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An adaptive position-tracking control scheme is proposed for vertical take-off and landing (VTOL) unmanned airborne vehicles (UAVs) for a set of bounded external disturbances. The control design is achieved in three main steps. The first step is devoted to the design of an a priori bounded linear acceleration driving the translational dynamics toward the desired trajectory. In the second step, we extract the required a priori bounded thrust and the desired attitude, in terms of unit quaternion, from the desired acceleration derived in the first step. In the last step, we design the required torque for the rotational dynamics, allowing the system's attitude to be driven toward the desired attitude obtained at the second step. Two control laws for the system control torque are rigorously designed. The first control law ensures that the position-tracking objective is satisfied for any initial conditions, whereas the second ensures that the tracking objective is satisfied for a set of initial conditions, which is dependant on the control gains. The latter case is included, since it is less complicated than the former control law and may be advantageous from a practical point of view. Finally, simulation results are provided to illustrate the effectiveness of the proposed control strategy.