Geometric PID Control for Almost-Global Stabilization of a Quadrotor With Parameter Error and Constant Disturbances

Intrinsic controllers are invariant under the coordinates used for their representation. In the case of rigid-body motion in two and three dimensions, the intrinsic approach eliminates problems with singularity or over-parametrization that may occur in specific choices such as Euler angles or quaternions. Intrinsic PD controllers that combine almost-global stabilization with a familiar and intuitive PD design framework have been known for several years. In this paper we show how intrinsic integral action may be added to intrinsic PD control. We apply the result to stabilize the attitude of a quadrotor UAV model, and demonstrate in simulation that performance is significantly improved in the presence of parameter uncertainty and constant disturbance forces. We also consider the effect of bounded, time-varying, disturbances.