Revisiting Euler-Angle Regression with Kolmogorov-Arnold Networks

2026-07-10

AI Summary

This work addresses the instability in Euler angle regression caused by angular discontinuities and singularities, which particularly degrades performance in bounded rotation modeling tasks such as joint-space representation. For the first time, Kolmogorov–Arnold Networks (KANs) are introduced to this problem, combined with range-aware Euler angle modeling. The authors demonstrate that regression functions over bounded angular intervals exhibit an approximately additive structure, enabling the design of a more suitable network architecture. By replacing conventional fixed activation functions with KAN’s learnable spline-based edge functions, the proposed method significantly enhances approximation capability. Empirical evaluations across rotation regression, object pose estimation, and inverse kinematics for both robotic and human articulation consistently show marked improvements in accuracy, convergence speed, and computational efficiency.

Abstract

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.

Problem

• Euler-angle regression
• rotation representation
• discontinuities
• singularities
• bounded ranges

Innovation

• Euler-angle regression
• Kolmogorov-Arnold Networks
• range-aware modeling
• additive function approximation
• inverse kinematics