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A Dimension-Decomposed Learning Framework for Online Disturbance Identification in Quadrotor SE(3) Control

Tianhua Gao

TL;DR

The paper tackles quadrotor stability under complex disturbances by introducing Dimension-Decomposed Learning (DiD-L) and its SANM instantiation for online disturbance identification on $SE(3)$. SANM decomposes a 12-dimensional disturbance feature into 12 low-dimensional slices, each learned by shallow RBF networks and updated via Lyapunov-based laws, enabling full-state compensation without pre-training or persistent excitation. A rigorous NES (near-exponential stability) guarantee is established for the rotational dynamics and extended to the full dynamics under uncertain mass and inertia, supported by Lyapunov analysis. Real-time Gazebo simulations demonstrate feasibility, highlighting improved interpretability, adaptation speed, and robustness against time-varying disturbances and model uncertainties.

Abstract

Quadrotor stability under complex dynamic disturbances and model uncertainties poses significant challenges. One of them remains the underfitting problem in high-dimensional features, which limits the identification capability of current learning-based methods. To address this, we introduce a new perspective: Dimension-Decomposed Learning (DiD-L), from which we develop the Sliced Adaptive-Neuro Mapping (SANM) approach for geometric control. Specifically, the high-dimensional mapping for 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 tasks addressed by shallow neural networks and adaptive laws. These neural networks and adaptive laws are updated online via Lyapunov-based adaptation without any pre-training or persistent excitation (PE) condition. To enhance the interpretability of the proposed approach, we prove that the full-state closed-loop system exhibits arbitrarily close to exponential stability despite multi-dimensional time-varying disturbances and model uncertainties. This result is novel as it demonstrates exponential convergence without requiring pre-training for unknown disturbances and specific knowledge of the model.

A Dimension-Decomposed Learning Framework for Online Disturbance Identification in Quadrotor SE(3) Control

TL;DR

The paper tackles quadrotor stability under complex disturbances by introducing Dimension-Decomposed Learning (DiD-L) and its SANM instantiation for online disturbance identification on . SANM decomposes a 12-dimensional disturbance feature into 12 low-dimensional slices, each learned by shallow RBF networks and updated via Lyapunov-based laws, enabling full-state compensation without pre-training or persistent excitation. A rigorous NES (near-exponential stability) guarantee is established for the rotational dynamics and extended to the full dynamics under uncertain mass and inertia, supported by Lyapunov analysis. Real-time Gazebo simulations demonstrate feasibility, highlighting improved interpretability, adaptation speed, and robustness against time-varying disturbances and model uncertainties.

Abstract

Quadrotor stability under complex dynamic disturbances and model uncertainties poses significant challenges. One of them remains the underfitting problem in high-dimensional features, which limits the identification capability of current learning-based methods. To address this, we introduce a new perspective: Dimension-Decomposed Learning (DiD-L), from which we develop the Sliced Adaptive-Neuro Mapping (SANM) approach for geometric control. Specifically, the high-dimensional mapping for 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 tasks addressed by shallow neural networks and adaptive laws. These neural networks and adaptive laws are updated online via Lyapunov-based adaptation without any pre-training or persistent excitation (PE) condition. To enhance the interpretability of the proposed approach, we prove that the full-state closed-loop system exhibits arbitrarily close to exponential stability despite multi-dimensional time-varying disturbances and model uncertainties. This result is novel as it demonstrates exponential convergence without requiring pre-training for unknown disturbances and specific knowledge of the model.

Paper Structure

This paper contains 23 sections, 103 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Quadrotor Dynamics with Augmented Disturbance
  4. Control Problem Formulation on $\mathbf{SE}(3)$.
  5. Sliced Adaptive-Neuro Mapping for Geometric Control on $\mathbf{SE}(3)$
  6. Quadrotor Geometric Control on $\mathbf{SE}(3)$
  7. Wrench Controller with Sliced Adaptive-Neuro Mapping
  8. Wrench Controller Design
  9. SANM Design-Adaptive Laws
  10. SANM Design-Shallow Neural Networks (SNN)
  11. Propositions
  12. Conclusion
  13. Error Dynamics
  14. Translational Error Dynamics
  15. Rotational Error Dynamics
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Quadrotor modeling and geometric control on $\mathbf{SE}(3)$. The vectors $\bm{\vec{b}}_{1\bm{d}}$, $\bm{\vec{b}}_{1\bm{c}}$ and $\bm{\vec{b}}_{3\bm{c}}$ are coplanar and form the desired heading plane, while the vectors $\bm{\vec{b}}_{1\bm{c}}$ and $\bm{\vec{b}}_{2\bm{c}}$ are coplanar and form the desired body plane.
  • Figure 2: The structure of Sliced Adaptive-Neuro Mapping (SANM). The 12 slices Correspond to 12-dimensional state, respectivly.
  • Figure 3: The structure of SANM-geometric control strategy.