用可学习函数网络提升欧拉角回归的稳定性和精度
Revisiting Euler-Angle Regression with Kolmogorov-Arnold Networks
- 结合范围感知欧拉角建模与可学习函数网络（KAN）
- 在旋转回归、姿态估计等任务中准确率与收敛速度显著提升
- 特别适合关节空间中的机器人/生物力学系统建模
在众多现实系统中，如关节型机器人和生物力学模型，旋转通常以关节空间定义，并自然地通过有界范围的欧拉角参数化。然而，欧拉角的不连续性和奇点常导致训练不稳定。本文重新审视欧拉角回归，发现其效果关键取决于旋转表示、回归架构与领域约束之间的相互作用。我们提出一种新框架，将范围感知的欧拉角建模与科尔莫戈罗夫-阿诺尔德网络（KAN）结合，后者以可学习的一元函数替代传统固定激活函数。理论分析表明，有界欧拉角范围促使回归函数呈现近加性结构，有利于KAN的加性函数形式；实验验证了该趋势。在受控旋转回归、物体姿态估计、机器人与人体逆运动学任务上的大量实验表明，本方法在准确性、收敛性和效率上均有持续提升。代码将公开。
原文摘要 · Abstract (English)
In many real-world systems, including articulated robots and biomechanical models, rotations are defined in joint space and naturally parameterized by Euler angles with bounded ranges. Yet regressing Euler angles remains challenging, as their discontinuities and singularities often destabilize training. In this work, we revisit Euler-angle regression and show that its effectiveness depends critically on the interaction between rotation representation, regression architecture, and domain constraints. We introduce a new framework that combines range-aware Euler modeling with Kolmogorov-Arnold Networks (KAN), which replace fixed node-wise activations with learnable univariate functions on edges. We further provide theoretical analysis indicating that bounded Euler ranges motivate a near-additive structure in the regression function, which favors the additive functional form of KAN, and we confirm this trend empirically. Extensive experiments on controlled rotation regression, object pose estimation, and robotic and human inverse kinematics demonstrate consistent improvements in accuracy, convergence, and efficiency. The code will be publicly available.
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