This paper presents the development of a fully non-linear quadrotor aircraft simulator together with a non-linear control system design methodology which stabilizes the system and is robust to a class of measurement errors. The focus of this work is on design of a robust nonlinear Backstepping control system capable of handling some of the disturbances modeled in the simulator. The controller synthesis is performed into two steps: first a nominal controller is designed for attitude stabilization, then measurement disturbances are introduced in the design; as second step, the control laws are redesigned, so that, given bounds on the maximum absolute values of the measurement disturbances, the closed-loop system is robustly stable and the maximum absolute values of steady state tracking error fall within a desired bound. The new control laws are shown to Practically Asymptotically Stabilize the system, and to bring the tracking error inside an area of the state space of desired dimensions; furthermore, bounds on the control gains, which ensure convergence and stability, are derived. The new control laws were extensively tested with the simulator and yielded the desired bounds on the tracking error. An outer loop controller for position control was designed as well, in order to be able to test the overall system. Simulation results are presented.