Biomedical Engineering Reference
assure an immediate robot stop. Finally, we employ realistic scenarios to test the
FTA sensor's performance in emergency situations.
First, we evaluate the accuracy of the calibration from IMU to FT sensor.
Therefore, we perform the presented calibration method with two different FT
sensors and two IMUs (including circuit board with ES), resulting in a total of four
FTA sensors. For each FTA sensor, we perform three sets of calibrations with 20
calibrations in a 15-min-interval. We therefore have 60 calibrations of IMU to FT
sensor for each FTA sensor that we use for evaluation.
Quality of the fit:
As the calibration is based on fitted values (cf. Eq. 6.5 ), the quality of the fit is
essential for the accuracy of the calibration. Therefore, we estimate for each
recording of each modality the absolute distance to the fitted curve.
For calculating errors of the calibration, we first transfer the recorded accelerations
A IMU into the FT coordinate frame by applying the computed transformation matrix
FT T IMU (cf. Eq. 6.1 ). We fit the transferred accelerations to a cosine with the
formula from Eq. 6.5 . We compare the phase angles of the forces (estimated during
calibration) to the phase angle of the transferred accelerations (A FT ) and compute
the error for each spatial axis by applying the inverse sine to the phase difference:
e calib x ¼ arcsin ðj b F x b A FT x jÞ;
ð 6 : 13 Þ
e calib y ¼ arcsin ðj b F y b A FT y jÞ;
ð 6 : 14 Þ
e calib z ¼ arcsin ðj b F z b A FT z jÞ;
ð 6 : 15 Þ
Stability of calibration:
The stability of the calibration shows the dependency of the calibration to noise
and errors in the measurements. For calculating the stability of the calibration, we
proceed analogously to the error computation for the robot online calibration
( Sect. 4.2.5 ). We therefore use two calibration results T 1 and T 2 . To compare the
difference between these two, we use