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.

翻译：本文提出了一种称为切片学习的维度分解几何学习框架，用于四旋翼几何姿态控制中的扰动识别。该框架摒弃传统的状态学习策略，转而采用误差学习策略，以李代数误差表示作为输入特征，在保持SO(3)结构的同时实现轴向空间分解（“切片”）。这与神经科学中观察到的认知控制几何机制高度一致——神经系统在结构化子空间内组织自适应表征以实现认知灵活性与效率。基于此框架，我们开发了一个轻量化且结构可解释的切片自适应神经映射（SANM）模块。在线识别所需的高维映射被轴向“切片”为多个低维子映射（“切片”），由浅层神经网络和自适应律实现。这些神经网络与自适应律通过各自共享子空间内基于李雅普诺夫的适应机制进行在线更新。为增强可解释性，我们证明了在时变扰动和转动惯量不确定性条件下仍能实现指数收敛。据我们所知，切片学习是首批能在资源受限微控制器单元（如STM32）上以400赫兹频率实现轻量化在线神经自适应、并经过真实实验验证的框架之一。