FTA-Sensor: Combination of Force/Torque and Acceleration - Robotized Transcranial Magnetic Stimulation - page 109

t stop ¼ t ð max ð f z ÞÞ t ð f z [ 10 N Þ: ð 6 : 19 Þ

Note that the rubber foam is used to have an additional elastic layer to protect
robot and sensor from damage. However, the iron plate is heavy enough to produce
forces at impact larger than the security limit.

6.2 Performance of the FTA Sensor

6.2.1 Calibration

As the performance of the FTA sensor strongly depends on the accuracy of the
calibration of IMU to FT sensor, we have systematically analyzed the accuracy of
the calibration method. Therefore, we have performed 60 calibrations with 4
different FTA sensors that we have utilized for evaluation.

6.2.1.1 Quality of the Fit

As a cosine fit is the basis for calibration of IMU to FT sensor, we have foremost
estimated the quality of the fit. The quality of the fit is expressed as the absolute
distance of the measured values to the fitted cosine.
Figure 6.9 shows the overall cosine fitting quality used for calibration as
Boxplot. The median deviations for forces are 0.14, 0.11 and 0.15 N for the three
spatial axes. For torques, the deviations are 0.0034, 0.0023 and 0.0017 Nm,
respectively. The median deviations for the accelerations are 0.016, 0.027 and
0.022 g, respectively. Due to noise, we were not able to perform a valid cosine
fitting in two recordings. Therefore, these two recordings are excluded from fur-
ther analysis.

6.2.1.2 Calibration Error

In order to estimate the calibration error, we have transferred the measured
acceleration into the FT coordinate frame and have compared the angle difference
to the measured FT recordings.
We have found that the median calibration error is 3.4 for the x-axis and 3.5
and 1.6 for the y- and z-axis, respectively. Figure 6.10 shows these results as
Boxplot. Interestingly, the median calibration error in the z-axis is essentially
smaller than for the x- and y-axis, respectively, but has some larger outliers
(around 12 N).