Biomedical Engineering Reference

In-Depth Information

safety features. We also address the issue of calibration of IMU to FT sensor.

Beside evaluation of the calibration, we evaluate the FTA sensor's latency and

evaluate the system in realistic worst-case scenarios. We further show that the use

of acceleration recordings is sufficient for gravity compensation for robotized

TMS.

6.1 The FTA Sensor

6.1.1 Combining Acceleration with Force-Torque

We already know that gravity compensation is necessary to subtract the gravity

impact on the tool from the force/torque recordings. So far, we have used the

current

robot

end

effector

pose

R
T
E

from

the

robot

for

this

compensation

(
Sect. 5.1.2
).

In contrast, an IMU can measure accelerations relative to gravity acceleration.

Hence, the IMU is able to measure the gravity direction in relation to its coordinate

frame. By combining such an IMU with an FT sensor, we can use the accelerations

for gravity compensation. The combination of both sensors will be called FTA

sensor. In contrast to FT sensors, IMUs are available as integrated circuits. As

both, IMU and FT sensor, have their specific coordinate frame, we must perform a

calibration between both sensors. Thereby, we get the transformation matrix

FT
T
IMU
to convert the accelerations A from the IMU to the FT coordinate system:

A
FT
¼
FT
T
IMU
A
IMU
:

ð
6
:
1
Þ

Now, we can use the accelerations to compensate for gravity. We calculate the

expected force F
0

for the current orientation with:

F
0
¼
A
FT
f
g
;

ð
6
:
2
Þ

where f
g
is the tool's gravity force corresponding to its weight. We estimate the

applied forces F
user
and torques M
user
corresponding to the equations for FT-

F
user
¼
F
A
FT
f
g
;
and

ð
6
:
3
Þ

s
;

M
user
¼
M
A
FT

f
g

ð
6
:
4
Þ

with
s being the tool's centroid. In this way, robot input is not required for

computing the spatial orientation of the sensor. Hence, it operates independently.

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