A　space　robot　will　violently　collide　with　satellites　in　the　capture　operation.　If　its　fragile　joints　are　not　protected,　the　space　robot　may　be　damaged.　Therefore,　a　spring-damper　device　is　added　between　a　joint　motor　and　a　manipulator,　which　can　not　only　digest　and　absorb　the　impact　energy　in　the　collision　process,　but　also　design　a　compliance　strategy　matched　with　the　buffer　device　to　realize　the　calm　control　of　the　hybrid　system.　Firstly,　the　dynamic　modes　of　the　dual-arm　space　robot　open-loop　system　and　target　satellite　system　before　capturing　are　established　using　the　Lagrange　function　and　newton-Euler.　Combined　with　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　impact　effect　and　impact　force　are　calculated.　Then,　in　order　to　control　the　hybrid　system,　an　integral　terminal　sliding　mode　control　matched　with　the　spring-damper　device　is　proposed.　The　parameters　of　the　sliding　mode　controler　are　optimized　by　the　grey　wolf　optimizer　to　realize　fast　and　stable　calm　control　of　the　hybrid　system.　Finally,　the　stability　of　the　hybrid　system　is　proved　using　the　Lyapunov　theorem,　and　the　anti-impact　performance　of　the　spring-damper　device　and　the　effectiveness　of　compliance　strategy　are　verified　by　numerical　simulation.　©　2022　Northeast　University.　All　rights　reserved.