Interpretable Robotic Friction Learning via Symbolic Regression

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.