Self-Tuning Geometric Control for a Quadrotor UAV Based on Lyapunov Stability Analysis

Abstract

A Lyapunov-based self gain tuning geometric nonlinear controller for a quadrotor UAV has been developed on SE(3) in this paper. By designing an adaptive law with Lyapunov stability analysis for the controller gains, the proposed control system can asymptotically follow an attitude and position command while tuning the PID gains online, and it is extended to guarantee boundedness of tracking errors in the presence of unstructured disturbances. This introduce an unprecedented algorithm to autonomously tune the controller gains without need of extra effort or introducing boundary conditions. Proposed controller considers all the coupling effects between rotational and translational dynamics, and it is developed in a coordinate-free fashion to avoid complexities and ambiguities associated with other attitude representations such as Euler angles or quaternions. The desirable features of the proposed controller are illustrated by numerical simulations and juxtaposed with a well-known offline gain tuning method. The proposed algorithm is ultimately validated with an experimental example.