Fig. 1. Sketch of branch chain drive and constraint distribution
Fig. 2. Sketch of the force on the offset linkage
Fig. 3. Binding force load distribution diagram
Fig. 4. Drive force deformation distribution diagram
Fig. 5. Binding force load sketch
Fig. 6. Platform force deformation cloud map
Fig. 7. Comparison of simulation results and stiffness model prediction results
Fig. 8. Comparison of simulation results and stiffness model prediction results
Fig. 9. Data acquisition Simulink control system diagram
Fig. 10. Position error distribution chart
Fig. 11. Stiffness model prediction flow chart
Fig. 12. Stiffness model predicts cornering error diagram
Fig. 13. Effect diagram of stiffness model prediction error
Fig. 14. Neural network structure diagram
Fig. 15. Loss value change diagram of model01
Fig. 16. Loss value change diagram of model02
Fig. 17. Loss value change diagram of model03
Fig. 18. Comparison of the effect of drive error prediction
Fig. 19. Error compensation flow 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x轴![]() 角度 | beta_real_output | 输出 | 调姿平台绕y轴![]() 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 |
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Table 1. Simulink and Adams co-simulation data transmission signal table
编号 | ![]() /rad | ![]() /rad | ![]() /mm | ![]() /mm | ![]() /rad | ![]() /rad | ![]() /mm | ![]() /mm |
---|
1 | -0.140 | -0.084 | 701.106 | 614.398 | -0.131 | -0.093 | 704.847 | 617.847 | 2 | 0.175 | 0.047 | 650.004 | 737.750 | 0.182 | 0.038 | 653.847 | 740.847 | 3 | -0.052 | 0.182 | 598.746 | 648.001 | -0.044 | 0.174 | 602.097 | 651.097 | 4 | 0.175 | 0.154 | 610.246 | 737.753 | 0.182 | 0.144 | 614.097 | 740.847 | 5 | 0.175 | -0.042 | 684.484 | 737.766 | 0.182 | -0.052 | 688.347 | 740.847 | 6 | -0.122 | 0.103 | 628.500 | 621.250 | -0.114 | 0.095 | 631.847 | 624.347 | 7 | 0.175 | 0.099 | 630.491 | 737.757 | 0.182 | 0.089 | 634.347 | 740.847 | 8 | -0.174 | 0.122 | 622.127 | 601.850 | -0.167 | 0.111 | 626.097 | 604.597 | 9 | 0.018 | 0.132 | 617.243 | 675.256 | 0.025 | 0.122 | 621.097 | 678.347 | 10 | 0.123 | -0.209 | 750.723 | 717.028 | 0.130 | -0.217 | 754.097 | 719.847 |
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Table 2. Attitude and drive data sheets
编号 | ![]() /N | ![]() /N | ![]() /N | ![]() /(N·m-1) | ![]() /(N·m-1) | ![]() /(N·m-1) |
---|
1 | -36.200 | 34.446 | -5.415 | -23 103.390 | -25 070.880 | 2 506.712 | 2 | -1.222 | 0.613 | -3.934 | -105.952 | -803.991 | -110.028 | 3 | 0.553 | -0.695 | -5.230 | 275.456 | 773.382 | -96.211 | 4 | 0.950 | -0.612 | -4.032 | 700.720 | 909.381 | 46.906 | 5 | 5.849 | -5.323 | -4.907 | 3 856.979 | 3 889.783 | 723.520 | 6 | -0.305 | 0.018 | -2.468 | -174.750 | -120.763 | 31.912 | 7 | 2.894 | -2.041 | -5.466 | 1 748.686 | 2 200.867 | 187.711 | 8 | 39.159 | -37.624 | -13.199 | 22 967.717 | 27 074.169 | -7 718.717 | 9 | 2.222 | -2.072 | -5.071 | 1 350.870 | 1 801.997 | -157.752 | 10 | 9.564 | -11.141 | -1.386 | 7 316.494 | 6 425.502 | 1 919.056 |
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Table 3. External Load Data Sheet
编号 | ![]() /rad | ![]() /rad | ![]() /rad | ![]() /rad |
---|
1 | -0.330 88 | -0.144 78 | -0.009 33 | 0.009 10 | 2 | 0.114 59 | -0.056 31 | -0.006 59 | 0.007 98 | 3 | 0.048 08 | 0.073 82 | -0.006 73 | 0.009 60 | 4 | 0.018 12 | -0.025 92 | -0.007 28 | 0.008 05 | 5 | 0.014 69 | -0.015 57 | -0.007 27 | 0.009 38 | 6 | 0.297 89 | -0.018 13 | -0.007 01 | 0.008 25 | 7 | -0.068 59 | -0.308 67 | -0.007 90 | 0.008 00 | 8 | 0.094 53 | -0.063 64 | -0.006 80 | 0.009 39 | 9 | 0.007 54 | 0.009 02 | -0.007 18 | 0.009 37 | 10 | -0.008 56 | -0.013 48 | -0.007 94 | 0.008 99 |
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Table 4. Stiffness model prediction error comparison data table
编号 | ![]() /mm | ![]() /mm | ![]() /mm | ![]() /mm |
---|
1 | 2.626 54 | -6.271 16 | -3.740 94 | -3.449 43 | 2 | 0.626 43 | 0.527 63 | -3.843 02 | -3.096 76 | 3 | -0.114 18 | 0.319 11 | -3.350 20 | -3.095 95 | 4 | -0.133 53 | 0.426 58 | -3.850 36 | -3.093 61 | 5 | -0.358 79 | -0.147 79 | -3.862 59 | -3.081 32 | 6 | 0.184 46 | 0.073 65 | -3.346 78 | -3.097 22 | 7 | -0.457 10 | 0.336 42 | -3.855 70 | -3.089 64 | 8 | -10.757 58 | 6.424 19 | -3.969 88 | -2.747 18 | 9 | -0.316 61 | 0.423 31 | -3.853 94 | -3.091 10 | 10 | 0.589 86 | 0.990 93 | -3.373 54 | -2.818 80 |
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Table 5. Stiffness prediction comparison data table
序号 | 名称 | 输入 | 输出 | 结构 |
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1 | model01 | αt,βt | δL1,δL2 | (2,20,10,2) | 2 | model02 | αt,βt,Fe,Me | δL1,δL2 | (8,20,10,2) | 3 | model03 | ΔL1,ΔL2 | δL1,δL2 | (2,20,10,2) |
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Table 6. Built neural structure
编号 | 实际补偿值/mm | model01补偿值/mm | model02补偿值/mm | model03补偿值/mm |
---|
![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
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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 |
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Table 7. Data table of prediction results of three networks
编号 | 姿态角 | 外部力 | 外力偶 |
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α/rad | β/rad | Fex/N | Fey/N | Fez/N | Mex/(N·mm-1) | Mey/(N·mm-1) | Mez/(N·mm-1) |
---|
1 | -0.120 | -0.176 | 0 | 0 | -4 151.79 | -301 051.28 | -459 749.94 | 0 | 2 | -0.033 | 0.101 | 0 | 0 | -4 151.79 | -106 502.24 | 176 054.63 | 0 | 3 | -0.047 | -0.120 | 0 | 0 | -4 151.79 | -137 849.22 | -332 487.49 | 0 | 4 | -0.085 | -0.191 | 0 | 0 | -4 151.79 | -221 843.27 | -493 609.78 | 0 | 5 | -0.084 | -0.023 | 0 | 0 | -4 151.79 | -223 862.99 | -109 816.38 | 0 | 6 | 0.174 | -0.166 | 0 | 0 | -4 151.79 | 362 026.06 | -437 118.77 | 0 | 7 | 0.111 | 0.147 | 0 | 0 | -4 151.79 | 223 223.07 | 281 649.50 | 0 | 8 | 0.080 | 0.052 | 0 | 0 | -4 151.79 | 153 782.74 | 63 168.79 | 0 | 9 | -0.008 | 0.165 | 0 | 0 | -4 151.79 | -48 893.74 | 322 819.34 | 0 | 10 | 0.188 | -0.006 | 0 | 0 | -4 151.79 | 400 907.45 | -70 625.68 | 0 |
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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) |
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α/rad | β/rad | L1/mm | L2/mm | αr/rad | βr/rad | αe/rad | βe/rad |
---|
1 | -0.120 | -0.176 | 737.852 | 737.852 | -0.128 1 | -0.168 1 | 8.212 2 | -7.895 3 | 2 | -0.033 | 0.101 | 629.250 | 629.250 | -0.041 1 | 0.109 4 | 8.029 1 | -8.498 8 | 3 | -0.047 | -0.120 | 715.875 | 715.875 | -0.054 7 | -0.112 1 | 7.833 5 | -7.830 9 | 4 | -0.085 | -0.191 | 744.061 | 744.061 | -0.093 0 | -0.183 1 | 8.046 2 | -7.857 9 | 5 | -0.084 | -0.023 | 677.366 | 677.366 | -0.092 2 | -0.015 0 | 8.101 7 | -8.120 0 | 6 | 0.174 | -0.166 | 733.401 | 733.401 | 0.166 2 | -0.157 7 | 7.773 8 | -8.298 0 | 7 | 0.111 | 0.147 | 612.244 | 612.244 | 0.103 1 | 0.155 6 | 7.894 4 | -8.619 0 | 8 | 0.080 | 0.052 | 648.127 | 648.127 | 0.072 4 | 0.060 2 | 7.645 5 | -8.127 6 | 9 | -0.008 | 0.165 | 605.170 | 605.170 | -0.016 0 | 0.173 8 | 8.069 9 | -8.828 5 | 10 | 0.188 | -0.006 | 670.662 | 670.662 | 0.180 2 | 0.002 3 | 7.738 1 | -8.266 8 |
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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) |
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α/rad | β/rad | ![]() /mm | ![]() /mm | αr/rad | βr/rad | αe/rad | βe/rad |
---|
1 | -0.120 | -0.176 | 741.467 | 740.943 | -0.119 9 | -0.177 0 | -8.173 5 | 7.882 3 | 2 | -0.033 | 0.101 | 632.897 | 632.332 | -0.033 1 | 0.099 7 | -7.987 1 | 8.429 6 | 3 | -0.047 | -0.120 | 719.610 | 718.931 | -0.046 8 | -0.121 5 | -7.811 1 | 7.823 0 | 4 | -0.085 | -0.191 | 747.663 | 747.156 | -0.084 9 | -0.192 0 | -8.018 0 | 7.855 6 | 5 | -0.084 | -0.023 | 681.101 | 680.422 | -0.084 2 | -0.024 5 | -8.058 1 | 8.074 8 | 6 | 0.174 | -0.166 | 737.029 | 736.488 | 0.173 8 | -0.167 0 | -7.795 3 | 8.347 1 | 7 | 0.111 | 0.147 | 615.880 | 615.329 | 0.110 9 | 0.145 9 | -7.880 0 | 8.577 6 | 8 | 0.080 | 0.052 | 651.776 | 651.208 | 0.080 2 | 0.050 8 | -7.634 0 | 8.107 9 | 9 | -0.008 | 0.165 | 608.817 | 608.251 | -0.008 2 | 0.163 8 | -8.031 4 | 8.745 3 | 10 | 0.188 | -0.006 | 674.326 | 673.739 | 0.187 8 | -0.007 1 | -7.752 6 | 8.289 3 |
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Table 10. Compensated attitude error data table