Biomedical Engineering Reference
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positioning accuracy. Therefore, we use a realistic TMS coil positioning scenario.
For each evaluation of the online calibration method, we use the marker calibration
which has been calculated with 500 randomly chosen robot positions within a
sphere of 200 mm radius (see above).
World Calibration Setup:
For evaluation of the online calibration method and to determine the accuracy of
the setup, calibration is performed on a 3
3
3 grid spaced at 100 mm. The
tracking camera is moved with the Kuka robot to each grid point, the matrices
T
T
ð Þ
i
and
R
T
S
ð Þ
i
are recorded, and calibration is performed. For hand-eye
calibration, 100 randomly selected points are taken within a radius of 100 mm.
Online calibration is performed five times at each grid position with different
initial (Adept) robot positions, resulting in a total of 135 online calibrations for
evaluation. This evaluation setup with the tracking camera mounted to the Kuka
robot is shown in Fig.
4.7
.
We thus have a ground truth that can be used for evaluation: As the tracking
camera is moved on a fixed grid, adjacent calibration results should have a
translational difference of 100 mm and an identical rotational part. We use the
error estimation method presented in
Sect. 4.2.5
to compare neighboring cali-
bration results. The translational error is then compared to 100 mm and the
rotational error to 0
as the orientation of the tracking system is not changed.
Variance in Robot Workspace:
To measure the accuracy of calibration within the full robot workspace, we
evaluate the variance of the calibration procedures for one fixed robot/tracking
system position. Therefore, we perform the hand-eye calibration seven times. For
each calibration, we move the robot effector (with the attached marker) to another
initial position to cover multiple regions of the robot's workspace. For each cal-
ibration, we use a radius of 300 mm for collecting 1000 points.
Furthermore, we move the robot's third link to twelve different random posi-
tions within the full robot workspace with a fixed robot/tracking system position.
At each position, we perform the presented online calibration approach.
Robotized TMS Application—Overall System Error:
To verify the effect of the different calibration algorithms on the overall system
accuracy, we measure the accuracy of coil targeting for the robotized TMS system
with these methods. To this end, we use a head phantom with Computer
Tomography (CT) data. On five positions of the phantom head, tiny metal implants
are placed which are visible in the CT-scan. These five points are selected as
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