融合温度与速度因素的机器人摩擦力补偿算法

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

系统仿真学报 ›› 2026, Vol. 38 ›› Issue (6): 1722-1733.doi: 10.16182/j.issn1004731x.joss.25-0725

• 论文 • 上一篇

融合温度与速度因素的机器人摩擦力补偿算法

吕金旺¹^,², 应安凯¹^,², 李明³, 宋涛¹^,², 张洁⁴, 邱芳晖⁵, 施长城¹^,²^,⁶, 左国坤¹^,²^,⁶, 徐佳琳¹^,²^,⁶

^1.中国科学院宁波材料技术与工程研究所，浙江宁波 315201
^2.宁波慈溪生物医学工程研究所，浙江宁波 315300
^3.宁波市第六医院，浙江宁波 315040
^4.浙江大学滨江研究院，浙江杭州 310053
^5.西湖大学医学院附属杭州市第一人民医院，浙江杭州 310030
^6.中国科学院大学，北京 101408

收稿日期:2025-07-26 修回日期:2025-11-27 出版日期:2026-06-25 发布日期:2026-06-25
通讯作者: 徐佳琳
第一作者简介:吕金旺(2000-)，男，硕士，研究方向为机器人柔顺控制。
基金资助:
宁波市重点研发计划(2022Z147);浙江省“领雁”研发攻关计划(2024C03040);国家重点研发计划(2022YFC3601700)

Robot Friction Force Compensation Algorithm Integrating Temperature and Speed Factors

Lü Jinwang¹^,², Ying Ankai¹^,², Li Ming³, Song Tao¹^,², Zhang Jie⁴, Qiu Fanghui⁵, Shi Changcheng¹^,²^,⁶, Zuo Guokun¹^,²^,⁶, Xu Jialin¹^,²^,⁶

^1.Ningbo Institute of Materials Technology & Engineering, Chinese Academy of Sciences, Ningbo 315201, China
^2.Ningbo Cixi Institute of Biomedical Engineering, Ningbo 315300, China
^3.Ningbo No. 6 Hospital, Ningbo 315040, China
^4.Binjiang Institute of Zhejiang University, Hangzhou 310053, China
^5.Affiliated Hangzhou First People's Hospital, School of Medicine, Westlake University, Hangzhou 310030, China
^6.University of Chinese Academy of Sciences, Beijing 101408, China

Received:2025-07-26 Revised:2025-11-27 Online:2026-06-25 Published:2026-06-25
Contact: Xu Jialin

摘要/Abstract

摘要：

为解决摩擦力补偿精度不足而降低肘关节康复机器人的运动平滑性、稳定性及辅助柔顺性，提出一种融合温度与速度的改进Stribeck摩擦模型。模型通过指数衰减摩擦因子，描述随机器人运行速度提高摩擦力增速放缓的特性，并设计考虑温度效应的粘滞函数，抑制温度改变引起的摩擦力波动。实验结果表明：该模型在机器人不同运行状态下均能实现稳定的摩擦力补偿，温度适应性较强。频率响应分析证实该模型对机器人的稳态跟踪精度、抗干扰性与鲁棒性均有改善。

关键词: Stribeck摩擦模型, 温度效应, 速度效应, 粘滞系数, 肘关节康复机器人

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

中图分类号:

TP241.2

吕金旺,应安凯,李明等 . 融合温度与速度因素的机器人摩擦力补偿算法[J]. 系统仿真学报, 2026, 38(6): 1722-1733.

Lü Jinwang,Ying Ankai,Li Ming,et al . Robot Friction Force Compensation Algorithm Integrating Temperature and Speed Factors[J]. Journal of System Simulation, 2026, 38(6): 1722-1733.

图/表 20

图1

图2

图3

图4

表1

改进的Stribeck模型参数（电机正转）

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

表1

表2

改进的Stribeck模型参数（电机反转）

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

表2

图5

图6

图7

图8

图9

表3

图10

表4

图11

图12

图13

图14

表5

图15

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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

融合温度与速度因素的机器人摩擦力补偿算法

Robot Friction Force Compensation Algorithm Integrating Temperature and Speed Factors

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