A Global Tracking Controller for Underactuated Aerial Vehicles: Design, Analysis, and Experimental Tests on Quadrotor

This paper investigates the global tracking control of underactuated aerial vehicles. In particular, the globally exponentially stable attitude tracking controller serving as the inner loop of the overall controller is investigated. It can avoid the common problems that may be accompanied by other attitude controllers, such as singularity and unwinding. In order to overcome the topological obstacles of global control on $SO(3)$, rotational motion of a rigid body is expressed in the exponential coordinate restricted in a compact domain. We then construct a hybrid tracking error dynamics whose states are all represented in Euclidean space. The geometric properties of the state space are mathematically analyzed. The tracking controller of underactuated aerial vehicles is, thus, designed based on the hybrid tracking error dynamics. The global exponential stability of the closed-loop attitude subsystem, as well as the global asymptotical stability of the closed-loop overall system under assumptions, is analyzed using Lyapunov's method strictly. These properties are demonstrated by simulation results. The proposed controller is also implemented and tested on our self-developed quadrotor, showing the feasibility of the controller in realtime applications.