The　robust　control　problem　of　a　free-floating　flexible-joint　space　robot　with　an　uncontrolled　base　to　track　the　desired　trajectory　in　workspace　is　discussed.　With　the　system　linear　and　angular　momentum　conservation　and　Lagrangian　method,　the　dynamic　equations　are　derived.　In　the　consideration　of　the　strong　joint　flexibility　of　a　space　robot,　a　joint　flexibility　compensation　controller　is　designed　to　compensate　the　effects　of　the　joint　flexibility　to　the　system　control　precision.　Then　by　using　of　the　singular　perturbation　technology,　a　robust　control　scheme　for　the　robot　system　with　uncertain　inertial　parameters　to　track　the　desired　trajectory　in　workspace　is　presented.　A　planar　space　robot　system　with　flexible　joints　is　simulated　to　verify　the　effectiveness　of　the　proposed　control　method.