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.　©　2022,　Science　Press.　All　right　reserved.