A Sliced Learning Framework for Online Disturbance Identification in Quadrotor SO(3) Attitude Control

TL;DR

Sliced Learning is among the first frameworks to demonstrate lightweight online neural adaptation at 400 Hz on resource-constrained microcontroller units (MCUs) with real-world experimental validation, and proves exponential convergence despite time-varying disturbances and inertia uncertainties.

Abstract

This paper introduces a dimension-decomposed geometric learning framework called Sliced Learning for disturbance identification in quadrotor geometric attitude control. Instead of conventional learning-from-states, this framework adopts a learning-from-error strategy by using the Lie-algebraic error representation as the input feature, enabling axis-wise space decomposition (``slicing") while preserving the SO(3) structure. This is highly consistent with the geometric mechanism of cognitive control observed in neuroscience, where neural systems organize adaptive representations within structured subspaces to enable cognitive flexibility and efficiency. Based on this framework, we develop a lightweight and structurally interpretable Sliced Adaptive-Neuro Mapping (SANM) module. The high-dimensional mapping for online identification is axially ``sliced" into multiple low-dimensional submappings (``slices"), implemented by shallow neural networks and adaptive laws. These neural networks and adaptive laws are updated online via Lyapunov-based adaptation within their respective shared subspaces. To enhance interpretability, we prove exponential convergence despite time-varying disturbances and inertia uncertainties. To our knowledge, Sliced Learning is among the first frameworks to demonstrate lightweight online neural adaptation at 400 Hz on resource-constrained microcontroller units (MCUs), such as STM32, with real-world experimental validation.

Figures (15)

• Figure 1: Quadrotor under time-varying disturbances and unknown inertia.
• Figure 2: The structure of Sliced Adaptive-Neuro Mapping (SANM) module. The high-dimensional mapping for disturbance and uncertainty identification is axially "sliced" into multiple low-dimensional submappings ("slices"). This module is a clear embodiment of the proposed Sliced Learning paradigm. Each "slice" learns directly from the geometric error representation induced on $\mathfrak{so}(3)$, thereby preserving the $\mathbf{SO}(3)$ structure while decomposing high-dimensional features into low-dimensional, axis-wise "slices". This yields independent and parallel online neural adaptation, and the axis-aligned subspace structure enables direct subspace sharing with other adaptive mechanisms, which in turn provides strong modularity and extensibility.
• Figure 3: The architecture of the SANM-augmented geometric attitude control system based on Sliced Learning. The SANM module serves as a feedforward compensator for the geometric attitude controller.
• Figure 4: Experiment 1- Numerical validation of the almost-global attractiveness and local exponential convergence. (a) During large-error convergence, increasing the bound of the network weights ($\overset{\tiny \text{max}}{W}_{j}$) tends to slow down the convergence process. (b) Near the equilibrium, higher learning rates ($\gamma_{\bm{\textit{R}}j}$) yield superior disturbance rejection performance.
• Figure 5: Experiment 2-Attitude tracking experiments under realistic wind disturbances. Three benchmark geometric controllers (baseline PD 2011 Geometric tracking control of the attitude dynamics of a rigid body on SO(3), PID 2013 Geometric nonlinear PID control of a quadrotor UAV on SE(3), and $\mathcal{L}_1\,\mathrm{Quad}$2025 L1Adaptive Augmentation of Geometric Control for Agile Quadrotors With Performance Guarantees) are included for comparison. Four SANM variants v1, v2, v3, v4 are further included as ablation groups, where the adaptive law "slices" are disabled to evaluate the neural-network-only (NN-only) mode. v1, v2 and v3 share the same learning rates $\{\gamma_{\bm{\textit{R}}j}\}_{j=1,2,3}\!:=\!\{35,35,10\}$ but use 3, 9, and 7 RBF neurons, respectively, yielding different RBF coverage densities under identical widths. v4 adopts the same 7-neuron structure as v3 but increases the learning rates to $\{120,120,50\}$ to examine their effect on the residual error ball size.