This dissertation presents several novel robust tracking control schemes of rotorcraft unmanned aerial vehicles under realistic atmospheric turbulence. To achieve fast converging and stable performance of the rotorcraft control scheme, a new H\ {o}lder-continuous differentiator, similar to the super-twisting algorithm used in the second-order sliding model control scheme, is proposed with guaranteed fast finite-time stability. Unlike the super-twisting algorithm, which uses a sliding-mode structure to achieve finite-time stability, the proposed differentiator maintains its fast finite-time stability with H\ {o}lder continuity, theoretically eliminating the harmful chattering phenomenon in practical control applications. Perturbation and noise robustness analyses are conducted for the proposed differentiator. The dissertation formulates the rotorcraft tracking control and disturbance estimation problems separately. The rotorcraft aerial vehicle is modeled as a rigid body with control inputs that actuate all degrees of freedom of rotational motion and only one degree of freedom of translational motion. The motion of the aircraft is globally represented on \TSE, which is the tangent bundle of the special Euclidean group \SE. The translational and attitude control schemes track the desired position and attitude on \SE. The disturbance estimation problem is formulated as an extended states observer on \TSE. Next, two rotorcraft control schemes on \SE with disturbance rejection mechanisms are presented. The proposed disturbance rejection control systems comprise two parts: an extended states observer for disturbance estimation and a tracking control scheme containing the disturbance rejection term to track the trajectory. The first disturbance rejection control scheme comprises an exponentially stable extended states observer and an asymptotically stable tracking control scheme. The second system comprises a fast finite-time stable extended state observer and a fast finite-time stable tracking control scheme. The fast finite-time stable extended state observer uses the \textup{H\ {o}}lder-continuous differentiator to estimate the resultant external disturbance force and disturbance torque acting on the vehicle. It ensures stable convergence of disturbance estimation errors in finite time when the disturbances are constant. Software-in-the-loop simulation is carried out for the active disturbance rejection control scheme with an open-source autopilot and a physics-based simulation tool. The simulation utilizes simulated wind gusts, propeller aerodynamics, actuator limitation, and measurement noise to validate the disturbance rejection control systems in a simulated environment with high fidelity. Two sets of flight experiments are conducted to investigate the autonomous rotorcraft flight control performance under turbulent income flows. A wind tunnel composed of fan arrays is involved in both experiments to provide different turbulent incoming flows by adjusting the duty of individual fans. The first set of experiments conducts income flow measurements for wind tunnel calibration. For the turbulent flows generated by different fan configurations, their steady velocity field and unsteady turbulence characteristics are measured by a pressure scanner and hot-wire anemometer. The second set of experiments involves flight tests of a rotorcraft within the turbulent environment measured and calibrated in the first experiment set. The proposed extended states observer is implemented onto a rotorcraft by customizing an open-source autopilot software. With this implementation, the flight control performance of the proposed disturbance rejection control schemes is presented and compared with the autopilot without customization. The experimental results show that the proposed disturbance rejection control scheme enhanced by the disturbance estimation schem
