In　order　to　achieve　fast　and　high　precision　force/position　control　of　on-orbit　mission,　the　impedance　control　problem　of　dual-arm　space　robot　on-orbit　auxiliary　docking　operation　is　studied.　Firstly,　the　dynamics　equation　of　the　closed　chain　hybrid　system　formed　after　the　capture　operation　of　the　dual-arm　space　robot　is　established　by　using　the　Lagrange　method.　A　second-order　linear　impedance　model　and　a　second-order　approximate　environment　model　are　established　based　on　impedance　control　theory.　Then,　theradial　basis　function　neural　networks(RBFNNs)　are　used　for　blocking　approximation　of　the　system　uncertainties.　Considering　the　control　requirement　of　convergence　in　finite　time,　the　fast　nonlinear　sliding　mode　surface(FNSMS)　is　introduced,　and　the　buffeting　caused　by　the　introduced　sliding　mode　surface　is　suppressed　by　designing　the　boundary　layer　function.　Finally,　the　stability　of　the　system　is　verified　by　Lyapunov　stability　determination.　The　simulation　results　show　that　the　proposed　control　algorithm　has　fast　convergence　speed,　good　stability　and　strong　robustness,　and　can　simultaneously　achieve　high-precision　force/position　control.　The　attitude　control　accuracy　is　better　than　0.5°,　the　position　control　accuracy　is　better　than　0.001　m,　and　the　output　force　control　accuracy　is　better　than　0.5　N,　which　can　meet　the　task　requirements　of　the　dual-arm　space　robot　on-orbit　auxiliary　docking　operation.　©　2025　Northeast　University.　All　rights　reserved.