Geometric Active Disturbance Rejection Control of Rotorcraft on $SE(3)$ with Fast Finite-Time Stability

Abstract: This article presents a tracking control framework enhanced by an extended state observer for a rotorcraft aerial vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The system is considered as an underactuated system on the tangent bundle of the six-dimensional Lie group of rigid body motions, $SE(3)$. The extended state observer is designed to estimate the resultant external disturbance force and disturbance torque acting on the vehicle. It guarantees stable convergence of disturbance estimation errors in finite time when the disturbances are constant and finite time convergence to a bounded neighborhood of zero errors for time-varying disturbances. This extended state observer design is based on a H\"{o}lder-continuous fast finite time stable differentiator that is similar to the super-twisting algorithm, to obtain fast convergence. A tracking control scheme that uses the estimated disturbances from extended state observer for disturbance rejection, is designed to achieve fast finite-time stable tracking control. Numerical simulations are conducted to validate the proposed extended state observer and tracking control scheme with disturbance rejection. The proposed extended state observer is compared with other existing research to show its supremacy.