Physics-informed Machine Learning for Static Friction Modeling in Robotic Manipulators Based on Kolmogorov-Arnold Networks

TL;DR

This work addresses the challenge of static friction modeling in robotic manipulators by learning physically interpretable friction laws directly from data. It introduces Kolmogorov–Arnold Networks (KAN) with spline-based, B-spline activations, multiplicative interactions, and residual paths, combined with pruning and symbolic regression to yield compact, symbolic friction expressions. Across synthetic and real six-DOF manipulator data, the method achieves $R^{2}$ values above $0.95$ and demonstrates strong generalization from single-axis to multi-axis scenarios, as well as robust performance under noise. The approach bridges data-driven learning with physical interpretability, enabling deployable friction models for high-precision robotic control and opening paths for real-time friction compensation and broader physics-informed modeling in robotics.

Abstract

Friction modeling plays a crucial role in achieving high-precision motion control in robotic operating systems. Traditional static friction models (such as the Stribeck model) are widely used due to their simple forms; however, they typically require predefined functional assumptions, which poses significant challenges when dealing with unknown functional structures. To address this issue, this paper proposes a physics-inspired machine learning approach based on the Kolmogorov Arnold Network (KAN) for static friction modeling of robotic joints. The method integrates spline activation functions with a symbolic regression mechanism, enabling model simplification and physical expression extraction through pruning and attribute scoring, while maintaining both high prediction accuracy and interpretability. We first validate the method's capability to accurately identify key parameters under known functional models, and further demonstrate its robustness and generalization ability under conditions with unknown functional structures and noisy data. Experiments conducted on both synthetic data and real friction data collected from a six-degree-of-freedom industrial manipulator show that the proposed method achieves a coefficient of determination greater than 0.95 across various tasks and successfully extracts concise and physically meaningful friction expressions. This study provides a new perspective for interpretable and data-driven robotic friction modeling with promising engineering applicability.

Figures (16)

• Figure 1: Classical static friction models, where velocity denotes tangential relative motion: (a) classical Coulomb model coulomb1781theorie, (b) Coulomb model with static friction, (c) Coulomb model with viscous term, (d) Stribeck model without viscosity, (e) smoothed Bengisu–Akay model bengisu1994stability, (f) Awrejcewicz envelope model, with the gray line showing the model’s envelope range awrejcewicz2008404.
• Figure 2: The Stribeck effect: (a) schematic illustration of the Stribeck curve, showing boundary, mixed, and hydrodynamic lubrication regimes he2017experimental; (b) velocity–friction predictions of the static Stribeck-type model.
• Figure 3: Schematic of KAN-based friction model identification, consisting of six steps: (1) collection of friction data by robotic engineers, (2) initialization of the KAN network, (3) model fitting with KAN, (4) pruning followed by refitting, (5) symbolic regression and subsequent refitting, and (6) derivation of the final friction model.
• Figure 4: Comparison between the original $\mathrm{sign}$ and the smoothed $\tanh$ in the Stribeck static friction model.
• Figure 5: Predictions of the friction torque model across six axes. The coefficient of determination $R^{2}$ is used as the regression metric.