Abstract: The robust control problem of a free-floating flexible-joint space robot with an uncontrolled base to track the desired trajectory in workspace is discussed. With the system linear and angular momentum conservation and Lagrangian method, the dynamic equations are derived. In the consideration of the strong joint flexibility of a space robot, a joint flexibility compensation controller is designed to compensate the effects of the joint flexibility to the system control precision. Then by using of the singular perturbation technology, a robust control scheme for the robot system with uncertain inertial parameters to track the desired trajectory in workspace is presented. A planar space robot system with flexible joints is simulated to verify the effectiveness of the proposed control method.