Geometric Nonlinear PID Control of a Quadrotor UAV on SE(3)

TL;DR

This paper introduces a geometric nonlinear PID control approach for quadrotor UAVs on SE(3), ensuring stability and avoiding singularities, with theoretical proofs and practical demonstrations.

Contribution

It develops a novel geometric nonlinear PID control method directly on SE(3), incorporating integral terms for robustness against uncertainties, with rigorous stability analysis.

Findings

Achieved almost global asymptotic stability.

Successfully demonstrated complex maneuvers in simulations.

Provided preliminary experimental validation.

Abstract

Nonlinear PID control systems for a quadrotor UAV are proposed to follow an attitude tracking command and a position tracking command. The control systems are developed directly on the special Euclidean group to avoid singularities of minimal attitude representations or ambiguity of quaternions. A new form of integral control terms is proposed to guarantee almost global asymptotic stability when there exist uncertainties in the quadrotor dynamics. A rigorous mathematical proof is given. Numerical example illustrating a complex maneuver, and a preliminary experimental result are provided.