In　this　paper,　the　impedance　control　of　the　on-orbit　insertion　and　extraction　of　a　space　robot　with　external　disturbances　and　modelling　uncertainties　based　on　variable　structure　with　fuzzy　neural　network　is　studied.　Firstly,　by　using　the　Lagrange　method　and　the　dynamic　relationship　in　the　base　body　coordinate　system,　the　dynamic　equation　and　the　Jacobian　relationship　of　motion　of　the　on-orbit　insertion　and　extraction　of　the　space　robot　are　derived.　Then,　according　to　the　dynamic　relationship　between　the　output　force　of　the　end　of　the　space　robot　and　the　environment　and　the　impedance　control　principle,　a　second-order　linear　impedance　model　is　established.　For　the　deterministic　part　of　the　above　dynamic　equation,　a　nominal　PD　controller　is　designed　for　general　feedback　control;　For　its　uncertain　part,　a　variable　structure　controller　is　designed　for　precise　compensation.　As　a　kind　of　precision　operation,　the　on-orbit　insertion　and　extraction　hole　operation　of　space　robot　requires　higher　control　accuracy.　In　order　to　achieve　its　high-quality　control　requirements,　a　fuzzy　neural　network　control　is　considered　to　eliminate　chattering　caused　by　variable　structure　controller.　In　the　fuzzy　controller,　the　sliding　surface　is　used　as　the　input,　the　compensation　weight　is　used　as　the　output　and　the　fuzzy　membership　function　is　obtained　by　neural　network　fitting.　The　scheme　avoids　the　use　of　differential　signals　of　sliding　mode　surface　and　reduces　the　calculation　amount.　The　simulation　results　show　that　under　the　influence　of　external　disturbances　and　uncertainties,　the　space　robot　can　not　only　successfully　complete　the　in-orbit　insertion　and　extraction　hole　operation,　but　also　effectively　suppress　the　buffeting.　Copyright　©　2023　by　the　International　Astronautical　Federation　(IAF).　All　rights　reserved.