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This article presents an extended state observer for vehicle modeled as arigid body in three-dimensional translational and rotational motions. Theextended state observer is applicable to a rotorcraft aerial vehicle with afixed plane of rotors, modeled as an under-actuated system on the tangentbundle of the six-dimensional Lie group of rigid body motions, SE(3). Theextended state observer is designed to estimate the resultant externaldisturbance force and disturbance torque acting on the vehicle. It guaranteesstable convergence of disturbance estimation errors in finite time when thedisturbances are constant and finite time convergence to a bounded neighborhoodof zero errors for time-varying disturbances. This extended state observerdesign is based on a H\"{o}lder-continuous fast finite time stabledifferentiator that is similar to the super-twisting algorithm, to obtain fastconvergence. Numerical simulations are conducted to validate the proposedextended state observer. The proposed extended state observer is compared withother existing research to show its advantages. A set of experimental resultsimplementing disturbance rejection control using feedback of disturbanceestimates from the extended state observer is also presented.

Geometric Extended State Observer on SE(3) with Fast Finite-Time Stability: Theory and Validation on a Rotorcraft Aerial Vehicle