Robot Friction Force Compensation Algorithm Integrating Temperature and Speed Factors

doi:10.16182/j.issn1004731x.joss.25-0725

Abstract

Abstract:

Insufficient friction force compensation accuracy degrades motion smoothness, stability, and assistive compliance of elbow joint rehabilitation robots. To address this issue, an improved Stribeck friction force model integrating temperature and speed factors was proposed. The model employed an exponentially decaying friction factor to describe the characteristic that the increase rate of friction force slowed down with the rise of the robot's operating speed and designed a viscous function considering temperature effects to suppress friction force fluctuations caused by temperature changes. Experimental results indicate that the model achieves stable friction force compensation under different operating states of the robot and has strong temperature adaptability. Frequency response analysis confirms that the model improves the steady-state tracking accuracy, disturbance resistance, and robustness of the robot.

Key words: Stribeck friction force model, temperature effect, speed effect, viscosity coefficient, elbow joint rehabilitation robot

CLC Number:

TP241.2

Lü Jinwang, Ying Ankai, Li Ming, Song Tao, Zhang Jie, Qiu Fanghui, Shi Changcheng, Zuo Guokun, Xu Jialin. Robot Friction Force Compensation Algorithm Integrating Temperature and Speed Factors[J]. Journal of System Simulation, 2026, 38(6): 1722-1733.

Figures/Tables 20

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Table 1

Parameters of improved Stribeck model (motor in forward rotation)

温度/℃	$F c$	$F s$	$θ ˙ v$	G_T	$α$	$β$
29	4.639	7.263	0.318	0.006 199	-2.263	0.1
33	4.639	7.263	0.318	0.000 100	-2.263	0.1

Table 1

Table 2

Parameters of improved Stribeck model (motor in reverse rotation)

温度/℃	$F c$	$F s$	$θ ˙ v$	G_T	$α$	$β$
29	4.035	7.242	0.342	0.008 29	-2.241	0.1156
33	4.035	7.242	0.342	0.000 20	-2.241	0.1156

Table 2

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Table 3

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Table 4

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Table 5

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References 23

[1]	罗林坡, 李萍, 罗嘉慧. 阶梯性康复训练联合持续静态牵伸技术对肘关节骨折患者术后关节功能恢复及预后的影响[J]. 中国康复, 2020, 35(7): 362-365.
	Luo Linpo, Li Ping, Luo Jiahui. Effect of Stepped Rehabilitation Training Combined with Continuous Static Stretching on Joint Function Recovery and Prognosis of Patients with Elbow Fracture After Operation[J]. Chinese Journal of Rehabilitation, 2020, 35(7): 362-365.
[2]	纪振钢, 韩天宇, 周大鹏, 等. 创伤性肘关节僵硬的松解治疗[J]. 局解手术学杂志, 2022, 31(7): 619-623.
	Ji Zhengang, Han Tianyu, Zhou Dapeng, et al. Release of Traumatic Elbow Stiffness[J]. Journal of Regional Anatomy and Operative Surgery, 2022, 31(7): 619-623.
[3]	陈辰, 肖丹, 花克涵, 等. 改良肘关节松解术治疗创伤后肘关节僵硬预后不良的危险因素分析[J]. 中国医刊, 2023, 58(9): 1004-1007.
[4]	刘延斌, 庞翔元, 张彦斌, 等. 踝关节康复机器人主动训练柔顺控制研究[J]. 系统仿真学报, 2020, 32(1): 54-60.
	Liu Yanbin, Pang Xiangyuan, Zhang Yanbin, et al. Research on Active Training Compliance Control of Ankle Rehabilitation Robot[J]. Journal of System Simulation, 2020, 32(1): 54-60.
[5]	Trinh Minh, Yadav Ritesh, Schwiedernoch Ruben, et al. Modeling of Temperature-dependent Joint Friction in Industrial Robots Using Neural Networks[C]//2023 Seventh IEEE International Conference on Robotic Computing (IRC). Piscataway: IEEE, 2023: 206-213.
[6]	Yan Qi, Li Rui, Meng Xianghui. Tribo-dynamic Analysis and Motion Control of a Rotating Manipulator Based on the Load and Temperature Dependent Friction Model[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2021, 235(7): 1335-1352.
[7]	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.
[8]	王晓强, 穆春阳, 马行, 等. 基于改进LuGre摩擦模型的机器人关节摩擦力辨识研究[J]. 机床与液压, 2023, 51(17): 26-31.
	Wang Xiaoqiang, Mu Chunyang, Ma Xing, et al. Robot Joint Friction Identification Based on Improved LuGre Friction Model[J]. Machine Tool & Hydraulics, 2023, 51(17): 26-31.
[9]	Peyret Nicolas, Rosatello Marco, Chevallier Gaël, et al. A Mindlin Derived Dahl Friction Model[J]. Mechanism and Machine Theory, 2017, 117: 48-55.
[10]	张铁, 胡亮亮, 邹焱飚. 基于混合遗传算法的机器人改进摩擦模型辨识[J]. 浙江大学学报(工学版), 2021, 55(5): 801-809, 854.
	Zhang Tie, Hu Liangliang, Zou Yanbiao. Identification of Improved Friction Model for Robot Based on Hybrid Genetic Algorithm[J]. Journal of Zhejiang University(Engineering Science), 2021, 55(5): 801-809, 854.
[11]	Liu Shiping, Ma Ziyan, Chen Jinliang, et al. An Improved Parameter Identification Method of Redundant Manipulator[J]. International Journal of Advanced Robotic Systems, 2021, 2021(3): 1-8.
[12]	张一楠, 丁建完. 考虑温度影响的机器人关节摩擦模型[J]. 中国机械工程, 2023, 34(2): 127-134.
	Zhang Yinan, Ding Jianwan. Friction Model of Robot Joints Considering Influences of Temperature[J]. China Mechanical Engineering, 2023, 34(2): 127-134.
[13]	Simoni Luca, Beschi Manuel, Legnani Giovanni, et al. Friction Modeling with Temperature Effects for Industrial Robot Manipulators[C]//2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Piscataway: IEEE, 2015: 3524-3529.
[14]	吴晓敏, 刘暾东, 贺苗, 等. 机器人关节摩擦建模与补偿研究[J]. 仪器仪表学报, 2018, 39(10): 44-50.
	Wu Xiaomin, Liu Tundong, He Miao, et al. Research on Friction Modeling and Compensation of Robot Manipulator[J]. Chinese Journal of Scientific Instrument, 2018, 39(10): 44-50.
[15]	汪朋朋, 殷兴国, 寇斌. 基于深度学习的工业机器人摩擦力补偿方法研究[J]. 河北工业大学学报, 2022, 51(1): 27-34.
	Wang Pengpeng, Yin Xingguo, Kou Bin. Research on Friction Compensation of Industrial Robot Based on Deep Learning[J]. Journal of Hebei University of Technology, 2022, 51(1): 27-34.
[16]	贺苗, 吴晓敏, 邵桂芳, 等. 基于RBFNN的机器人关节摩擦建模与补偿研究[J]. 仪器仪表学报, 2020, 41(11): 278-284.
	He Miao, Wu Xiaomin, Shao Guifang, et al. Research on Friction Modeling and Compensation of Robot Joint Based on RBFNN[J]. Chinese Journal of Scientific Instrument, 2020, 41(11): 278-284.
[17]	Scholl Philipp, Iskandar Maged, Wolf Sebastian, et al. Learning-based Adaption of Robotic Friction Models[J]. Robotics and Computer-Integrated Manufacturing, 2024, 89: 102780.
[18]	Gao Liming, Yuan Jianjun, Han Zhedong, et al. A Friction Model with Velocity, Temperature and Load Torque Effects for Collaborative Industrial Robot Joints[C]//2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Piscataway: IEEE, 2017: 3027-3032.
[19]	曹振乾, 印江, 张津华. 基于改进粒子群算法的主蒸汽温度系统辨识[J]. 系统仿真学报, 2021, 33(10): 2411-2419.
	Cao Zhenqian, Yin Jiang, Zhang Jinhua. Identification of Main Steam Temperature System Based on Improved Particle Swarm Optimization[J]. Journal of System Simulation, 2021, 33(10): 2411-2419.
[20]	甄鸿越, 赵利刚, 周保荣, 等. 粒子群和强化学习结合的双馈式风机系统模型参数智能辨识方法[J]. 电力系统及其自动化学报, 2025, 37(8): 106-114.
	Zhen Hongyue, Zhao Ligang, Zhou Baorong, et al. Intelligent Parameter Identification Method for DFIG System Based on Particle Swarm Optimization and Reinforcement Learning[J]. Proceedings of the CSU-EPSA, 2025, 37(8): 106-114.
[21]	张相胜, 陈佳明. 一种改进的机器人动力学参数辨识方法[J]. 江苏大学学报(自然科学版), 2025, 46(1): 50-56.
	Zhang Xiangsheng, Chen Jiaming. Improved Identification Method of Robot Dynamic Parameter[J]. Journal of Jiangsu University(Natural Science Edition), 2025, 46(1): 50-56.
[22]	姚建勇, 焦宗夏. 改进型LuGre模型的负载模拟器摩擦补偿[J]. 北京航空航天大学学报, 2010, 36(7): 812-815, 820.
	Yao Jianyong, Jiao Zongxia. Friction Compensation for Hydraulic Load Simulator Based on Improved LuGre Friction Model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2010, 36(7): 812-815, 820.
[23]	彭建伟, 廖哲霖, 姚瀚晨, 等. 基于拓展社会力的机器人柔顺跟随与避障控制[J]. 系统仿真学报, 2023, 35(8): 1776-1787.
	Peng Jianwei, Liao Zhelin, Yao Hanchen, et al. A Compliant Robot Control Based on Extended Social-force Model for Human-following and Obstacle Avoidance[J]. Journal of System Simulation, 2023, 35(8): 1776-1787.

温度/℃	第1次实验		第2次实验
温度/℃	本文模型	Stribeck	本文模型	Stribeck
24	4.42	7.01	4.28	5.71
25	4.48	6.26	4.48	5.97
26	4.67	6.03	4.16	5.85
27	4.81	5.51	4.35	5.95
28	4.66	5.31	4.24	5.49
29	4.54	4.91	4.20	5.40
30	4.77	4.66	4.38	4.93
31	4.51	4.59	4.37	4.66
32	4.45	4.53	4.37	4.59
33	4.60	4.51	4.54	4.62
均值	4.62	5.36	4.34	5.32
均方差	0.018	0.744	0.120	0.568

温度/℃	本文模型	Stribeck模型
24	4.32	6.54
25	5.08	6.60
26	4.90	6.24
27	4.64	6.01
28	4.64	5.53
29	5.03	5.55
30	5.22	5.17
31	4.92	5.29
32	5.37	5.46
33	5.23	5.63
34	5.31	5.82
均值	5.07	5.73
均方差	0.095	0.236

运行顺序	误差	运行顺序	误差
1	4.49	4	4.33
2	4.43	5	4.22
3	4.36	6	4.71