工程科学学报，第41卷，第8期：1085-1091,2019年8月 Chinese Journal of Engineering,Vol.41,No.8:1085-1091,August 2019 DOI:10.13374/j.issn2095-9389.2019.08.014;http://journals.ustb.edu.cn 基于BP神经网络的机器人波动摩擦力矩修正方法 张铁)，洪景东)，李秋奋)，刘晓刚) 1)华南理工大学机械与汽车工程学院，广州5106412)桂林航天工业学院广西高校机器人与焊接重点实验室，桂林541004 区通信作者，E-mail:merobot(@scut.edu.cn 摘要针对机器人谐波减速器关节在转动过程中存在的波动摩擦力矩，提出一种基于傅里叶级数函数和BP神经网络的建 模方法，并完善机器人的动力学模型，修正了因波动摩擦力矩带来的关节力矩计算误差.通过研究谐波减速器关节的波动摩 擦力矩在不同影响因素下的变化特性，采用傅里叶级数与BP神经网络结合的方法对波动摩擦力矩进行建模.通过添加傅里 叶级数函数作为B神经网络的辅助输入，克服了力矩误差曲线因存在高频周期性波动而难以拟合的困难.在离线环境下训 练神经网络，完成对关节波动摩擦力矩的建模，进而完善机器人的动力学模型和修正关节中存在的波动摩擦力矩.验证实验 表明，使用完善后的动力学模型可以有效计算谐波减速器关节的波动摩擦力矩，并使修正后的力矩误差维持在[-0.5,0.5]N m的范围之内，方差为0.1659N2m2,是修正前的24.23%. 关键词机器人动力学：关节波动摩擦力矩：BP神经网络：傅里叶级数函数：误差修正 分类号TP242.2 Wave friction correction method for a robot based on BP neural network ZHANG Tie HONG Jing-dong,LI Qiu-fen,LIU Xiao-gang 1)School of Mechanical and Automotive Engineering,South China University of Technology,Guangzhou 510641,China 2)Guangxi Key Laboratory of Robotics and Welding,Guilin University of Aerospace Technology,Guilin 541004,China Corresponding author,E-mail:merobot@scut.edu.cn ABSTRACT For sensorless force control of a robot such as by drag-teaching and collision detection,the control accuracy depends on the accuracy of the robot dynamics model.The error of the robot dynamics model comes from two aspects,modeling and identification errors and from unmodeled dynamics.Among the unmodeled dynamics,one of the important sources of unmodeled dynamic is the fric- tion inside the robot reducer.When the reducer rotates,there is mutual extrusion and friction between the internal components of the reducer.This kind of friction will change as the gear meshing state transforms,resulting in the phenomenon of wave friction torque.A remarkable feature of wave friction torque is that it has a periodic relationship with the joint location and it is often modeled by the Fou- rier series function.Wave friction torque is obvious when the rotational speed of the joint is low and decreases with the increase in rota- tional speed.In order to improve the accuracy of the robot dynamics model,the wave friction torque needs to be modeled and elimina- ted.Aiming at the wave friction of the robot harmonic joint during the rotation process,a modeling method based on a Fourier series function and BP neural network was proposed,the dynamic model of the robot was optimized,and the calculation error of the joint torque caused by the wave friction was corrected.By studying the variation characteristics of the wave friction of the harmonic reducer joint under different influencing factors,the combination of the Fourier series and BP neural network was used to model the wave fric- tion.By adding the Fourier series function as the auxiliary input of the BP neural network,the difficulty of fitting the torque error curve due to the presence of high frequency periodic fluctuations was overcome.The neural network was trained in the off-line environment to complete the modeling of the wave friction,and then to improve the dynamic model of the robot and correct the wave friction.The ex- 收稿日期：2018-07-20 基金项目：国家科技重大专项资助项目(2015ZX04005006):广东省科技重大专项资助项目(2014B090921004,2014B090920002):中山市科技 重大资助项目(2016F2FC0006):广西高校机器人与焊接重点实验室课题基金资助项目(JQR2015KF02)工程科学学报,第 41 卷,第 8 期:1085鄄鄄1091,2019 年 8 月 Chinese Journal of Engineering, Vol. 41, No. 8: 1085鄄鄄1091, August 2019 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2019. 08. 014; http: / / journals. ustb. edu. cn 基于 BP 神经网络的机器人波动摩擦力矩修正方法 张 铁1) 苣 , 洪景东1) , 李秋奋1) , 刘晓刚2) 1)华南理工大学机械与汽车工程学院, 广州 510641 2)桂林航天工业学院广西高校机器人与焊接重点实验室, 桂林 541004 苣通信作者, E鄄mail: merobot@ scut. edu. cn 摘 要 针对机器人谐波减速器关节在转动过程中存在的波动摩擦力矩,提出一种基于傅里叶级数函数和 BP 神经网络的建 模方法,并完善机器人的动力学模型,修正了因波动摩擦力矩带来的关节力矩计算误差. 通过研究谐波减速器关节的波动摩 擦力矩在不同影响因素下的变化特性,采用傅里叶级数与 BP 神经网络结合的方法对波动摩擦力矩进行建模. 通过添加傅里 叶级数函数作为 BP 神经网络的辅助输入,克服了力矩误差曲线因存在高频周期性波动而难以拟合的困难. 在离线环境下训 练神经网络,完成对关节波动摩擦力矩的建模,进而完善机器人的动力学模型和修正关节中存在的波动摩擦力矩. 验证实验 表明,使用完善后的动力学模型可以有效计算谐波减速器关节的波动摩擦力矩,并使修正后的力矩误差维持在[ - 0郾 5,0郾 5] N ·m 的范围之内,方差为 0郾 1659 N 2·m 2 ,是修正前的 24郾 23% . 关键词 机器人动力学; 关节波动摩擦力矩; BP 神经网络; 傅里叶级数函数; 误差修正 分类号 TP242郾 2 收稿日期: 2018鄄鄄07鄄鄄20 基金项目: 国家科技重大专项资助项目(2015ZX04005006);广东省科技重大专项资助项目(2014B090921004,2014B090920002);中山市科技 重大资助项目(2016F2FC0006);广西高校机器人与焊接重点实验室课题基金资助项目(JQR2015KF02) Wave friction correction method for a robot based on BP neural network ZHANG Tie 1) 苣 , HONG Jing鄄dong 1) , LI Qiu鄄fen 1) , LIU Xiao鄄gang 2) 1) School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China 2) Guangxi Key Laboratory of Robotics and Welding, Guilin University of Aerospace Technology, Guilin 541004, China 苣Corresponding author, E鄄mail: merobot@ scut. edu. cn ABSTRACT For sensorless force control of a robot such as by drag鄄teaching and collision detection, the control accuracy depends on the accuracy of the robot dynamics model. The error of the robot dynamics model comes from two aspects, modeling and identification errors and from unmodeled dynamics. Among the unmodeled dynamics, one of the important sources of unmodeled dynamic is the fric鄄 tion inside the robot reducer. When the reducer rotates, there is mutual extrusion and friction between the internal components of the reducer. This kind of friction will change as the gear meshing state transforms, resulting in the phenomenon of wave friction torque. A remarkable feature of wave friction torque is that it has a periodic relationship with the joint location and it is often modeled by the Fou鄄 rier series function. Wave friction torque is obvious when the rotational speed of the joint is low and decreases with the increase in rota鄄 tional speed. In order to improve the accuracy of the robot dynamics model, the wave friction torque needs to be modeled and elimina鄄 ted. Aiming at the wave friction of the robot harmonic joint during the rotation process, a modeling method based on a Fourier series function and BP neural network was proposed, the dynamic model of the robot was optimized, and the calculation error of the joint torque caused by the wave friction was corrected. By studying the variation characteristics of the wave friction of the harmonic reducer joint under different influencing factors, the combination of the Fourier series and BP neural network was used to model the wave fric鄄 tion. By adding the Fourier series function as the auxiliary input of the BP neural network, the difficulty of fitting the torque error curve due to the presence of high frequency periodic fluctuations was overcome. The neural network was trained in the off鄄line environment to complete the modeling of the wave friction, and then to improve the dynamic model of the robot and correct the wave friction. The ex鄄