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A new nonlinear tracking controller is presented for an underactuated quadrotor unmanned aerial vehicle (UAV) in this paper. The vehicle is subject to parametric uncertainties. A continuous nonlinear robust control design is combined with an on-line parameter estimation scheme to develop the control law. A Lyapunov based stability analysis is utilized to prove that asymptotic tracking of the quadrotor UAV's position and regulation of yaw orientation are achieved under parametric uncertainties. Compared with sliding mode based control approaches, the proposed control design in this paper is free of chattering. Numerical simulation results of a 6 DOF quadrotor UAV model are included to demonstrate the good tracking performance of the proposed control strategy.