发表机构
Michigan State University（密歇根州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究欧拉角回归难题，提出结合范围感知欧拉建模与柯尔莫哥洛夫 - 阿诺德网络的新框架，经理论分析和实验验证，该框架在控制旋转回归等多方面能提升精度、收敛性和效率。
AI 中文摘要
在许多现实世界系统中，如关节机器人和生物力学模型，旋转在关节空间中定义并由有界范围的欧拉角自然参数化。然而，回归欧拉角仍具挑战性，因其不连续性和奇异性常使训练不稳定。本文重新审视欧拉角回归，表明其有效性关键取决于旋转表示、回归架构和域约束间的相互作用。引入新框架，将范围感知欧拉建模与柯尔莫哥洛夫 - 阿诺德网络（KAN）结合，KAN用可学习单变量函数取代固定节点激活。理论分析表明有界欧拉范围促使回归函数具有近加性结构，有利于KAN的加性函数形式，实验也证实了这一趋势。在控制旋转回归、物体姿态估计及机器人和人类逆运动学上的大量实验表明在精度、收敛性和效率上有持续改进。代码将公开。
英文摘要
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.
