Biomedical Engineering Reference
In-Depth Information
application. However, our realistic setup equally employs all the steps required for
a robotized TMS application. It is therefore a valid substitution for a practical
evaluation during stimulation.
4.3 Evaluation of Online Calibration
4.3.1 Accuracy of Marker Calibration
To evaluate the accuracy of the marker calibration, we have estimated the distance
of the marker to the axis of rotation in joint 3. In this way, we calculate the
translational error for the x- and y-axis of the marker calibration, as described in
Sect. 4.2.4
. We have found that the mean error is 0.16 mm for the marker cali-
bration with a standard deviation (SD) of 0.11 mm and an RMS error of 0.19 mm.
The results found for all five calibrations are summarized in Table
4.1
. As the
accuracy of the tracking system is typically in the range of roughly 0.2-0.3 mm
[
12
,
27
], an RMS error of less than 0.2 mm is entirely satisfactory. This result
shows that the transformation of the marker to the third link can be performed very
accurately. This is a key factor for the accuracy of the online calibration as it is
based on that transformation.
Furthermore, we have analyzed the stability of the marker calibration. There-
fore, we have performed the marker calibration seven times with the same position
of the marker at link three. By comparison of the resulting transformation matrices
among one another (cf.
Sect. 4.2.5
), we have found that the mean translational
deviation for the marker calibration is 0.34 mm with an SD of 0.23 mm. The RMS
error is 0.41 mm. The mean rotational deviation is 0.14
with an SD of 0.08
and
the RMS error is 0.16
. These results suggest that the marker calibration method
provides stable results for calculation of the transformation between marker and
link three.
Table 4.1 Translational error of marker calibration for the online calibration method
# of calibration
q
S
2
T
M
r
e
Þ
1
;
4
þ
S
2
T
M
Þ
2
;
4
ð
ð
1
199
:
05
198
:
87
0.177
2
192
:
65
192
:
60
0.051
3
252
:
64
252
:
31
0.330
4
195
:
60
195
:
43
0.169
5
165
:
03
164
:
96
0.076
Mean
0.161
q
S
2
T
M
Þ
1
;
4
þ
S
2
T
M
Þ
2
;
4
r gives the distance of the marker to the axis of rotation in joint 3.
ð
ð
describes the distance of the marker to joint 3 based on the marker calibration (only x- and y-
axis). e is the error found (all values in mm)
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