This paper considers about the control problem for an underactuated quadrotor UAV system with model parameter uncertainty. Backstepping based techniques are utilized to design a nonlinear adaptive controller which can compensate for the mass uncertainty of the vehicle. Lyapunov based stability analysis shows that the proposed control design yields asymptotic tracking for the UAV's motion in x, y, z direction and the yaw rotation, while keep the stability of the closed loop dynamics of the quadrotor UAV. Numerical simulation results are provided to show the good tracking performance of proposed control laws. I. INTRODUCTIONThe automatic control of a quadrotor UAV is not a straight on mainly due to its underactuated properties [1]. The dynamic model of quadrotor UAV has six degree-of-freedom (DOF) with only four independent thrust forces generated by four rotors. It is difficult to control all these six outputs with only four control inputs. Moreover, uncertainties associate with dynamic model also bring more challenge for control design. Different strategies have been proposed to deal with uncertain quadrotor model, such as adaptive control, neural network based control, sliding mode control, H ∞ control and so on. In [2], a direct adaptive control algorithm was designed for the tracking control of a quadrotor UAV's roll, pitch, yaw angles, together with altitude while compensating for the model parameter uncertainties. A reference system corresponding to a virtual UAV which contains a third order oscillator was utilized to track the desired trajectory. In [3], a backstepping based approach was used for quadrotor UAV control, while two neural networks were used to approximate the uncertain aerodynamic components. By dividing the quadrotor's dynamic model into an underactuated subsystem and a full actuated system, [4] designed a sliding mode controller for the underactuated system and a bounded PID controller for the full actuated system, these two controller drove the UAV to reach a desired position with a desired yaw angle while keep roll and pitch angles zero. More literature review for quadrotor UAV control can be found in [5].One of the main parameter uncertainties associated with the quadoror UAV's dynamic model is the unknown mass

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