GOB: Geometric Observer on SO(3) for Disturbance Observation

The disturbance rejection problem of aerial vehicles is a widely concerned issue. For attitude dynamics, we propose a method for directly designing a geometric observer (GOB) based on the special orthogonal group SO(3), thus reducing the impact of model mismatch and being unrestricted by the aircraft attitude. Considering the type of measurement available, we have developed two GOBs: GOB-I, which uses both attitude and angular velocity measurements, and GOB-II, which uses only attitude measurement. The stability of GOB is theoretically proved, with the GOB-I exhibiting almost global asymptotic stability and the GOB-II demonstrating local asymptotic stability. We have compared the estimation performance of our proposed GOB with four other disturbance observers (DOBs) for five types of disturbances. The simulation results show that, in the small attitude scenarios, our proposed GOB-I observer performs comparably with the compensation function observer (CFO) and the nonlinear disturbance observer (NDOB) that use both attitude and angular velocity measurements, while the GOB-II performs comparably with the extended state observer (ESO) that uses only attitude measurements. In the agile attitude scenarios, our proposed GOB-I observer significantly outperforms CFO and NDOB, and GOB-II also performs much better than ESO. Compared with the reduced-order observer, which uses only angular velocity measurement, the GOB-I can handle more complex disturbances and provides compensation for sensor errors. Flight experiments conducted with a lifting-wing quadcopter demonstrate the efficiency of our method in resisting unknown payload in hover flight and model uncertainty in agile maneuver.