Abstract: Aiming at the problem that the inherent complex hysteresis characteristics in the transmission process for the flexible joints of collaborative robots seriously affect the execution accuracy, an improved weighted least squares support vector machine (WLSSVM) hysteresis model based on a nonlinear auto-regressive moving average with intermediate variables (NARMAX) structure is proposed. The PI operator is introduced as the intermediate variable to convert the multi-mapping of hysteretic into single-mapping, and the introduction of historical values of output torque and torsion angle makes the model have dynamic characteristics. The LSSVM is susceptible to the influence of data points with large model output errors when solving the problem, hence a regular term composed of model output errors with an adaptive adjustment factor is added to the objective optimization function to further improve the model accuracy and anti-interference capability. The proposed hysteresis model has been verified on the FRANKA collaborative robot platform. Compared with the LSSVM hysteresis model and the NARMAX hysteresis model, the improved WLSSVM hysteresis model has higher model accuracy.