Robust Nonlinear Control for Exact-time Stability of a Quadrotor UAV under Uncertainties

In this paper, we address the orientation-tracking problem of a quadrotor in the presence of inherent uncertainties and exogenous disturbances. We first present the Newton-Euler formulation-based mathematical model of a quadrotor whose inertia matrix is only partially known due to several reasons, including limited manufacturing accuracy. We also account for any disturbances that may be exogenous but unknown to the quadrotor system by treating them as a single lumped uncertain parameter whose upper bound can be identified. To mitigate the effects of uncertainties, we design robust nonlinear controllers for the quadrotor's orientation-tracking, where the time of error convergence is predefined during design. Then, we rigorously prove the exact-time stability and the convergence properties of the dual-layer sliding manifold used in the controller design. The proposed design is further simplified by making use of almost the same design parameters for roll, pitch, and yaw tracking controllers. Numerical simulations validate the proposed claims.