Precision improvement method for serial robot localization based on a new calibration and compensation strategy
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摘要:
在使用串联机器人进行定位操作前，首先需要对机器人基坐标系与测量坐标系进行位姿关系的标定，针对具有隐藏机器人基坐标系以及机器人法兰坐标系的串联机构，本文提出一种等价变换思想并结合应用激光跟踪仪测得机器人末端靶标点的坐标数据建立标定矩阵方程，应用罗德里格矩阵变换将标定方程转化为三元二次矩阵方程形式，采用最小二乘法和牛顿迭代法求出数值解进而完成机器人基坐标系与测量坐标系标定的方法。然后应用这种方法进行标定试验得到了20组标定结果，通过比较标定结果偏差进而验证了这种方法的正确性。最后，本文验证了应用这种标定方法的标定结果并结合一种新的位姿补偿算法后，能极大地提高机器人末端的定位精度。
Abstract:Before the localization operation, the serial robot position relationship between base coordinate system and measurement coordinate system needs to be demarcated. For the hidden robot base and flange coordinate systems of serial mechanism, a kind of equivalent transformation method is presented in this paper, which is combined with the application of the target-points coordinate measurement data at the end of the robot using laser tracker to establish the calibration matrix equation. Calibration equation can be transformed into the ternary quadratic matrix equation form by Rodrigo matrix. Then the matrix equation between the robot base and measurement coordinate systems can be solved by using least square method and Newton iteration method. This method is verified by calibration test and 20 groups of calibration results are obtained. The calibration results combined with a position compensation algorithm can greatly improve the localization precision of robot.
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Key words:
- robot /
- calibration /
- equivalent transformation method /
- compensation /
- localization precision
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表 1 标定试验记录
Table 1. Records of calibration experiment
序号 1 2 3 4 5 6 X/mm 787.08 1 034.80 781.15 920.70 845.21 1 260.31 Y/mm 652.11 421.65 789.07 716.23 624.32 779.90 Z/mm 1 397.13 1 510.33 1 421.27 1 300.67 1 336.91 1 256.55 A/(°) -17.88 3.59 15.65 34.18 0.52 26.86 B/(°) -34.95 -14.42 13.12 14.70 26.71 50.43 C/(°) -131.82 -108.07 -77.79 -48.75 -122.20 -80.52 靶标点PP1/mm -1 451.694 1 -1 532.075 4 -1 389.275 6 -1 388.278 1 -1 465.091 5 -1 104.085 2 1 261.126 1 939.940 5 1 342.042 8 1 159.200 2 1 207.296 0 920.818 0 870.637 0 1 016.827 0 975.633 1 864.795 4 882.391 6 836.600 1 靶标点PP2/mm -1 481.243 6 -1 511.547 8 -1 356.844 6 -1 341.088 7 -1 492.635 2 -1 124.393 0 1 176.577 6 874.397 1 1 337.026 3 1 197.063 4 1 173.368 3 946.855 1 849.137 2 955.521 8 889.580 0 795.399 4 801.334 9 750.644 5 靶标点PP3/mm -1 429.139 9 -1 466.628 8 -1 306.996 3 -1 288.543 3 -1 413.111 0 -1 046.697 3 1 170.211 8 853.476 0 1 275.929 2 1 125.866 1 1 127.190 6 891.396 3 928.905 5 1 037.245 2 943.469 3 831.433 4 827.094 3 747.072 6 
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表 2 标定试验结果
Table 2. Results of calibration experiment
参数 Xr/mm Yr/mm Zr/mm Ar/(°) Br/(°) Cr/(°) 数值 2 614.63 1 173.67 490.06 55.31 -0.08 -0.21
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表 3 通用补偿算法补偿实验靶标数据记录
Table 3. Target data records in compensation experimentwith universal compensation algorithmmm
mm 靶标序号 初始靶标 目标靶标 补偿前 补偿后 靶标点1 -1 408.80 -1 455.28 -1 455.39 -1 455.30 1 398.80 1 263.11 1 263.22 1 263.21 1 027.63 848.95 849.21 848.94 靶标点2 -1 416.39 -1 463.87 -1 463.99 -1 463.87 1 347.08 1 211.64 1 211.75 1 211.74 1 081.34 902.76 903.00 902.74 靶标点 -1 416.51 -1 450.18 -1 450.29 -1 450.18 1 400.22 1 262.90 1 263.00 1 263.00 1 140.48 961.97 962.22 961.95
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表 4 通用补偿算法补偿前后靶标误差值
Table 4. Target error values before and afteruniversal compensation algorithmmm
mm 过程 靶标点1 靶标点2 靶标点3 补偿前 0.30 0.29 0.29 补偿后 0.10 0.10 0.10
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表 5 新补偿算法补偿实验靶标数据记录1
Table 5. Target data record 1 in compensation experiment with the new compensation algorithmmm
mm 靶标序号 初始靶标 目标靶标 补偿前 补偿后 靶标点1 -1 408.82 -1 455.28 -1 455.34 -1 455.30 1 398.83 1 263.11 1 263.31 1 263.13 1 027.55 848.95 849.28 848.95 靶标点2 -1 416.41 -1 463.87 -1 463.94 -1 463.88 1 347.13 1 211.64 1 211.85 1 211.66 1 081.25 902.76 903.07 902.75 靶标点3 -1 416.52 -1 450.18 -1 450.25 -1 450.18 1 400.27 1 262.90 1 263.10 1 262.91 1 140.39 961.97 962.29 961.97
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表 6 新补偿算法补偿前后靶标误差值
Table 6. Target error values before and after the new compensation algorithmmm
mm 过程 靶标点1 靶标点2 靶标点3 补偿前 0.39 0.38 0.39 补偿后 0.03 0.02 0.02
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表 7 新补偿算法补偿实验靶标数据记录2
Table 7. Target error values before and after the new compensation algorithmmm
mm 靶标序号 初始靶标 目标靶标 补偿前 补偿后 靶标点1 -1 630.62 -1 470.65 -1 470.99 -1 470.67 631.62 385.45 385.36 385.43 888.57 875.46 876.05 875.47 靶标点2 -1 632.82 -1 458.37 -1 458.74 -1 458.38 681.02 434.08 433.99 434.06 940.35 926.55 927.13 926.57 靶标点3 -1 648.09 -1 473.47 -1 473.83 -1 473.49 611.25 364.67 364.57 364.65 947.85 937.06 937.64 937.08
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表 8 补偿前后靶标误差值
Table 8. Target error values before and after compensation
mm 过程 靶标点1 靶标点2 靶标点3 补偿前 0.69 0.69 0.69 补偿后 0.03 0.03 0.03
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