A　space　robot　inevitably　impacts　a　satellite　in　a　capture　operation.　If　its　fragile　joints　are　not　protected,　they　may　be　damaged,　resulting　in　failure　of　the　capture　operation.　Thus,　a　spring　damper　buffer　device　(SDBD)　is　added　between　the　joint　motors　and　manipulators　to　absorb　the　impact　energy,　and　provide　a　compliance　strategy　matched　with　the　SDBD　for　stable　control　of　the　hybrid　system.　The　dynamic　modes　of　the　dual-arm　space　robot　open-loop　system　and　target　satellite　system　are　established　by　the　Lagrange　function　before　capture.　From　the　momentum　theorem,　velocity　constraints,　closed-chain　geometric　constraints,　and　Newton’s　third　law,　the　closed-chain　dynamic　model　of　the　hybrid　system　after　capture　is　obtained,　and　the　impact　effect　and　impact　force　are　calculated.　For　stable　control　of　the　hybrid　system　while　limiting　joint?　impact　torque　within　the　safe　range,　an　adaptive　fractional-order　super-twisting　sliding　mode　compliance　control　strategy　matching　the　SDBD　is　proposed.　It　can　effectively　improve　the　fast　convergence　and　trajectory　tracking　performance　of　the　system　whose　velocity　and　acceleration　cannot　be　measured.　The　stability　of　the　hybrid　system　is　demonstrated　by　the　Lyapunov　theorem,　and　the　anti-impact　performance　of　the　SDBD　and　the　effectiveness　of　the　compliance　strategy　are　demonstrated　through　numerical　simulation.　Copyright　©　2023　by　ASME.