Abstract: With the developments in space technology and exploration, the space manipulator has become a better choice than astronauts for performing long-time and high-precision operation tasks, such as orbit assembly, orbit maintenance, and orbit refueling. In carrying out the above orbit service tasks, the space manipulator must perform insertion and extraction operations. By considering the impedance control, a dynamic relationship can be established between the pose and output force during insertion and extraction tasks. In this paper, the impedance control problems associated with the insertion and extraction operation of the space manipulator were discussed. By combining the conservation of the momentum of the system, relationship between the driving forces of insertion and extraction at the end of the replacement parts, friction resistance in the holes, and second Lagrange equation, we derived dynamic equations for the space manipulator during the orbit insertion and extraction operation when the position and attitude of the carrier were not controlled. In addition, based on the design requirements of the related operation and control systems, we established the Jacobian relation of the relative motion between the end of the replacement parts and the basic coordinate system by performing a geometric relation analysis of the system position. Then, we established a second-order linear impedance control model based on the dynamic relationship between the pose and driving force of the end of the replacement parts and the impedance control principle. Based on the above work, to address the uncertainty of the kinematics and dynamics of the orbit insertion and extraction operation, performed by the space manipulator, we designed an exponential impedance control strategy on the basis of force/pose tracking, and confirmed the stability of the control system based on the Lyapunov theory. The proposed control strategy has a simple structure, fast convergence speed, and good stability. As such, it is suitable for situations with limited computing and storage capacities, such as the space station computer. The numerical simulation results of this system verify the effectiveness of the proposed control strategy.