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Multirotor aerial vehicles are versatile flying robots that perform hovering, vertical take-off and landing, and aggressive maneuvers in a 3D environment. Due to their underactuated nature, the aerial vehicles' position and orientation cannot be controlled independently. For this reason, most of the quadrotors' tasks involved position tracking or regulation tasks. This paper focuses on the position-tracking problem of quadrotors using the reduced orientation of the vehicle, meaning that only two degrees of freedom of the robot's orientation are controlled. We propose an almost global exponential reduced attitude control law that aligns the aerial robot's thrust direction with the desired force that drives the robot along the desired position trajectory. For the translational subsystem, we propose a dynamic control law that drives the position and velocity of the quadrotors asymptotically to the desired trajectories. The proposed attitude control law is computationally simple, and thus, it is suitable to run on board. Finally, we provide experimental results performed on a low-cost quadrotor and a comparison study with a full-attitude controller to illustrate the performance and advantages of the proposed control laws. • Position trajectory tracking is achieved by properly controlling the quadrotor's reduced attitude. • The proposed reduced attitude control law guarantees almost global exponential stability. • The position controller generates a bounded signal and guarantees asymptotic tracking of the reference signals. • The effectiveness of the proposed feedback control laws was successfully validated by real-time experiments. [ABSTRACT FROM AUTHOR]