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

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.

💡 Research Summary

The paper proposes a novel “Sliced Learning” framework for online disturbance identification in geometric SO(3) attitude control of quadrotors. Traditional learning‑from‑states approaches either use Euler angles (which suffer from singularities) or quaternions (which have double‑coverage issues) and typically rely on high‑dimensional multilayer perceptrons or deep neural networks. These methods break the intrinsic SO(3) geometry, are computationally heavy, and provide little theoretical guarantee.

The authors instead use the Lie‑algebraic error representation—specifically the attitude error (e_R = \frac12(R_d^\top R - R^\top R_d)^\vee) and angular‑velocity error (e_\Omega = \Omega - R^\top R_d \Omega_d)—as the input to the learning system. Because these errors live in the tangent space (\mathfrak{so}(3) \cong \mathbb{R}^3), they can be decomposed axis‑wise into three one‑dimensional subspaces. The high‑dimensional mapping from desired moment, inertia, and unknown disturbance to the error vector is assumed to have a locally existing pseudo‑inverse (S^\dagger). Crucially, the authors hypothesize that this pseudo‑inverse can be “sliceable,” i.e., expressed as a sum of three independent sub‑mappings (S_j^\dagger(e_R