Quasi-Static Fault-Tolerant Feedback Control of a Quadrotor under Rotor Failure with Provable Safety Guarantees

Abstract

This paper presents a nonlinear control law for a quadrotor unmanned aerial vehicle (UAV) under single-rotor failure that guarantees set stabilization via quasi-static feedback (QSF). Given a geometric curve in three-dimensional space, we characterize and stabilize the zero-dynamics manifold, also known as the path-following manifold, which represents all feasible motions along the path. Stabilizing this manifold ensures path-invariance: a UAV with a failed rotor initialized on the path with an appropriate orientation remains on the path for all future time. Furthermore, local exponential convergence to the manifold is guaranteed under certain conditions, implying that, under the stated assumptions, rotor failure during flight does not cause transverse deviation from the path. The proposed controller thus provides theoretical safety guarantees, which are validated through numerical experiments in the Drake physics-based simulation engine. The code is publicly available at https://gradslab.github.io/quasistatic-ftc/.