Dimension-Decomposed Learning for Quadrotor Geometric Attitude Control with Almost Global Exponential Convergence on SO(3)

2025-08-20

AI Summary

To address convergence and robustness challenges in quadrotor geometric attitude control under time-varying disturbances and inertial uncertainties, this paper proposes DiD-L—a lightweight, interpretable online disturbance identification method. DiD-L employs dimensional decomposition to decouple high-dimensional disturbances into multiple low-dimensional sub-mappings, integrating sliced adaptive neural mapping (SANM), shallow neural networks, and a Lyapunov-driven online adaptation mechanism. For the first time on the SO(3) manifold, it achieves almost global exponential convergence without requiring persistent excitation or pretraining. Theoretical analysis guarantees strong adaptability and stability. Implemented on a microcontroller unit (MCU), DiD-L runs in real time at 400 Hz. Experimental validation on a physical quadrotor platform demonstrates its effectiveness in suppressing time-varying disturbances and parametric uncertainties, with attitude errors rapidly converging to an arbitrarily small neighborhood.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper introduces a lightweight and interpretable online learning approach called Dimension-Decomposed Learning (DiD-L) for disturbance identification in quadrotor geometric attitude control. As a module instance of DiD-L, we propose the Sliced Adaptive-Neuro Mapping (SANM). Specifically, to address underlying underfitting problems, the high-dimensional mapping for online identification is axially ``sliced"into multiple low-dimensional submappings (slices). In this way, the complex high-dimensional problem is decomposed into a set of simple low-dimensional subtasks addressed by shallow neural networks and adaptive laws. These neural networks and adaptive laws are updated online via Lyapunov-based adaptation without the persistent excitation (PE) condition. To enhance the interpretability of the proposed approach, we prove that the state solution of the rotational error dynamics exponentially converges into an arbitrarily small ball within an almost global attraction domain, despite time-varying disturbances and inertia uncertainties. This result is novel as it demonstrates exponential convergence without requiring pre-training for unseen disturbances and specific knowledge of the model. To our knowledge in the quadrotor control field, DiD-L is the first online learning approach that is lightweight enough to run in real-time at 400 Hz on microcontroller units (MCUs) such as STM32, and has been validated through real-world experiments.

Problem

• Online disturbance identification for quadrotor attitude control
• Decomposing high-dimensional mapping into low-dimensional subtasks
• Achieving exponential convergence without persistent excitation condition

Innovation

• Sliced Adaptive-Neuro Mapping for disturbance identification
• Lyapunov-based online adaptation without PE condition
• Lightweight real-time execution on microcontroller units