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The real-time unknown parameter estimation and adaptive tracking control problems are investigated in this paper for a six degrees of freedom (6-DOF) of under-actuated quadrotor unmanned aerial vehicle (UAV). A virtual proportional derivative (PD) controller is designed to maintain the translational dynamics. Two adaptive schemes are developed to handle the attitude dynamics of the UAV with several unknown parameters. In the beginning, a classical adaptive scheme (CAS) using the certainty equivalence principle is proposed and designed. The idea is to design a controller for an ideal situation by assuming the unknown parameters were known. Then the unknown parameters are replaced by their estimation. A theoretical analysis is provided to ensure the trajectory tracking of the adaptive controller. However, an inherent drawback of this scheme is that there is no guarantee for the estimated parameters to converge to the actual values. To address this issue, a new adaptive scheme (NAS) is developed as the next step by adding a continuously differentiable function to the control structure. The proposed technique guarantees handling of the parametric uncertainties with an appropriate design manifold. A rigorous analytical proof, numerical simulation analyses, and experimental validation are presented to show the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]