A Rapid Coordinate Transformation Method Applied in Industrial Robot Calibration Based on Characteristic Line Coincidence
"> Figure 1
<p>Online calibration system of robot kinematic parameters.</p> "> Figure 2
<p>The schematic diagram of coordinate transformation method.</p> "> Figure 3
<p>Schematic diagram of a vector rotated around an arbitrary axis.</p> "> Figure 4
<p>The processes of the coordinate transformation method.</p> "> Figure 5
<p>Transformation error from robot to photogrammetric system.</p> "> Figure 6
<p>Transformation error from robot to laser tracker.</p> "> Figure 7
<p>Measurement system.</p> "> Figure 8
<p>Position errors after robot calibration.</p> "> Figure 9
<p>Transformation error compared with different algorithms.</p> ">
Abstract
:1. Introduction
2. Online Calibration System of Robot
3. Methods of Online Calibration System
3.1. Method of Coordinate Transformation
- (a)
- Translate the rotation axis to the coordinate origin. The corresponding transformation matrix can be calculated as:
- (b)
- Rotate the axis α1 degrees to Plane XOZ.is the angle between the axis and plane XOZ. It can be obtained by , , where, (a1, b1, c1) are the coordinates of vector C, as Figure 3b shows.
- (c)
- Rotate the axis β1 degrees to coincide with Axis Z.
- (d)
- Rotate the axis degrees around Axis Z, as shown in Figure 3d.
- (e)
- Rotate the axis by reversing the process of Step (c)
- (f)
- Rotate the axis by reversing the process of Step (b).
- (g)
- Rotate the axis by reversing the process of Step (a)
3.2. Method of Robot Calibration
4. Experiments and Analysis
4.1. Coordinate Transformationin an On-line Robot Calibration System
4.2. Position Error of Robot after Coordinate Transformation and Calibration
4.3. Accuracy of Coordinate Transformation Method
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Robot to Photogrammetric System | Robot to Laser Tracker | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
a1 | b1 | c1 | α1 | β1 | θ1 | a1 | b1 | c1 | α1 | β1 | θ1 |
−2588.9 | 81326 | −62472 | 127.53° | 1.4461° | 256.282° | −3.0135 | 11.132 | −5.8921 | 117.89° | 13.456° | 0.007° |
a2 | b2 | c2 | α2 | β2 | θ2 | a2 | b2 | c2 | α2 | β2 | θ2 |
−30491 | −39586 | 1397.2 | 87.979° | 37.588° | 208.161° | −6.143 | 0.26899 | −5.9267 | 177.4° | 45.997° | 0.004° |
a3 | b3 | c3 | α3 | β3 | θ3 | a3 | b3 | c3 | α3 | β3 | θ3 |
210.37 | −155.16 | 194.69 | 38.555° | 40.198° | 176.953° | 200.03 | 159.99 | −200.07 | 141.35° | 37.984° | 0.005° |
Robot to Photogrammetric System | Robot to Laser Tracker | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Photogrammetric system | Robot | Laser tracker | Robot | ||||||||
Px | Py | Pz | Rx | Ry | Rz | Lx | Ly | Lz | Rx | Ry | Rz |
42.728 | 138.567 | 109.566 | 895 | 30 | 875 | 1048.620 | 29.944 | 875.077 | 895 | 30 | 875 |
108.751 | 140.724 | 108.418 | 961 | 30 | 875 | 1114.679 | 29.985 | 874.995 | 961 | 30 | 875 |
175.846 | 143.007 | 107.153 | 1028 | 30 | 875 | 1181.646 | 29.955 | 874.989 | 1028 | 30 | 875 |
242.882 | 145.388 | 105.845 | 1095 | 30 | 875 | 1248.689 | 29.935 | 874.791 | 1095 | 30 | 875 |
76 points are ignored | 76 points are ignored | ||||||||||
Transformation result | error | Transformation result | error | ||||||||
Tx | Ty | Tz | Δx | Δy | Δz | Tx | Ty | Tz | Δx | Δy | Δz |
42.975 | 138.590 | 109.751 | −0.247 | −0.023 | −0.185 | 1048.624 | 29.967 | 875.024 | −0.004 | −0.023 | 0.053 |
108.921 | 140.822 | 108.277 | −0.170 | −0.098 | 0.141 | 1114.625 | 29.956 | 875.012 | 0.054 | 0.029 | −0.017 |
175.866 | 143.088 | 106.780 | −0.020 | −0.081 | 0.373 | 1181.624 | 29.944 | 875.001 | 0.022 | 0.011 | −0.012 |
242.812 | 145.355 | 105.282 | 0.070 | 0.033 | 0.563 | 1248.624 | 29.932 | 874.890 | 0.065 | 0.003 | −0.099 |
76 points are ignored | 76 points are ignored |
Region | O | O1 | O2 | O3 | O4 | O5 |
---|---|---|---|---|---|---|
Position error/mm | 0.200 | 0.330 | 0.360 | 0.271 | 0.335 | 0.319 |
Points | Station 1 | Station 2 | ||||
x/mm | y/mm | z/mm | x/mm | y/mm | z/mm | |
1 | 3049.626 | −188.668 | −1403.555 | 1484.68 | 1639.268 | −1401.164 |
2 | 4247.93 | 991.939 | −1401.334 | 1050.101 | 3264.365 | −1396.089 |
3 | 1678.935 | 1946.842 | −1380.022 | −1049.19 | 1502.397 | −1379.453 |
4 | 3688.375 | 2777.637 | −1403.824 | −778.88 | 3659.965 | −1398.95 |
5 | 3802.578 | 1207.190 | −1397.241 | 642.931 | 2983.472 | −1392.788 |
Points | Three-Point | Rodrigo Matrix | SVD | Quaternion | Characteristic Line | |
RMS/mm | RMS/mm | RMS/mm | RMS/mm | RMS/mm | ||
1 | 0.013 | 0.006 | 0.015 | 0.015 | 0.008 | |
2 | 0.050 | 0.041 | 0.041 | 0.041 | 0.008 | |
3 | 0.012 | 0.013 | 0.011 | 0.011 | 0.034 | |
4 | 0.029 | 0.009 | 0.021 | 0.021 | 0.031 | |
5 | 0.061 | 0.053 | 0.053 | 0.053 | 0.026 | |
0.033 | 0.024 | 0.027 | 0.028 | 0.025 | ||
Execution time/s | 0.021 | 0.203 | 0.031 | 0.023 | 0.029 |
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Liu, B.; Zhang, F.; Qu, X.; Shi, X. A Rapid Coordinate Transformation Method Applied in Industrial Robot Calibration Based on Characteristic Line Coincidence. Sensors 2016, 16, 239. https://doi.org/10.3390/s16020239
Liu B, Zhang F, Qu X, Shi X. A Rapid Coordinate Transformation Method Applied in Industrial Robot Calibration Based on Characteristic Line Coincidence. Sensors. 2016; 16(2):239. https://doi.org/10.3390/s16020239
Chicago/Turabian StyleLiu, Bailing, Fumin Zhang, Xinghua Qu, and Xiaojia Shi. 2016. "A Rapid Coordinate Transformation Method Applied in Industrial Robot Calibration Based on Characteristic Line Coincidence" Sensors 16, no. 2: 239. https://doi.org/10.3390/s16020239