Measurement-Driven Hysteresis-Aware Friction Identification for Harmonic-Drive Robot Joints Using Symbolic Regression

Accurate residual-torque measurement and friction identification are essential for high-performance robot joint modeling, yet harmonic-drive transmissions exhibit reversal induced hysteresis peaks that are difficult to characterize from current-based torque data. Traditional parametric friction mod els are structurally rigid, whereas neural-network models often lack interpretability and extrapolate poorly outside the mea sured operating region. This paper proposes a measurement driven hysteresis-aware symbolic identification framework for harmonic-drive robot joints. First, rigid-body dynamics are iden tified and decoupled from current-based torque measurements to obtain residual torque, so that the symbolic model is fitted to the measured non-rigid residual rather than to raw motor-current data. Second, a physics-informed hysteresis state and its deriva tive are introduced to augment velocity with reversal-memory information. Third, the ParFam symbolic regression algorithm is used to identify compact explicit residual-torque equations from the augmented data. Experiments on a UFACTORY-850 manipulator show that the proposed ParFam-H model achieves the lowest offline residual-torque prediction RMSE among Lu Gre, Stribeck, RBFNN, RBFNN-H, and velocity-only symbolic baselines. In ±0.1 s reversal windows, ParFam-H reduces RMSE by up to 45.5% compared with a velocity-only RBFNN, demon strating improved characterization of transient reversal peaks. Variable-frequency Chirp validation further indicates stable out of-distribution generalization from 0.1 to 1.0 Hz. Finally, because the learned model is an explicit algebraic equation with only a bounded hysteresis-state update, closed-loop experiments verify its real-time deployability, reducing trajectory-tracking RMSE by 49.3% when used as a feedforward compensation term.