HESR: A Hysteresis-Enhanced Symbolic Regression Framework for Dynamic Friction Modeling and Compensation in Robot Manipulators

Precise friction compensation in harmonic drives is critical for high-performance robotic control, yet it remains challenged by complex nonlinear hysteresis, the rigidity of traditional physical models, and the poor out-of-distribution generalization of neural networks. We propose HESR, a novel three-stage symbolic regression framework that introduces a hysteresis-enhanced state variable to address these limitations. Driven by the ParFam-H algorithm, our approach automatically evolves explicit and interpretable friction equations. Experiments on a UFACTORY-850 manipulator demonstrate that HESR reduces Root Mean Square Error (RMSE) by over 30% compared to baselines like LuGre and RBF neural networks. Furthermore, it exhibits superior cross-frequency generalization (0.1--1.0 Hz) and decreases real-time trajectory tracking errors by 49.3%, providing a highly robust and transparent compensation strategy.