The　problems　of　joint　motion　control　and　flexible　vibration　suppression　of　a　flexible　joint　space-based　robot　for　manipulating　an　unknown　payload　are　studied.　Based　on　the　system　linear　momentum　conservation　and　the　Lagrange　method,　the　under-actuated　dynamics　model　of　the　space　robot　is　established.　For　convenience　of　the　design　of　its　control　system,　the　system　is　divided　into　both　fast　and　slow　subsystems　by　using　the　joint　flexibility　compensation　technique　and　the　singular　perturbation　theory.　A　torque　differential　feedback　controller　is　proposed　for　the　fast　subsystem　to　suppress　the　joints＇　flexible　vibration,　meanwhile　an　adaptive　control　scheme　based　on　the　augmentation　approach　is　designed　for　the　slow　subsystem　to　realize　the　joint　trajectory　asymptotic　tracking　under　the　condition　of　unknown　payload　parameters.　Because　of　introduction　of　the　flexibility　compensation　technique,　the　presented　control　scheme　can　equivalently　increase　the　joint　stiffness,　and　it　is　suitable　to　control　the　space　robot　systems　with　low　joint　stiffness.　Moreover,　the　effect　of　unknown　parameters　is　real-time　compensated　by　its　adaptive　controller,　and　then　the　specified　joint　motion　task　is　achieved　precisely.　The　effectiveness　of　the　scheme　is　verified　by　the　corresponding　simulation　results.