• Optics and Precision Engineering
  • Vol. 30, Issue 24, 3139 (2022)
Yi LIU, Xiaoteng MA, Zongqiang FENG, Jiantao YAO*, and Yongsheng ZHAO
Author Affiliations
  • Laboratory of Parallel Robotics and Mechatronic Systems in Hebei Province, Yanshan University, Qinhuangdao066004, China
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    DOI: 10.37188/OPE.20223024.3139 Cite this Article
    Yi LIU, Xiaoteng MA, Zongqiang FENG, Jiantao YAO, Yongsheng ZHAO. Stiffness prediction-neural network based error compensation for attitude adjustment platform[J]. Optics and Precision Engineering, 2022, 30(24): 3139 Copy Citation Text show less
    Sketch of branch chain drive and constraint distribution
    Fig. 1. Sketch of branch chain drive and constraint distribution
    Sketch of the force on the offset linkage
    Fig. 2. Sketch of the force on the offset linkage
    Binding force load distribution diagram
    Fig. 3. Binding force load distribution diagram
    Drive force deformation distribution diagram
    Fig. 4. Drive force deformation distribution diagram
    Binding force load sketch
    Fig. 5. Binding force load sketch
    Platform force deformation cloud map
    Fig. 6. Platform force deformation cloud map
    Comparison of simulation results and stiffness model prediction results
    Fig. 7. Comparison of simulation results and stiffness model prediction results
    Comparison of simulation results and stiffness model prediction results
    Fig. 8. Comparison of simulation results and stiffness model prediction results
    Data acquisition Simulink control system diagram
    Fig. 9. Data acquisition Simulink control system diagram
    Position error distribution chart
    Fig. 10. Position error distribution chart
    Stiffness model prediction flow chart
    Fig. 11. Stiffness model prediction flow chart
    Stiffness model predicts cornering error diagram
    Fig. 12. Stiffness model predicts cornering error diagram
    Effect diagram of stiffness model prediction error
    Fig. 13. Effect diagram of stiffness model prediction error
    Neural network structure diagram
    Fig. 14. Neural network structure diagram
    Loss value change diagram of model01
    Fig. 15. Loss value change diagram of model01
    Loss value change diagram of model02
    Fig. 16. Loss value change diagram of model02
    Loss value change diagram of model03
    Fig. 17. Loss value change diagram of model03
    Comparison of the effect of drive error prediction
    Fig. 18. Comparison of the effect of drive error prediction
    Error compensation flow chart
    Fig. 19. Error compensation flow chart
    Drive compensation error comparison chart
    Fig. 20. Drive compensation error comparison chart
    输入信号类型信号说明
    L1_drive_input输入位置模式驱动RRPU支链电动缸
    L2_drive_input输入位置模式驱动RPU支链电动缸
    revolve_acc_input输入加速度模式驱动跟踪平台回转电机
    Pitch_acc_input输入加速度模式驱动跟踪平台俯仰电机
    L1_length_output输出RRPU支链电动缸的实际长度
    L2_length_output输出RPU支链电动缸的实际长度
    alpha_real_output输出调姿平台绕xα角度
    beta_real_output输出调姿平台绕yβ角度
    revolve_angle_output输出跟踪平台实时回转角度
    Pitch_angle_output输出跟踪平台实时俯仰角度
    Fe_x_output输出上平台沿z轴方向的受力
    Fe_y_output输出上平台沿y轴方向的受力
    Fe_z_output输出上平台沿z轴方向的受力
    Me_x_output输出上平台沿x轴方向的力偶
    Me_y_output输出上平台沿y轴方向的力偶
    Me_z_output输出上平台沿z轴方向的力偶
    Time_output输出仿真过程Adams的实时时间
    Table 1. Simulink and Adams co-simulation data transmission signal table
    编号αr/radβr/radL1r/mmL2r/mmαt/radβt/radL1t/mmL2t/mm
    1-0.140-0.084701.106614.398-0.131-0.093704.847617.847
    20.1750.047650.004737.7500.1820.038653.847740.847
    3-0.0520.182598.746648.001-0.0440.174602.097651.097
    40.1750.154610.246737.7530.1820.144614.097740.847
    50.175-0.042684.484737.7660.182-0.052688.347740.847
    6-0.1220.103628.500621.250-0.1140.095631.847624.347
    70.1750.099630.491737.7570.1820.089634.347740.847
    8-0.1740.122622.127601.850-0.1670.111626.097604.597
    90.0180.132617.243675.2560.0250.122621.097678.347
    100.123-0.209750.723717.0280.130-0.217754.097719.847
    Table 2. Attitude and drive data sheets
    编号Fexr/NFeyr/NFezr/NMexr/(N·m-1Meyr/(N·m-1Mezr/(N·m-1
    1-36.20034.446-5.415-23 103.390-25 070.8802 506.712
    2-1.2220.613-3.934-105.952-803.991-110.028
    30.553-0.695-5.230275.456773.382-96.211
    40.950-0.612-4.032700.720909.38146.906
    55.849-5.323-4.9073 856.9793 889.783723.520
    6-0.3050.018-2.468-174.750-120.76331.912
    72.894-2.041-5.4661 748.6862 200.867187.711
    839.159-37.624-13.19922 967.71727 074.169-7 718.717
    92.222-2.072-5.0711 350.8701 801.997-157.752
    109.564-11.141-1.3867 316.4946 425.5021 919.056
    Table 3. External Load Data Sheet
    编号Δαr/radΔβr/radδαsiffpre/radδβsiffpre/rad
    1-0.330 88-0.144 78-0.009 330.009 10
    20.114 59-0.056 31-0.006 590.007 98
    30.048 080.073 82-0.006 730.009 60
    40.018 12-0.025 92-0.007 280.008 05
    50.014 69-0.015 57-0.007 270.009 38
    60.297 89-0.018 13-0.007 010.008 25
    7-0.068 59-0.308 67-0.007 900.008 00
    80.094 53-0.063 64-0.006 800.009 39
    90.007 540.009 02-0.007 180.009 37
    10-0.008 56-0.013 48-0.007 940.008 99
    Table 4. Stiffness model prediction error comparison data table
    编号ΔL1r/mmΔL2r/mmδL1siffpre/mmδL2siffpre/mm
    12.626 54-6.271 16-3.740 94-3.449 43
    20.626 430.527 63-3.843 02-3.096 76
    3-0.114 180.319 11-3.350 20-3.095 95
    4-0.133 530.426 58-3.850 36-3.093 61
    5-0.358 79-0.147 79-3.862 59-3.081 32
    60.184 460.073 65-3.346 78-3.097 22
    7-0.457 100.336 42-3.855 70-3.089 64
    8-10.757 586.424 19-3.969 88-2.747 18
    9-0.316 610.423 31-3.853 94-3.091 10
    100.589 860.990 93-3.373 54-2.818 80
    Table 5. Stiffness prediction comparison data table
    序号名称输入输出结构
    1model01αtβtδL1δL2(2,20,10,2)
    2model02αtβtFeMeδL1δL2(8,20,10,2)
    3model03ΔL1,ΔL2δL1δL2(2,20,10,2)
    Table 6. Built neural structure
    编号实际补偿值/mmmodel01补偿值/mmmodel02补偿值/mmmodel03补偿值/mm
    ΔL1rΔL2rΔL1pre1ΔL2pre1ΔL1pre2ΔL2pre2ΔL1pre3ΔL2pre3
    1-3.740 9-3.449 4-3.601 8-3.609 2-3.570 9-4.012 6-3.416 6-3.180 1
    2-3.843 0-3.096 8-3.601 8-3.609 2-3.850 7-3.597 8-3.660 7-3.105 6
    3-3.350 2-3.095 9-3.602 9-3.607 9-3.380 6-3.624 0-3.589 5-3.123 3
    4-3.850 4-3.093 6-3.602 1-3.608 9-3.835 4-3.597 8-3.593 9-3.122 2
    5-3.862 6-3.081 3-3.601 8-3.609 2-3.853 0-3.597 7-3.576 8-3.126 5
    6-3.346 8-3.097 2-3.601 9-3.609 1-3.392 5-3.629 4-3.589 9-3.123 2
    7-3.855 7-3.089 6-3.601 9-3.609 1-3.834 4-3.597 8-3.588 2-3.123 6
    8-3.969 9-2.747 2-3.601 9-3.609 1-3.851 9-3.196 5-3.543 1-2.783 6
    9-3.853 9-3.091 1-3.601 9-3.609 1-3.850 2-3.598 7-3.592 6-3.122 5
    10-3.373 5-2.818 8-3.593 8-3.341 6-3.525 3-3.594 2-3.685 2-3.099 2
    Table 7. Data table of prediction results of three networks
    编号姿态角外部力外力偶
    α/radβ/radFex/NFey/NFez/NMex/(N·mm-1Mey/(N·mm-1Mez/(N·mm-1
    1-0.120-0.17600-4 151.79-301 051.28-459 749.940
    2-0.0330.10100-4 151.79-106 502.24176 054.630
    3-0.047-0.12000-4 151.79-137 849.22-332 487.490
    4-0.085-0.19100-4 151.79-221 843.27-493 609.780
    5-0.084-0.02300-4 151.79-223 862.99-109 816.380
    60.174-0.16600-4 151.79362 026.06-437 118.770
    70.1110.14700-4 151.79223 223.07281 649.500
    80.0800.05200-4 151.79153 782.7463 168.790
    9-0.0080.16500-4 151.79-48 893.74322 819.340
    100.188-0.00600-4 151.79400 907.45-70 625.680
    Table 8. Theoretical external load data sheet
    编号目标姿态理论驱动杆长实际姿态角度误差值(×10-3
    α/radβ/radL1/mmL2/mmαr/radβr/radαe/radβe/rad
    1-0.120-0.176737.852737.852-0.128 1-0.168 18.212 2-7.895 3
    2-0.0330.101629.250629.250-0.041 10.109 48.029 1-8.498 8
    3-0.047-0.120715.875715.875-0.054 7-0.112 17.833 5-7.830 9
    4-0.085-0.191744.061744.061-0.093 0-0.183 18.046 2-7.857 9
    5-0.084-0.023677.366677.366-0.092 2-0.015 08.101 7-8.120 0
    60.174-0.166733.401733.4010.166 2-0.157 77.773 8-8.298 0
    70.1110.147612.244612.2440.103 10.155 67.894 4-8.619 0
    80.0800.052648.127648.1270.072 40.060 27.645 5-8.127 6
    9-0.0080.165605.170605.170-0.016 00.173 88.069 9-8.828 5
    100.188-0.006670.662670.6620.180 20.002 37.738 1-8.266 8
    Table 9. Theoretically driven data sheets
    编号姿态角补偿后的驱动实际姿态角误差量(×10-3
    α/radβ/radL1c/mmL2c/mmαr/radβr/radαe/radβe/rad
    1-0.120-0.176741.467740.943-0.119 9-0.177 0-8.173 57.882 3
    2-0.0330.101632.897632.332-0.033 10.099 7-7.987 18.429 6
    3-0.047-0.120719.610718.931-0.046 8-0.121 5-7.811 17.823 0
    4-0.085-0.191747.663747.156-0.084 9-0.192 0-8.018 07.855 6
    5-0.084-0.023681.101680.422-0.084 2-0.024 5-8.058 18.074 8
    60.174-0.166737.029736.4880.173 8-0.167 0-7.795 38.347 1
    70.1110.147615.880615.3290.110 90.145 9-7.880 08.577 6
    80.0800.052651.776651.2080.080 20.050 8-7.634 08.107 9
    9-0.0080.165608.817608.251-0.008 20.163 8-8.031 48.745 3
    100.188-0.006674.326673.7390.187 8-0.007 1-7.752 68.289 3
    Table 10. Compensated attitude error data table
    Yi LIU, Xiaoteng MA, Zongqiang FENG, Jiantao YAO, Yongsheng ZHAO. Stiffness prediction-neural network based error compensation for attitude adjustment platform[J]. Optics and Precision Engineering, 2022, 30(24): 3139
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