Biomedical Engineering Reference
In-Depth Information
4.3.2 Accuracy of Online Calibration
As the marker calibration is only one, however important, part of the accuracy of
the online calibration method, we have conducted three further experiments. For
evaluation, we compare the results of the online calibration to the QR24 algorithm
for hand-eye calibration and to the hand-eye calibration method by Tsai and Lenz.
4.3.2.1 Accuracy in a World Calibration Setup
Primarily, we have evaluated the calibration methods in a world calibration setup
in which a ground truth as reference can be utilized. Therefore, we have performed
the calibrations within a grid of different tracking system positions. By comparison
of neighboring calibration results, we have found the errors of the different cali-
bration methods as summarized in Table
4.2
and visualized in Fig.
4.9
.
The mean translational error for the QR24 algorithm for hand-eye calibration is
0.88 mm. The mean error of the online calibration is slightly larger with 1.36 mm.
However, the online calibration method performs better than the standard method
for hand-eye calibration, which is the method by Tsai and Lenz. The mean error
for this method is 1.94 mm. For the rotational part of the calculated transforms, the
mean errors are 0.027
, 0.11
and 0.056
for the QR24 algorithm, the method by
Tsai and Lenz, and the online calibration approach, respectively.
4.3.2.2 Variance in the Robot Workspace
Furthermore, we have tested the variance of the accuracy of the calibration within
the robot workspace. To this end, we have moved the robot to different initial
positions at which we have performed the calibrations. Again, we have compared
the calibration results among one another (cf.
Sect. 4.2.5
).
Table 4.2
Errors of the different calibration methods when using a 3
3
3 grid spaced at
100 mm
QR24
Tsai-Lenz
Online calibration
Translational error (mm)
Mean
0.88
1.94
1.36
RMS
1.29
2.66
1.86
Max
3.10
6.96
5.30
Rotational error (
)
Mean
0.027
0.111
0.056
RMS
0.061
0.253
0.123
Max
0.102
0.387
0.243
Neighboring calibration results are compared to the grid's ground truth
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