The　control　problem　of　free-floating　space　manipulator　system　was　discussed,　and　the　kinematics　and　dynamics　of　the　system　were　analyzed.　It　is　shown　that　the　Jacobi　matrix　and　the　dynamic　equations　of　the　system　are　nonlinearly　dependent　on　inertial　parameters.　By　use　of　the　idea　of　augmentation　approach,　it　is　verified　that　the　augmented　generalized　Jacobi　matrix　and　the　dynamic　equations　of　the　system　can　be　linearly　dependent　on　a　group　of　inertial　parameters.　Based　on　the　results,　the　robust　and　adaptive　composite　control　scheme　for　free-floating　space　manipulator　system　with　uncertain　inertial　parameters　to　track　the　desired　trajectory　in　inertia　space　was　proposed,　and　a　two-link　planar　space　manipulator　system　was　simulated　to　verify　the　proposed　control　scheme.