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In this paper, a nonlinear adaptive regulation controller is presented for a class of underactuated quadrotor unmanned aerial vehicle (UAV). The vehicle's dynamics is subject to modeling impression associated with the inertia matrix, aerodynamic damping coefficients, and some other system parameters. The on-line parameter estimation scheme is combined with feedback control to develop the adaptive control laws. Lyapunov based approaches are utilized to prove that the quadrotor UAV's position and yaw angle regulation errors are ultimately driven to zero under parametric uncertainties. Simulation results are included to demonstrate the performance of the control strategy.