FT-Control - Robotized Transcranial Magnetic Stimulation - page 86

which we can refine to:

0
@

1
A ;

f y i s z f z i s y
f z i s x f x i s z
f x i s y f y i s x

M i ¼

8 i 2½ 1 ; n : ð 5 : 12 Þ

We thus transfer this equation into a system of linear equations. At least 3 inde-
pendent measurements are required to solve this equation. To reduce the impact of
noise in the recordings on the calculated parameters, we use at least n ¼ 20
measurements. Note that the gravity force for each tool is constant. However, the
centroid changes for every re-mounting (as long as no fixed arrester is used).
Therefore, the tool calibration must be re-performed if the tool is re-mounted.
Further, note that the tool calibration, in contrast to the sensor calibration, is
required frequently. However, it is possible to apply the same recordings for the
tool calibration as utilized for the sensor calibration. Furthermore, both calibra-
tions can be united into one (larger) system of linear equations. Nevertheless, this
requires the full set of measurements used for the sensor calibration. As this takes
additional time and is not needed for the tool calibration, we separated the
calibrations.

5.1.3 Influence of the Coil's Supply Cable

For a rigid tool, we expect that the tool calibration and therefore the gravity
compensation provides accurate results. However, the TMS coil can only partially
be considered as a rigid tool. Only the transducer head (the coil itself) is a rigid
part. The, partially, heavy supply cable that connects the coil to the stimulator is
rather non-rigid. It therefore introduces an additional, flexible weight to the coil.
Typically, the cable weighs more than 0.5 kg per meter. Table 5.1 summarizes the
cable length and the coil weight for different TMS coils that are in operation with
the robotized TMS system.
Depending on the spatial orientation (and the position of the stimulator), the
impact of the cable on the recordings drastically changes. As the tool calibration
cannot deal with these non-rigid changes, the impact of the supply cable can only
be averaged within the calibration procedure. Thus, the calibrated values are
always afflicted by an error. Hence, well chosen thresholds are necessary for the
implemented FT-control.

5.2 Implementation of FT-Control

For improvement of the system's usability, safety and precision, two FT-based
control mechanisms are implemented. Hand-assisted positioning allows for
increased usability as it enables the robot moving and positioning the coil in a