The　end-effector　of　the　manipulator　needs　to　maintain　contact　with　external　environments　in　course　of　its　on-orbit　wiping　operation.　To　protect　the　manipulator　and　the　object　to　be　cleaned,　as　well　as　to　ensure　the　surface　to　be　cleaned　effectively,　the　contact　surface　pressure　and　friction　need　to　be　maintained　their　expectations.　However,　friction　has　been　ignored　in　course　of　the　previous　dynamic　modeling,　which　may　affect　the　surface　contact　forces＇　tracking　accuracy.　Meanwhile,　the　complex　and　variable　environments　make　it　more　difficult　to　track　the　desired　surface　contact　forces.　Therefore,　dynamic　modeling　and　an　adaptive　impedance　control　of　a　free-floating　space　manipulator＇s　wiping　a　surface　are　studied.　First,　the　Lagrange　dynamic　model　of　a　free-floating　space　manipulator＇s　wiping　operation　was　derived,　in　which　the　contact　surface　forces　were　involved.　Second,　the　impedance　control　model　was　established　based　on　position　constraints　and　contact　forces　constraints　between　the　end-effector　and　the　surface.　Then,　a　time-delay　estimation　based　adaptive　impedance　control　was　proposed,　in　which　the　estimators　of　the　dynamic　uncertainties　and　the　damping　parameters　were　adjusted　adaptively.　Finally,　numerical　simulations　were　conducted,　in　which　the　desired　contact　forces　were　followed　perfectly　while　the　expected　trajectories　were　asymptotically　tracked.　Copyright　©　2023　by　Mr.　Tao　Lin.　Published　by　the　IAF,　with　permission　and　released　to　the　IAF　to　publish　in　all　forms.