitude angle velocity and attitude angle acceleration of the floating base. At the same time, no requirements for the dynamic equations of the system are linearly dependent on inertial parameters. A two space-based manipulator system is simulated to verify the proposed control scheme.