Almost Global Trajectory Tracking for Quadrotors Using Thrust Direction Control on S2

Many of the existing works on quadrotor control address the trajectory tracking problem by employing a cascade design in which the translational and rotational dynamics are stabilized by two separate controllers. The stability of the cascade is often proved by employing trajectory-based arguments, most notably, integral input-to-state stability. In this paper, we follow a different route and present a control law ensuring that a composite function constructed from the translational and rotational tracking errors is a Lyapunov function for the closed-loop cascade. In particular, starting from a generic control law for the double integrator, we develop a suitable attitude control extension, by leveraging a backstepping-like procedure. Using this construction, we provide an almost global stability certificate. The proposed design employs the unit sphere S2 to describe the rotational degrees of freedom required for position control. This enables a simpler controller tuning and an improved tracking performance with respect to previous global solutions. The new design is demonstrated via numerical simulations and on real-world experiments.