Biomedical Engineering Reference
In-Depth Information
7.3 TMS Coil Calibration
Theoretically, only a single force/torque measurement is required to compute the
gravity force of a rigid tool and three independent measurements are necessary to
calculate the tool's centroid. However, this is not applicable for a TMS coil
calibration. Due to noise, the recordings are imperfect. Even more problematic is
that the heavy coil supply cable interferes with the measurements (cf. Chap. 5 ).
Therefore, we introduce a more robust coil calibration method that uses the
same approach as for the calibration of the Inertia Measurement Unit (IMU) to the
FT coordinate frame (cf. Sect. 6.1.4 ) . The cosine fitting of the recorded data
reduces the impact of noise and the supply cable to a minimum.
By using the extended robot server, we let the robot perform a full rotation around
joint 4 with the mounted coil and record the forces and torques from the FTA sensor
(not gravity compensated). We now perform a cosine fitting for each recorded
modality as described in Eq. ( 6.5 ). Hence, we compute the gravity force with:
q
ð a F x cos ð b F x ÞÞ 2 þð a F y cos ð b F y ÞÞ 2 þð a F z cos ð b F z ÞÞ 2
ð 7 : 3 Þ
f g ¼
:
For computation of the tool's centroid s, we discretize the cosine fits as:
0
1
a F x cos ð i þ b F x Þ
a F y cos ð i þ b F y Þ
a F z cos ð i þ b F z Þ
F i ¼
@
A ; i 2 p ; p
½
;
and
ð 7 : 4 Þ
0
1
a M x cos ð i þ b M x Þ
a M y cos ð i þ b M y Þ
a M z cos ð i þ b M z Þ
M i ¼
@
A ; i 2 p ; p
½
;
ð 7 : 5 Þ
with 3600 datapoints equally distributed in the interval p ; p
½
.
This results in a set of equations with the form:
0 ¼ F i s M i :
ð 7 : 6 Þ
Now, we use linear regression to solve this set of equations for s.
7.4 Data Acquisition for Realistic Evaluation of Optimized
FT-Control
In order to evaluate the performance of the optimized FT-control based on the
FTA sensor, we perform two realistic experiments. First, we measure the accuracy
of the presented coil calibration method. As the gravity compensation is based on
an accurate coil calibration, we use different TMS coils, calibrate the coils to the
 
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