基于改进Stribeck摩擦的协作机器人动力学参数辨识

doi:10.3901/JME.260234

机械工程学报 ›› 2026, Vol. 62 ›› Issue (5): 151-167.doi: 10.3901/JME.260234

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基于改进Stribeck摩擦的协作机器人动力学参数辨识

张涛^1,2, 何家豪¹, 施永平^1,3, 赵萍¹, 汪键⁴, 王伟¹

1. 合肥工业大学机械工程学院合肥 230009;
2. 埃夫特智能机器人股份有限公司芜湖 241007;
3. 拉彭兰塔理工大学拉彭兰塔 53850 芬兰;
4. 安徽理工大学机械工程学院淮南 232001

收稿日期:2025-08-04 修回日期:2025-12-30 出版日期:2026-03-05 发布日期:2026-04-23
作者简介:张涛(通信作者),男,1992年生,博士,副教授,硕士研究生导师。主要研究方向为机器人智能控制,机器人运动学和动力学,工业应用中人工智能算法。E-mail:tao.zhang@hfut.edu.cn
基金资助:
国家自然科学基金青年基金(12105070)、煤炭无人化开采数智技术全国重点实验室开放基金(SKLMRDPC22KF23)、国家磁约束核聚变能发展研究专项(2024YFE03260300)和中央高校基本科研业务费专项资金(JZ2024HGTB0221)资助项目。

Dynamic Parameter Identification of Collaborative Robot Based on Improved Stribeck Friction Model

ZHANG Tao^1,2, HE Jiahao¹, SHI Yongping^1,3, ZHAO Ping¹, WANG Jian⁴, WANG Wei¹

1. School of Mechanical Engineering, Hefei University of Technology, Hefei 230009;
2. EFORT Intelligent Robot Co., Ltd., Wuhu 241007;
3. Lappeenranta University of Technology (LUT), Lappeenranta 53850, Finland;
4. School of Mechanics Engineering, Anhui University of Science and Technology, Huainan 232001

Received:2025-08-04 Revised:2025-12-30 Online:2026-03-05 Published:2026-04-23

摘要/Abstract

摘要： 精确的动力学模型对于协作机器人的控制和安全在人机交互任务中至关重要，其研究核心为动力学模型参数辨识。动力学模型中的摩擦项建模不精确会导致机器人控制稳定性和运动精度较差，针对此问题提出一种改进Stribeck摩擦模型，其添加加速度项和速度项以更好地拟合动力学模型中的非线性。首先，利用拉格朗日法建立带关节摩擦力项的机器人动力学模型，并将其分为线性和非线性部分；通过六自由协作机器人平台，以三阶傅里叶级数信号作为关节轨迹输入，并对采集的数据处理并滤波，建立参数辨识的实验数据集；最后利用该数据集辨识动力学模型参数，即利用基于迭代加权的约束最小二乘法辨识线性部分；利用基于密度的带有噪声的空间聚类法(DBSCAN)和灰狼-布谷鸟混合优化算法(GWO-CS)辨识非线性部分。实验结果表明，改进Stribeck摩擦模型能准确拟合关节摩擦的非线性项，相比传统库仑-粘滞摩擦模型和标准Stribeck模型，关节力矩的均方根误差(RMSE)大幅降低，有效地提高协作臂动力学模型的参数辨识精度。

关键词: 协作机器人, 参数辨识, Stribeck摩擦, 优化算法

Abstract: Accurate dynamic models are crucial for the control and safety of collaborative robots in human–robot interaction tasks, and the core of this research is dynamic model parameter identification. Inaccurate modelling of friction terms in dynamic models can lead to poor robot control, stability, and motion accuracy. To address this issue, a modified Stribeck friction model is proposed, which adds acceleration and velocity terms to better fit the nonlinearities in the dynamic model. First, a robot dynamic model with joint friction terms is established using the Lagrangian method, and divided into linear and nonlinear components. Using a six-degree-of-freedom collaborative robot platform, third-order Fourier series signals are used as joint trajectory inputs. The collected data is processed and filtered to establish an experimental dataset for parameter identification. Finally, this dataset is used to identify the dynamic model parameters. The linear component is identified using the constrained iteratively reweighted least squares method, while the nonlinear component is identified using the density-based spatial clustering of applications with noise (DBSCAN) and the grey wolf optimization-cuckoo search hybrid optimization algorithm (GWO-CS). Experimental results show that the improved Stribeck friction model can accurately fit the nonlinear terms of joint friction. Compared with the traditional Coulomb–viscous friction model and the standard Stribeck model, the root mean square error (RMSE) of the joint torque is greatly reduced, effectively improving the parameter identification accuracy of the collaborative arm dynamics model.

Key words: collaborative robot, parameter identification, Stribeck friction, optimization algorithm

中图分类号:

TP242

张涛, 何家豪, 施永平, 赵萍, 汪键, 王伟. 基于改进Stribeck摩擦的协作机器人动力学参数辨识[J]. 机械工程学报, 2026, 62(5): 151-167.

ZHANG Tao, HE Jiahao, SHI Yongping, ZHAO Ping, WANG Jian, WANG Wei. Dynamic Parameter Identification of Collaborative Robot Based on Improved Stribeck Friction Model[J]. Journal of Mechanical Engineering, 2026, 62(5): 151-167.

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参考文献

[1] 吴其林，赵韩，陈晓飞，等. 多臂协作机器人技术与应用现状及发展趋势[J]. 机械工程学报，2023，59(15):1-16. WU Qilin，ZHAO Han，CHEN Xiaofei，et al. Review of technology，application status and development trend in multi-arm cooperative robots[J]. Journal of Mechanical Engineering，2023，59(15):1-16.
[2] 崔朝宇，伍国梁. 协作机器人性能标准研究与发展趋势[J]. 品牌与标准化，2024(1):51-53. CUI Zhaoyu，WU Guoliang. Research and development trends of performance standards for collaborative robots[J]. Brand & Standardization，2024(1):51-53.
[3] 刘畅，徐振伟，葛达明. 协作机器人应用现状与发展趋势研究[J]. 机床与液压，2025，53(9):44-51. LIU Chang，XU Zhenwei，GE Daming. Research on the current application and development trend of cobots[J]. Machine Tool & Hydraulics，2025，53(9):44-51.
[4] CHIRIATTI G，CARBONARI L，CERAVOLO M G，et al. A robot-assisted framework for rehabilitation practices:implementation and experimental results[J]. Sensors，2023，23(17):7652.
[5] 史玉红，蔡丽娟，蔡佳丽，等. 协作机器人在智能制造中的应用[J]. 集成电路应用，2022，39(2):196-197. SHI Yuhong，CAI Lijuan，CAI Jiali，et al. Application of intelligent robot in collaborative manufacturing[J]. Application of IC，2022，39(2):196-197.
[6] 赵彬，吴成东，孙若怀，等. 面向协作机器人的零力控制与碰撞检测方法研究[J]. 工程科学与技术，2024，56(1):1-10. ZHAO Bin，WU Chengdong，SUN Ruohuai，et al. Research on zero-force control and collision detection for collaborative robots[J]. Advanced Engineering Sciences，2024，56(1):1-10.
[7] SANTOS K R D S，VILLANI E，DE OLIVEIRA W R，et al. Comparison of visual servoing technologies for robotized aerospace structural assembly and inspection[J]. Robotics and Computer-Integrated Manufacturing，2022，73:102237.
[8] RAFFIK R，SATHYA R R，VAISHALI V，et al. Industry 5.0:Enhancing human-robot collaboration through collaborative robots-A review[C]//20232nd International Conference on Advancements in Electrical，Electronics，Communication，Computing and Automation (ICAECA)，2023:1-6.
[9] LI W，HU Y，ZHOU Y，et al. Safe human-robot collaboration for industrial settings:A survey[J]. Journal of Intelligent Manufacturing，2024，35(5):2235-2261.
[10] LI S，XU J. Multi-axis force/torque sensor technologies:Design principles and robotic force control applications:A review[J]. IEEE Sensors Journal，2025，25:4055-4069.
[11] HAN L，XU W，LI B，et al. Collision detection and coordinated compliance control for a dual-arm robot without force/torque sensing based on momentum observer[J]. IEEE/ASME Transactions on Mechatronics，2019，24(5):2261-2272.
[12] ATKESON C G，AN C H，HOLLERBACH J M. Estimation of inertial parameters of manipulator loads and links[J]. The International Journal of Robotics Research，1986，5(3):101-119.
[13] GAUTIER M，KHALIL W. Direct calculation of minimum set of inertial parameters of serial robots[J]. IEEE Transactions on Robotics and Automation，1990，6(3):368-373.
[14] HUANG W，MIN H，GUO Y，et al. A review of dynamic parameters identification for manipulator control[J]. Cobot，2022，1:5.
[15] 张一楠，丁建完. 基于WLS-MBO算法的串联机器人动力学参数辨识[J]. 计算机工程与科学，2023，45(7):1274-1281. ZHANG Yinan，DING Jianwan. Identification of dynamic parameters of tandem robot based on WLS-MBO algorithm[J]. Computer Engineering & Science，2023，45(7):1274-1281.
[16] 冯利民，俞经虎，王延玉，等. 基于IRLS算法的机器人动力学参数辨识[J]. 现代制造工程，2022(4):37-44. FENG Limin，YU Jinghu，WANG Yanyu，et al. Identification of robot dynamic parameters based on IRLS algorithm[J]. Modern Manufacturing Engineering，2022(4):37-44.
[17] YOSHIDA K，KHALIL W. Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters[J]. International Journal of Robotics Research，2000，19(5):498-510.
[18] GNAD D，GATTRINGER H，MUELLER A，et al. Identification of physically consistent dynamics parameter of the ABB IRB 360-6/1600 delta robot and its use for time-optimal motion planning under consideration of constraint forces[J]. Robotics and Autonomous Systems，2024，182:104823.
[19] MATA V，BENIMELI F，FARHAT N，et al. Dynamic parameter identification in industrial robots considering physical feasibility[J]. Advanced Robotics，2005，19(1):101-119.
[20] SOUSA C D，CORTESãO R. Physical feasibility of robot base inertial parameter identification:A linear matrix inequality approach[J]. The Intermational Journal of Robotics Research，2014，33(6):931-944.
[21] SOUSA C D，CORTESAO R. Inertia tensor properties in robot dynamics identification:A linear matrix inequality approach[J]. IEEE/ASME Transactions on Mechatronics，2019，24(1):406-411.
[22] 梁学修，巩潇，宋斌，等. 基于状态变量摩擦模型的振动控制[J]. 电子产品世界，2021，28(5):63-66. LIANG Xuexiu，GONG Xiao，SONG Bin，et al. Vibration control based on friction model with state variable[J]. Electronic Engineering & Product World，2021，28(5):63-66.
[23] 马立，王敬萍，李丰甜，等. 精密定位系统的摩擦力建模与补偿[J]. 光学精密工程，2019，27(1):121-128. MA Li，WANG Jingping，LI Fengtian et al. Friction modeling and compensation of precision position system[J]. Optics and Precision Engineering，2019，27(1):121-128.
[24] NGUYEN N T，NGUYEN T N T，TONG H N，et al. Dynamic parameter identification based on the least squares method for a 6-dof manipulator[C]//2023 International Conference on System Science and Engineering (ICSSE)，2023:301-305.
[25] 张师源，戴骏，邓华. 六自由度机械臂的动力学参数辨识[J]. 制造业自动化，2021，43(3):35-39. ZHANG Shiyuan，DAI Jun，DENG Hua. Dynamic parameter identification of the six freedoms manipulators[J]. Manufacturing Automation，2021，43(3):35-39.
[26] LIU K，WEI C，NI D，et al. Stribeck friction model identification based on genetic algorithm[C]//20225th International Conference on Robotics，Control and Automation Engineering (RCAE)，2022:174-179.
[27] KARAHAN O，KARCI H. Swarm intelligence based nonlinear friction and dynamic parameters identification for a 6-dof robotic manipulator[J]. Journal of Intelligent & Robotic Systems，2023，108(2):19.
[28] XU T，TUO H，WANG C，et al. Robot dynamic identification based on data weighting protection and nonlinear friction separation[J]. IEEE/ASME Transactions on Mechatronics，2025，1-12.
[29] PAUL R P. Robot manipulators:Mathematics，programming，and control:The computer control of robot manipulators[M]. Richard Paul，Cambridge，Massachusetts:MIT Press，1981.
[30] 霍伟. 机器人动力学与控制[M]. 北京:高等教育出版社，2005. HUO Wei. Robot dynamics and control[M]. Beijing:Higher Education Press，2005.
[31] 汪朋朋，卢浩，杨志强，等. 协作SCARA机器人关节综合动态摩擦辨识与补偿[J]. 机械工程学报，2025，61(7):325-337. WANG Pengpeng，LU Hao，YANG Zhiqiang，et al. Comprehensive dynamic friction identification and compensation in joints of collaborative scara robots[J]. Journal of Mechanical Engineering，2025，61(7):325-337.
[32] WANG C，WANG K，LI Z，et al. Nonlinear dynamic of the rod-fastening combined rotor system with rub-impact based on the stribeck friction model[J]. Applied Mathematical Modelling，2024，128:685-706.
[33] JANOT A，VANDANJON P O，GAUTIER M. Using robust regressions and residual analysis to verify the reliability of LS estimation:Application in robotics[C]//2009 IEEE/RSJ International Conference on Intelligent Robots and Systems，2009:1962-1967.
[34] HAN Y，WU J，LIU C，et al. An iterative approach for accurate dynamic model identification of industrial robots[J]. IEEE Transactions on Robotics，2020，36(5):1577-1594.
[35] SUN S，LEI K，XU Z，et al. Analysis of k-means and k-dbscan commonly used in data mining[C]//2023 International Conference on Intelligent Media，Big Data and Knowledge Mining (IMBDKM)，2023:37-41.
[36] MAKHADMEH S N，AL-BETAR M A，DOUSH I A，et al. Recent advances in grey wolf optimizer，its versions and applications:review[J]. IEEE Access，2023，12:22991-23028.
[37] LI J，AN Q，LEI H，et al. Survey of lévy flight-based metaheuristics for optimization[J]. Mathematics，2022，10(15):2785.
[38] 杨中华，俞经虎，俞哲，等. 应用于动力学参数辨识的激励轨迹优化研究[J]. 机械传动，2024，48(11):37-47. YANG Zhonghua，YU Jinghu，YU Zhe，et al. Optimization study of excitation trajectories for dynamic parameter identification[J]. Journal of Mechanical Transmission，2024，48(11):37-47.
[39] TIAN H，HUBER M，MOWER C E，et al. Excitation trajectory optimization for dynamic parameter identification using virtual constraints in hands-on robotic system[C]//2024 IEEE International Conference on Robotics and Automation (ICRA)，2024:11605-11611.
[40] SPONG M W. Modeling and control of elastic joint robots[J]. Mathematical and Computer Modelling，1989，12(7):912.

基于改进Stribeck摩擦的协作机器人动力学参数辨识

Dynamic Parameter Identification of Collaborative Robot Based on Improved Stribeck Friction Model

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