A hysteresis test bench for flexible joint driving force was constructed, in order to study the force hysteresis characteristic of the flexible joint actuator and improve the force control accuracy. The modified Bouc-Wen method was proposed to accurately model the force hysteresis of the joint actuator, and the parameters of the modified Bouc-Wen model were identified by the Runge-Kutta-Fehlberg method. On the basis of the conventional Bouc-Wen model, a directional correction term was introduced to overcome the asymmetry of the output force-angle hysteresis of the flexible joint actuator. The modified Bouc-Wen model was established, using the experimental data of force hysteresis of joint actuator at 60, 80, 100 and 120 kPa inflation pressure. The hysteresis curve predicted by the proposed Bouc-Wen model was compared with that of the conventional Bouc-Wen and the experimental curve at 70, 90 and 110 kPa inflation pressure. Experimental results show that the maximum relative error of the proposed Bouc-Wen based force hysteresis model for the flexible joint actuator under each inflation pressure was only 7.75%, the average deviation remained within 0.45 N, and the fitting goodness of the model was more than 0.99. Results show that the proposed modified Bouc-Wen model can accurately describe the force hysteresis of the flexible joint actuator, which lays a foundation for the force closed-loop control and also provides a promising method for the hysteresis modeling of other hyperelastic flexible actuators.
Ming XU,Di ZHANG,Cheng RONG,Li-rong SU,Wan-qiang WANG. Modified Bouc-Wen based hysteresis modeling of flexible joint actuator. Journal of ZheJiang University (Engineering Science), 2022, 56(8): 1560-1567, 1621.
Fig.1Principle of flexible joint actuator inspired by spider legs[18]
Fig.2Design of flexible joint actuator
参数
数值/mm
参数
数值/mm
w
15
a
7.5
w1
9
d1
3
R
30
d2
2
r
27
u
0.25
l1
24
b
3
Tab.1Structural parameters of flexible joint actuator
Fig.3Manufacturing method of flexible joint actuator
Fig.4Hysteresis test bench of flexible joint actuator
Fig.5Principle of actuator hysteresis test
Fig.6Driving force and rotation angle hysteresis under variable inflation pressure
p/kPa
A
β
n
γ
φ
60
3.102
?12.030
0.251
?10.110
3.249
80
1.674
?6.137
0.500
?5.615
1.965
100
0.625
0.004
4.440
0.004
1.845
120
0.350
1.265
?2.416
?1.277
0.494
Tab.2Parameters of modified Bouc-Wen model
Fig.7Comparison between two model simulation results and experiments
模型
p/kPa
状态
?FMAX/N
δMAX/%
A.D. /N
MSE/N
R2
经典Bouc-Wen模型
70
去程
1.990
30.48
1.284
1.1532
0.7036
回程
1.342
20.56
0.863
90
去程
2.440
27.11
1.381
0.6577
0.8796
回程
1.213
13.48
0.571
110
去程
3.050
26.99
1.396
0.8666
0.8789
回程
1.638
14.50
0.552
Bouc-Wen修正模型
70
去程
0.444
6.72
0.184
0.2144
0.9906
回程
0.507
7.57
0.139
90
去程
0.420
4.65
0.186
0.1967
0.9946
回程
0.341
3.78
0.142
110
去程
0.847
7.75
0.416
0.4146
0.9932
回程
0.637
5.83
0.287
Tab.3Evaluation of hysteresis modeling performance of flexible joint actuator
[1]
LI G R, CHEN X P, ZHOU F H, et al Self-powered soft robot in the Mariana Trench[J]. Nature, 2021, 591 (7848): 66- 71
doi: 10.1038/s41586-020-03153-z
[2]
管清华, 孙健, 刘彦菊, 等 气动软体机器人发展现状与趋势[J]. 中国科学:技术科学, 2020, 50 (7): 897- 934 GUAN Qing-hua, SUN Jian, LIU Yan-ju, et al Status of and trends in soft pneumatic robotics[J]. Scientia Sinica Technologica, 2020, 50 (7): 897- 934
[3]
CHEN Y H, CHUNG O A, CHEN B, et al A lobster-inspired bending module for compliant robotic applications[J]. Bioinspiration and Biomimetics, 2020, 15 (5): 056009
doi: 10.1088/1748-3190/ab9c8d
[4]
YE X, ZHU S D, QIAN X, et al. V-shape pneumatictorsional actuator: a building block for soft grasper and manipulator [J/OL]. (2021-6-24). https://www.liebertpub.com/doi/10.1089/soro.2020.0128.
[5]
PAEZ L, AGARWAL G, PAIK J Design and analysis of a soft pneumatic actuator with origami shell reinforcement[J]. Soft Robotics, 2016, 3 (3): 109- 119
doi: 10.1089/soro.2016.0023
[6]
LI M, PAL A, AGHAKHANI A, et al Soft actuators for real-world applications[J]. Nature Reviews Materials, 2022, 7 (3): 235- 249
doi: 10.1038/s41578-021-00389-7
[7]
ZHOU L, REN L L, CHEN Y Bio-inspired soft grippers based on impactive gripping[J]. Advanced Science, 2021, 8 (9): 2002017
doi: 10.1002/advs.202002017
[8]
郝天泽, 肖华平, 刘书海, 等 集成化智能软体机器人研究进展[J]. 浙江大学学报:工学版, 2021, 55 (2): 229- 243 HAO Tian-ze, XIAO Hua-ping, LIU Shu-hai, et al Research status of integrated intelligent soft robots[J]. Journal of Zhejiang University: Engineering Science, 2021, 55 (2): 229- 243
[9]
徐彦, 方琴, 张超, 等 气动软体自折叠机械臂的驱动和负载性能[J]. 浙江大学学报:工学版, 2020, 54 (2): 398- 406 XU Yan, FANG Qin, ZHANG Chao, et al Driving and load performance of pneumatic soft self-folding manipulator[J]. Journal of Zhejiang University: Engineering Science, 2020, 54 (2): 398- 406
[10]
ZOU J, GU G Y Modeling the viscoelastic hysteresis of dielectric elastomer actuators with a modified rate-dependent Prandtl-Ishlinskii model[J]. Polymers, 2018, 10 (5): 525
doi: 10.3390/polym10050525
[11]
KONDA R, ZHANG J Hysteresis with lonely stroke in artificial muscles: characterization, modeling, and inverse compensation[J]. Mechanical Systems and Signal Processing, 2022, 164: 108240
doi: 10.1016/j.ymssp.2021.108240
[12]
HASSANI V, TJAHJOWIDODO T, DO T N A survey on hysteresis modeling, identification and control[J]. Mechanical Systems and Signal Processing, 2014, 49 (1/2): 209- 233
[13]
CUI R G, LI S H, WANG Z, et al A modified residual stress dependent Jile-Atherton hysteresis model[J]. Journal of Magnetism and Magnetic Materials, 2018, 465: 578- 584
doi: 10.1016/j.jmmm.2018.06.021
[14]
SHAO B, CHEN B, CAO Y, et al Nonlinear tensile behavior of cotton fabric reinforced polypropylene composites[J]. Journal of Applied Polymer Science, 2020, 138 (5): 49780
[15]
李梦梦, 李原, 王庆林 EAP柔性智能驱动材料的建模、控制及应用研究进展[J]. 机器人, 2018, 40 (5): 660- 672 LI Meng-meng, LI Yuan, WANG Qing-lin Research progress on modeling, control and application of EAP flexible intelligent driving materials[J]. Robot, 2018, 40 (5): 660- 672
doi: 10.13973/j.cnki.robot.180210
[16]
THAI M T, PHAN P T, HOANG T T, et al Design, fabrication, and hysteresis modeling of soft microtubule artificial muscle (SMAM) for medical applications[J]. IEEE Robotics and Automation Letters, 2021, 6 (3): 5089- 5096
doi: 10.1109/LRA.2021.3072599
[17]
HEPP J, BADRI-SPRÖWITZ A. A novel spider-inspired rotary-rolling diaphragm actuator with linear torque characteristic and high mechanical efficiency [J/OL]. (2021-6-21). https://www.liebertpub.com/doi/full/10.1089/soro.2020.0108.
[18]
KELLARIS N, ROTHEMUND P, ZENG Y, et al Spider-inspired electrohydraulic actuators for fast, soft-actuated joints[J]. Advanced Science, 2021, 8 (14): 2100916
doi: 10.1002/advs.202100916
[19]
GÖTTLER C, AMADOR G, VAN D K T, et al Fluid mechanics and rheology of the jumping spider body fluid[J]. Soft Matter, 2021, 17 (22): 5532- 5539
doi: 10.1039/D1SM00338K
[20]
XU M, RONG C, HE L Design and modeling of a bio-inspired flexible joint actuator[J]. Actuators, 2021, 10 (5): 95
doi: 10.3390/act10050095
[21]
CHEN S E, CAO Y T, SARPARAST M, et al Soft crawling robots: design, actuation, and locomotion[J]. Advanced Materials Technologies, 2020, 5 (2): 1900837
doi: 10.1002/admt.201900837
[22]
LIN C J, LIN C R, YU S K, et al Hysteresis modeling and tracking control for a dual pneumatic artificial muscle system using Prandtl-Ishlinskii model[J]. Mechatronics, 2015, 28: 35- 45
doi: 10.1016/j.mechatronics.2015.03.006
[23]
ZHANG Q, DONG Y, PENG Y, et al Asymmetric Bouc-Wen hysteresis modeling and inverse compensation for piezoelectric actuator via a genetic algorithm-based particle swarm optimization identification algorithm[J]. Journal of Intelligent Material Systems and Structures, 2019, 30 (8): 1263- 1275
doi: 10.1177/1045389X19831360
[24]
PAUL S, MONDAL S P, BHATTACHARYA P Numerical solution of LotkaVolterra prey predator model by using Runge-Kutta-Fehlberg method and Laplace Adomian decomposition method[J]. Alexandria Engineering Journal, 2016, 55 (1): 613- 617
doi: 10.1016/j.aej.2015.12.026
