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

arXiv: https://arxiv.org/abs/1304.6765 · HTML: https://mlsanity.com/paper/1304.6765/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2013.

## Built on by (most cited first, 3 of 3)

- [Optimal Potential Shaping on SE(3) via Neural ODEs on Lie Groups](https://mlsanity.com/paper/2401.15107/) (2024)
- [Maintaining Plasticity in Reinforcement Learning: A Cost-Aware Framework for Aerial Robot Control in Non-stationary Environments](https://mlsanity.com/paper/2503.00282/) (2025)
- [Fly-by-Code: Embodied Coding Agents for Aerial Manipulation with Active Visual and Physical Feedback](https://mlsanity.com/paper/2610.12549/) (2026)

## Abstract (arXiv)

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.