引用本文: 邓金栋, 倪鹤鹏, 姬帅, 梁亮, 邹风山, 叶瑛歆. 机理模型与集成学习混合驱动的机器人关节摩擦建模方法[J]. 工程科学学报, 2024, 46(6): 1140-1150.
DENG Jindong, NI Hepeng, JI Shuai, LIANG Liang, ZOU Fengshan, YE Yingxin. Hybrid friction modeling method for robot joints integrating mechanistic model and ensemble learning[J]. Chinese Journal of Engineering, 2024, 46(6): 1140-1150.
 Citation: DENG Jindong, NI Hepeng, JI Shuai, LIANG Liang, ZOU Fengshan, YE Yingxin. Hybrid friction modeling method for robot joints integrating mechanistic model and ensemble learning[J]. Chinese Journal of Engineering, 2024, 46(6): 1140-1150.

## Hybrid friction modeling method for robot joints integrating mechanistic model and ensemble learning

• 摘要: 机器人一体化关节广泛应用于医疗、协作机器人等领域，其摩擦特性是影响机器人性能的关键因素. 为此，提出了一种机理模型与集成学习混合驱动的机器人关节摩擦建模方法，以提高模型精度. 首先，综合考虑转速、负载等关节摩擦特性的影响因素及其周期波动特性，基于先验知识和物理分析分别建立了伺服电机与谐波减速器的参数化机理模型，描述摩擦特性的变化规律. 然后，针对机理建模中因线性假设、忽略高阶项等产生的非线性残差，提出了基于eXtreme gradient boosting (XGBoost)的残差补偿模型建模方法，通过采用Boosting集成学习策略，提高残差补偿模型的泛化能力. 同时，采用贝叶斯优化方法进行XGBoost模型的超参数寻优，以提高模型精度和训练效率. 相比于传统的参数化机理模型，本文所提出的混合驱动模型具有更高精度. 与反向传播神经网络、支持向量机、长短时记忆神经网络等多种典型方法的对比实验表明，本文所提出的基于XGBoost的残差补偿模型具有更强的特征提取能力，能够较好地预测强非线性的波动摩擦残差，有效地提高了整体模型的精度.

Abstract: Robot integrated joints are extensively employed in the fields of medical and collaborative robots, and their friction characteristics are the crucial factors that affect robot performance. To improve the accuracy of the friction model, a hybrid friction modeling method integrating the mechanistic model and ensemble learning is proposed herein. First, the mechanistic model is developed based on the comprehensive analysis of various factors influencing joint friction and its periodic fluctuation. Assuming that the viscous friction and flow rate of lubricants are linear, the Stribeck model is used to describe the relationship between friction torque and motor velocity. Meanwhile, the Fourier series is used to model the periodic fluctuation of joint friction with the motor angle. The main harmonic components of the fluctuating friction torque are concentrated in the low frequency range. Considering the high frequency components will increase the complexity of the model, while the accuracy improvement of the parameterized model is limited. Therefore, the high-frequency components of the fluctuating friction torque are neglected. Moreover, considering the power function rule between external load and Coulomb friction, a simplified parametric mechanistic model is developed to describe the changes in joint friction under external load. Second, for the nonlinear residual error of the mechanistic model caused by linear hypothesis and neglecting higher-order terms, a residual compensation model based on eXtreme Gradient Boosting (XGBoost) is proposed. By adopting the boosting ensemble learning strategy, the generalization ability of the residual compensation model is enhanced. The input of the XGBoost model includes the independent variables of the parametric mechanistic model, namely the motor angle, motor velocity, and external load. The output is the difference between actual friction torque and its predicted value by the mechanistic model. Further, the Bayesian optimization method is employed for the optimization of the hyperparameters of the XGBoost model to improve model accuracy and training efficiency. Finally, a series of experiments are performed based on a joint-friction measurement platform and industrial robots to verify the effectiveness of the proposed method. Compared with the parametric mechanistic model, the prediction error of the proposed hybrid model is mainly maintained within ±0.005 N·m, and the peak error, mean absolute error (MAE), and root mean square error (RMSE) are reduced by more than 60%. Comparison experiments with backpropagation neural networks, support vector machines, and long short-term memory neural networks reveal that the nonlinear fluctuation of friction residuals can be well predicted by the proposed method and the MAE and RMSE are reduced by more than 40%. Thus, the proposed XGBoost-based residual compensation model exhibits stronger feature extraction ability and can effectively improve the accuracy of the hybrid friction modeling method.

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