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This study gives the mathematic model of a quadrotor unmanned aerial vehicle (UAV) and then proposes a robust nonlinear controller which combines the sliding-mode control technique and the backstepping control technique. To achieve Cartesian position trajectory tracking capability, the construction of the controller can be divided into two stages: a regular SMC controller for attitude subsystem (inner loop) is first developed to guarantee fast convergence rapidity of Euler angles and the backstepping technique is applied to the position loop until desired attitudes are obtained and then the ultimate control laws. The stability of the closed-loop system is guaranteed by stabilizing each of the subsystems step by step and the robustness of the controller against model uncertainty and external disturbances is investigated. In addition, an adaptive observer-based fault estimation scheme is also considered for taking off mode. Simulations are conducted to demonstrate the effectiveness of the designed robust nonlinear controller and the fault estimation scheme. [ABSTRACT FROM PUBLISHER]