###### Abstract  
Aiming at the force position control problem of the on-orbit insertion and extraction operation of the free-floating space robot, the system dynamics model is established. According to the interaction between the end of manipulator and the environment, the second-order impedance model is established. In order to improves the calculation efficiency, the above models are reconstructed to avoid the use of acceleration signal by introducing filtering operation. This is also conducive to the application of robot actual control. Then, an estimator requiring only the system inertia matrix is designed to compensate the modeling uncertainty, external bounded disturbance and impact effect in the process of inserting and extracting. Its structure is simple and reliable. Only one control parameter needs to be adjusted, which greatly reduces the amount of calculation. Considering that the on-orbit operation of insertion and extraction is a kind of precision operation, its control system needs to have a high-quality control performance. By introducing the prescribed performance method, the tracking error is constrained within the given range and to ensure the transient performance and steady-state performance of the control system is ensured. Finally, three simulation conditions are designed, and the results are presented to verify that the proposed algorithm has a faster convergence speed compared with traditional sliding mode controller. It can achieve vertically inserting and accurate force tracking of the manipulator end. free-floating space robot; impedance control; on-orbit insertion and extraction; prescribed performance method; second order impedance model +
Footnote †: journal: Applied  
mode control scheme for strong impact effects in the capture process, which effectively reduced the interference caused by impact effects. Considering the influence of base, joint and arm flexibility, [PERSON] et al. [14] carried out the dynamic analysis on a space robot capturing non-cooperative spacecraft, and designed a motion stabilization control scheme based on repetitive learning for the combination after capture. [PERSON] et al. [15] introduced spring compliant mechanisms at the joints of space robots to absorb impact energy, and designed a buffer compliant control scheme based on reinforcement learning which can effectively limit the impact moment at the joints within a safe range. [PERSON] et al. [16] used the principle of dissipating energy to reduce the angular velocity of space debris before capture, which effectively protects robots from space and other physical installations. [PERSON] et al. [17] designed an elastic hemispheric gripper and a compliant control scheme in sensorless condition to reduce the impact effect during the capture process. In addition, [PERSON] et al. [18] designed a new bionic impact resistant manipulator from the perspective of bionics, and verified its impact resistance performance through simulation and ground tests. [PERSON] et al. [19] proposed a novel low-chattering and global-nonsingular fixed-time terminal sliding mode control strategy for fixed-time trajectory tracking for a dual-arm free-floating space robot, and its tracking accuracy of end-effector was improved to the nanoscale. It can be found above that the researchers mainly focused on the impact effect produced by the capture of space robot to target and alleviated the impact by designing stabilization control and compliance control schemes or adding flexible parts. Nevertheless, the above research results also show that some points have not been considered, especially the issue of on-orbit operation of insertion and extraction of free-floating space robot. As a kind of precise space mission operation, on-orbit operation of insertion and extraction requires high precision of attitude control system of space robot. Due the strong nonlinear dynamic coupling of system, the relationship between force and position affects and interacts with each other.