This　article　presents　a　trajectory　tracking　control　method　for　the　unmanned　aerial　manipulator　robot　system　(UAMRS)　under　model　uncertainty　and　unknown　disturbances.　More　specifically,　a　low-complexity　prescribed　performance　controller　is　proposed　to　effectively　reduce　the　design　complexity　and　achieve　the　prescribed　transient　and　steady-state　performance.　First,　the　dynamics　model　of　the　UAMRS　is　analyzed　and　modeled,　where　the　unmeasured　internal　interaction　generated　by　the　coupling　effect　and　the　random　environmental　disturbances　are　considered　simultaneously.　Then,　utilizing　the　property　of　prescribed　performance,　the　UAMRS　with　model　uncertainty　and　external　disturbances　can　guarantee　preferable　trajectory　tracking　responses,　where　the　nonlinear　disturbance　observer　is　used　to　estimate　and　compensate　uncertainties　and　external　disturbances.　Moreover,　the　proposed　controller　defined　by　simple　expressions　does　not　require　accurate　knowledge　of　the　UAMRS,　which　is　of　low　complexity　and　can　effectively　reduce　the　amount　of　calculation.　The　stability　of　the　proposed　controller　is　analyzed.　Finally,　the　performances　of　the　proposed　scheme　are　demonstrated　by　the　numerical　simulation　comparisons　and　real-world　experiments,　where　a　quadrotor　with　a　3-DOF　onboard　active　manipulator　is　adopted　in　outdoor　experimental　validations.