In　this　paper,　a　robust　control　strategy　with　a　cascade　structure　is　designed　for　the　underactuated　unmanned　aerial　manipulator　(UAM)　to　perform　favorable　trajectory　tracking,　in　the　presence　of　model　uncertainties　and　time-varying　external　disturbances　(e.g.　wind　drag).　In　the　position　loop,　a　geometric　distance　is　adopted　as　the　criterion　for　the　thrust　design.　Besides,　both　the　model　uncertainties　and　external　disturbances　are　compensated　by　employing　a　robust　term.　In　the　attitude　loop,　the　prescribed　performance　guarantees　are　enforced　in　the　controller　design　to　standardize　transient　performance　on　attitude　errors.　In　particular,　just　relying　on　the　necessary　feedback　states,　an　auxiliary　system,　the　adaptive　control　technique,　and　the　disturbance　observer　are　respectively　designed　to　estimate　the　model　uncertainties　and　external　disturbances.　Through　the　Lyapunov　stability　theory　analysis,　the　proposed　approach　based　on　a　geometric　distance　can　effectively　track　the　desired　trajectory.　The　results　of　the　comparative　simulations　study　demonstrate　the　effectiveness　and　advantages　of　the　proposed　approach.　©　2021　ISA