Geometric Extended State Observer on SE(3) with Fast Finite-Time Stability: Theory and Validation on a Rotorcraft Aerial Vehicle
This article presents an extended state observer for vehicle modeled as a rigid body in three-dimensional translational and rotational motions. The extended state observer is applicable to a rotorcraft aerial vehicle with a fixed plane of rotors, modeled as an under-actuated 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. Numerical simulations are conducted to validate the proposed extended state observer. The proposed extended state observer is compared with other existing research to show its advantages. A set of experimental results implementing disturbance rejection control using feedback of disturbance estimates from the extended state observer is also presented.