In　order　to　prevent　joints　from　being　damaged　by　impact　force　in　a　space　robot　capturing　satellite,　a　spring-damper　device　(SDD)　is　added　between　the　joint　motor　and　manipulator.　The　device　can　not　only　absorb　and　attrition　impact　energy,　but　also　limit　impact　force　to　a　safe　range　through　reasonable　design　compliance　control　strategy.　Firstly,　the　dynamic　mode　of　the　space　robot　and　target　satellite　systems　before　capture　are　established　by　using　a　Lagrange　function　based　on　dissipation　theory　and　Newton-Euler　function,　respectively.　After　that,　the　impact　effect　is　analyzed　and　the　hybrid　system　dynamic　equation　is　obtained　by　combining　Newton＇s　third　law,　momentum　conservation,　and　a　kinematic　geometric　relationship.　To　realize　the　buffer　compliance　stability　control　of　the　hybrid　system,　a　reinforcement　learning　(RL)　control　strategy　based　on　a　fuzzy　wavelet　network　is　proposed.　The　controller　consists　of　a　performance　measurement　unit　(PMU),　an　associative　search　network　(ASN),　and　an　adaptive　critic　network　(ACN).　Finally,　the　stability　of　system　is　proved　by　Lyapunov　theorem,　and　both　the　impact　resistance　of　SDD　and　the　effectiveness　of　buffer　compliance　control　strategy　are　verified　by　numerical　simulation.