This　paper　discusses　the　collision　dynamics　modeling　of　a　free-floating　space-based　robot　in　the　process　of　on-orbit　satellite　capturing,　and　it　also　analyzes　the　stability　control　for　the　compounded　body　of　the　space-based　robot　and　target　after　the　capturing　operation　is　completed.　First　the　method　of　multibody　system　dynamics　modeling　is　employed　in　combination　with　the　characteristics　of　collision　dynamics　of　the　space-based　robot　while　it　captures　the　target　satellite　to　set　up　a　dynamics　model　for　the　free-floating　space-based　robot　during　its　on-orbit　capture　of　the　floating　satellite.　Based　on　it,　the　movement　speed　for　the　compounded　body　of　the　space-based　robot　and　target　is　calculated.　In　view　of　the　fact　that　for　the　inertia　parameters　of　both　the　satellite　and　the　space-based　robot　system　are　unknown,　the　model　and　the　theory　of　neural　network　control　and　Lyapunov　stability　theory　are　used　to　design　a　Gaussian　radial　basis　function　neural　network　control　scheme　for　the　compounded　body　to　move　stably　under　the　influence　of　collision　and　impact　during　the　capturing　process.　Thus,　the　effective　control　is　realized　for　capturing　a　target　satellite.　The　Gaussian　radial　basis　function　neural　network　control　scheme　has　the　obvious　advantages　of　requiring　no　feedback　and　measurement　of　the　position,　velocity,　acceleration,　attitude　angle　velocity　and　attitude　angle　acceleration　of　the　floating　base.　Finally,　the　validity　and　applicability　of　the　control　scheme　are　manifested　by　system　numerical　simulation.