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Interpretable Robotic Friction Learning via Symbolic Regression

Philipp Scholl, Alexander Dietrich, Sebastian Wolf, Jinoh Lee, Alin-Albu Schäffer, Gitta Kutyniok, Maged Iskandar

TL;DR

This work tackles the long-standing challenge of friction torque modeling in robotic joints by employing symbolic regression (SR) to learn interpretable, closed-form friction expressions from data collected on a KUKA LWR-IV+ robot. It compares three SR families—genetic-programming SR (PySR), continuous-optimization SR (ParFam), and neural-network–driven SR (uDSR)—and demonstrates that SR formulas can outperform traditional model-based friction models while remaining interpretable. The study shows SR formulas can incorporate load dependencies and external torque effects, enabling accurate joint torque estimation and external-torque inference in multi-joint motion. Overall, the approach provides robust, transparent friction models suitable for safety-critical robot control and human–robot interaction, without sacrificing accuracy.

Abstract

Accurately modeling the friction torque in robotic joints has long been challenging due to the request for a robust mathematical description. Traditional model-based approaches are often labor-intensive, requiring extensive experiments and expert knowledge, and they are difficult to adapt to new scenarios and dependencies. On the other hand, data-driven methods based on neural networks are easier to implement but often lack robustness, interpretability, and trustworthiness--key considerations for robotic hardware and safety-critical applications such as human-robot interaction. To address the limitations of both approaches, we propose the use of symbolic regression (SR) to estimate the friction torque. SR generates interpretable symbolic formulas similar to those produced by model-based methods while being flexible to accommodate various dynamic effects and dependencies. In this work, we apply SR algorithms to approximate the friction torque using collected data from a KUKA LWR-IV+ robot. Our results show that SR not only yields formulas with comparable complexity to model-based approaches but also achieves higher accuracy. Moreover, SR-derived formulas can be seamlessly extended to include load dependencies and other dynamic factors.

Interpretable Robotic Friction Learning via Symbolic Regression

TL;DR

This work tackles the long-standing challenge of friction torque modeling in robotic joints by employing symbolic regression (SR) to learn interpretable, closed-form friction expressions from data collected on a KUKA LWR-IV+ robot. It compares three SR families—genetic-programming SR (PySR), continuous-optimization SR (ParFam), and neural-network–driven SR (uDSR)—and demonstrates that SR formulas can outperform traditional model-based friction models while remaining interpretable. The study shows SR formulas can incorporate load dependencies and external torque effects, enabling accurate joint torque estimation and external-torque inference in multi-joint motion. Overall, the approach provides robust, transparent friction models suitable for safety-critical robot control and human–robot interaction, without sacrificing accuracy.

Abstract

Accurately modeling the friction torque in robotic joints has long been challenging due to the request for a robust mathematical description. Traditional model-based approaches are often labor-intensive, requiring extensive experiments and expert knowledge, and they are difficult to adapt to new scenarios and dependencies. On the other hand, data-driven methods based on neural networks are easier to implement but often lack robustness, interpretability, and trustworthiness--key considerations for robotic hardware and safety-critical applications such as human-robot interaction. To address the limitations of both approaches, we propose the use of symbolic regression (SR) to estimate the friction torque. SR generates interpretable symbolic formulas similar to those produced by model-based methods while being flexible to accommodate various dynamic effects and dependencies. In this work, we apply SR algorithms to approximate the friction torque using collected data from a KUKA LWR-IV+ robot. Our results show that SR not only yields formulas with comparable complexity to model-based approaches but also achieves higher accuracy. Moreover, SR-derived formulas can be seamlessly extended to include load dependencies and other dynamic factors.
Paper Structure (14 sections, 6 equations, 7 figures, 3 tables)

This paper contains 14 sections, 6 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. BACKGROUND
  3. SYMBOLIC REGRESSION
  4. Genetic programming based symbolic regression
  5. Continuous optimization based symbolic regression
  6. Neural network based symbolic regression
  7. Data Collection
  8. Dataset A
  9. Dataset B
  10. EXPERIMENTAL RESULTS
  11. Static friction without load dependency
  12. Static friction with load dependency
  13. Simultaneous motion and external torque estimation
  14. Conclusion

Figures (7)

  • Figure 1: The experimental setup: the robot is equipped with link-side torque sensors for the reference signals, while the measured motor current is used in the proposed method.
  • Figure 2: The measured friction torque-velocity behavior for Joint 2 and Joint 4 of the KUKA LWR-IV+ robot for the base data set.
  • Figure 3: Plots of velocity and motor torque of Dataset B without external load for Joint 2, measured with a sampling rate of 1kHz.
  • Figure 4: Friction estimation of (a) Joint 2 and (b) Joint 4 of the KUKA robot using Dataset A for the friction-velocity relationship, where the top diagram shows the friction torque vs. joint velocity while the bottom diagram depicts the error w.r.t. the considered range of velocity.
  • Figure 5: Friction torque prediction for (a) sinusoidal velocity input is shown for (b) Joint 2 and (c) Joint 4, respectively.
  • ...and 2 more figures