Using　space　robots　to　capture　satellite　has　excellent　economic　prospects,　but　it　requires　space　robots　to　have　the　ability　to　complete　the　auxiliary　docking　operation.　That　is,　the　controller　can　achieve　extremely　control　accuracy　of　position　and　output　force　of　the　post-capture　satellite　docking　device.　Based　on　this　analysis,　the　dynamic　modes　of　space　robot　open-loop　system　and　satellite　system　before　capture　are　established　by　using　Lagrange　function.　Then,　combined　with　Newton＇s　third　law,　velocity　constraints　of　capture　points　and　closed-chain　geometric　constraints,　the　closed-chain　dynamic　model　of　hybrid　system　after　capture　is　obtained,　and　the　impact　effect　and　impact　force　are　calculated　utilize　the　momentum　conservation.　In　order　to　achieve　high-precision　control　of　output　force,　the　impedance　model　is　established　based　on　the　Jacobian　relation　between　the　satellite　docking　device　relative　to　the　space　robot　base　coordinate　system.　An　adaptive　double-layer　sliding　mode　control　(ADLSMC)　is　proposed　based　on　the　impedance　model.　It　improves　the　control　accuracy　of　position　by　using　double-layer　sliding　mode　function　and　the　adaptive　gain　coefficient　to　decrease　the　chattering　in　the　equivalent　control　stage.　Finally,　the　stability　of　the　system　is　proved　by　the　Lyapunov　theorem,　and　the　effectiveness　of　the　proposed　strategy　is　verified　by　numerical　simulation.　The　simulation　results　indicate　that　the　buffer　device　can　reduce　the　impact　force　by　46.32%　to　the　maximum　at　the　given　velocities,　the　control　accuracy　of　the　output　force　is　better　than　0.5N,　and　the　position　and　attitude　is　better　than　10-3m　and　0.5o　Copyright　©　2023　by　the　International　Astronautical　Federation　(IAF).　All　rights　reserved.