This　paper　aims　at　the　stable　motion　control　problem　of　the　unmanned　aerial　manipulator　(UAM)　with　internal　interactions　and　external　environment　disturbances,　and　proposes　a　robust　observer-based　trajectory　tracking　control　framework.　Considering　the　large-dimensional　nonlinearity　and　underactuated　of　UAM　dynamics,　a　separate　control　scheme　is　adopted,　including　a　geometric　controller　for　quadrotor　UAV　and　prescribed　performance　control　(PPC)　method　for　onboard　active　manipulator　(OAM).　In　particular,　an　observer-based　geometric　control　scheme　is　developed　for　the　position　and　attitude　tracking　of　the　quadrotor　UAV　to　ensure　steady　flight,　where　the　quadrotor　UAV　attitude　is　represented　by　the　rotation　matrix　to　eliminate　singularities　or　ambiguities.　Subsequently,　an　observer-based　PPC　method　is　presented　for　the　OAM　to　guarantee　the　prescribed　transient　and　steady-state　performance　responses.　Finally,　the　simulation　comparisons　and　experimental　study　validate　the　effectiveness　and　performances　of　the　proposed　control　framework.