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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2022, Vol. 56 Issue (6): 1144-1151    DOI: 10.3785/j.issn.1008-973X.2022.06.011
    
Analysis and simulation of magnetic field for robot tactile perception
Mei-jiang GUI1,2(),Xiao-hu ZHOU1(),Xiao-liang XIE1,Shi-qi LIU1,Hao LI1,2,Jin-li WANG3,Zeng-guang HOU1,2,*()
1. State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
2. School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China
3. School of Mechanical Electronic and Information Engineering, China University of Mining and Technology-Beijing, Beijing 100083, China
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Abstract  

A sensing device with a convex structure was designed using elastic rubber and Hall devices, in order to explore the magnetic field calculation method suitable for the flexible tactile sensing device. The magnetic field generated by the deformed device was then calculated based on the magnetic equation of the Halbach cylinder. To further verify the proposed calculation method, finite element simulation models of the sensing device under different deformations were constructed and solved based on the COMSOL Multiphysics platform. Comparing the calculation results with the simulation results shows that the proposed calculation method has great applicability under different deformations. Moreover, data fitting demonstrates that the simulation value gradually approaches the theoretical value with the continuous refinement of the simulation network. The minimum error was 3.18%, proving the high consistency between the simulated value and the theoretical value.

Key words： tactile perception      elastic rubber      Hall device      Halbach cylinder      analytical calculation      finite element simulation     
Received: 21 March 2022      Published: 30 June 2022
CLC:  TP 2  
Fund:  国家自然科学基金资助项目（62003343, 62073325, U20A20224, U1913210）；北京市自然科学基金资助项目（M22008）；中国科学院青年创新促进会会员资助项目（2020140）
Corresponding Authors: Zeng-guang HOU     E-mail: guimeijiang2019@ia.ac.cn;xiaohu.zhou@ia.ac.cn;zengguang.hou@ia.ac.cn
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Mei-jiang GUI
Xiao-hu ZHOU
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Shi-qi LIU
Hao LI
Jin-li WANG
Zeng-guang HOU
Cite this article:

Mei-jiang GUI,Xiao-hu ZHOU,Xiao-liang XIE,Shi-qi LIU,Hao LI,Jin-li WANG,Zeng-guang HOU. Analysis and simulation of magnetic field for robot tactile perception. Journal of ZheJiang University (Engineering Science), 2022, 56(6): 1144-1151.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2022.06.011     OR     https://www.zjujournals.com/eng/Y2022/V56/I6/1144


面向机器人触力觉感知的磁场解析与仿真

为了探究适用于柔性机器人触力觉感知装置的磁场计算方法，利用弹性橡胶与霍尔器件设计带有凸起结构的感知装置. 利用环式Halbach阵列的磁场方程，对形变后装置的磁场进行计算. 为了验证所提出的计算方法，基于COMSOL Multiphysics平台构建并求解不同形变下感知装置的有限元仿真模型. 通过对比理论计算结果与模型仿真结果，验证了所提出的计算方法在不同形变下均有较好的适用性. 进一步的数据拟合表明，随着仿真网络的不断细化，仿真值逐渐逼近理论值，最小误差为3.18%，证明二者具有较高的一致性.


关键词： 触力觉感知,  弹性橡胶,  霍尔器件,  环式Halbach阵列,  解析计算,  有限元仿真 
Fig.1 Schematic diagram of flexible tactile sensor
Fig.2 Schematic diagram of second-oredr Halbach cylinder
Fig.3 Schematic diagram of deformed Halbach cylinder
d ai bi ao bo
mm
0.10 3.10s 2.90 4.60 4.40
0.20 3.21 2.80 4.71 4.30
0.30 3.33 2.70 4.82 4.20
0.40 3.46 2.60 4.94 4.10
0.50 3.60 2.50 5.06 4.00
0.60 3.75 2.40 5.19 3.90
0.70 3.91 2.30 5.33 3.80
0.80 4.09 2.20 5.47 3.70
0.90 4.29 2.10 5.63 3.60
1.00 4.50 2.00 5.79 3.50
1.10 4.74 1.90 5.96 3.40
1.20 5.00 1.80 6.14 3.30
1.30 5.29 1.70 6.33 3.20
1.40 5.63 1.60 6.53 3.10
1.50 6.00 1.50 6.75 3.00
Tab.1 Geometric parameters of elliptic cylinder
Fig.4 Schematic of block method
Fig.5 Heat map of magnetic field for Halbach cylinder under four different deformations and three different equal divisions
$ d/ $mm $ {B}_{\mathrm{c}}/\mathrm{m}\mathrm{T} $ $ {B}_{\mathrm{t}}/\mathrm{m}\mathrm{T} $ ${E}_{\mathrm{m} }$/%
N=16 N=32 N=48 N=64 N=80 N=96 N=112 N=128 N=144
0.10 540.14 551.03 552.52 553.54 553.32 553.77 553.89 553.94 553.90 572.16 3.18
0.20 541.16 551.57 553.85 554.38 554.59 554.72 554.91 555.00 555.07 573.60 3.23
0.30 543.58 554.12 556.08 556.49 557.08 557.19 557.36 557.52 557.75 576.16 3.20
0.40 546.79 557.38 559.01 560.24 560.38 560.73 560.76 560.94 560.81 579.99 3.29
0.50 550.85 561.47 563.56 564.30 564.60 564.52 564.86 564.92 565.02 585.25 3.46
0.60 557.21 566.69 569.89 570.76 571.01 571.15 571.29 571.30 571.31 592.13 3.52
0.70 565.92 576.82 578.92 579.75 579.87 580.08 579.92 580.23 580.48 600.84 3.39
0.80 575.28 586.54 588.57 589.37 589.44 589.60 589.83 589.90 589.98 611.62 3.54
0.90 587.83 599.18 603.12 602.14 602.42 602.70 602.67 602.67 602.72 624.74 3.46
1.00 602.58 614.23 616.54 617.39 617.55 618.15 617.91 618.02 618.38 640.50 3.45
1.10 620.49 632.49 634.79 635.50 635.96 636.26 636.14 636.26 636.48 659.26 3.46
1.20 641.58 653.93 656.20 657.08 657.35 657.83 657.79 658.04 657.93 681.43 3.43
1.30 666.77 679.59 682.13 683.13 683.35 683.54 683.64 683.73 683.75 707.47 3.35
1.40 695.35 708.90 711.46 712.31 712.66 712.82 713.40 713.34 713.41 737.94 3.32
1.50 729.39 743.55 746.09 747.10 747.75 747.71 748.19 748.05 748.10 773.48 3.27
Tab.2 Simulation and theoretical values of magnetic induction intensity
$ d/ $mm $T_{\rm{num} }/{{\rm{s}}}$ ${ {T} }_{ { {\rm{o} } }{ {\rm{u} } }{ {\rm{r} } } }/{{\rm{s}}}$
N=16 N=32 N=48 N=64 N=80 N=96 N=112 N=128 N=144
0.10 13 21 34 51 73 109 150 186 242 0.00303
0.20 11 20 34 52 72 107 147 182 245 0.00097
0.30 15 22 38 50 78 110 154 175 236 0.00107
0.40 14 23 39 50 76 105 148 173 245 0.00080
0.50 13 22 33 50 74 106 146 184 247 0.00281
0.60 14 21 37 51 74 113 149 182 249 0.00047
0.70 13 23 39 52 74 112 146 180 246 0.00040
0.80 11 20 35 49 75 106 146 186 241 0.00040
0.90 14 21 39 49 74 114 148 185 253 0.00040
1.00 11 21 38 51 78 104 144 185 247 0.00040
1.10 15 22 39 53 75 107 140 182 231 0.00038
1.20 13 22 33 52 75 104 142 185 246 0.00037
1.30 15 17 39 52 77 97 145 186 251 0.00037
1.40 13 20 34 51 75 101 143 177 232 0.00045
1.50 10 21 34 51 77 108 150 185 240 0.00044
Tab.3 Computation time of two methods under different deformations
$ d $/mm $ b $ $ l $ $ k $ $ {R}^{2} $ ${R}_{{\rm{A}}}^{2}$ RMSE
0.10 553.70 ?62.61 0.91 0.9961 0.9947 0.3239
0.20 554.82 ?55.22 0.92 0.9986 0.9981 0.1967
0.30 557.26 ?54.40 0.92 0.9949 0.9932 0.3719
0.40 560.65 ?52.01 0.92 0.9952 0.9936 0.3653
0.50 564.73 ?55.48 0.92 0.9978 0.9971 0.2460
0.60 571.26 ?43.54 0.93 0.9998 0.9998 0.0715
0.70 580.07 ?58.07 0.92 0.9978 0.997 0.2537
0.80 589.70 ?61.77 0.91 0.9979 0.9972 0.2494
0.90 602.70 ?70.88 0.91 0.9920 0.9893 0.5094
1.00 617.94 ?59.11 0.92 0.9969 0.9958 0.3274
1.10 636.13 ?62.45 0.92 0.9975 0.9967 0.2957
1.20 657.70 ?63.26 0.92 0.9968 0.9957 0.3468
1.30 683.55 ?67.03 0.92 0.9987 0.9983 0.2298
1.40 713.03 ?69.82 0.92 0.9963 0.9951 0.4088
1.50 747.84 ?72.55 0.92 0.9969 0.9959 0.3893
Tab.4 Fitting results and evaluation metrics under different deformations
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