Biomedical Engineering Reference

In-Depth Information

Fig. 6.6 Approximate spatial

relationship between FT

sensor coordinate system and

IMU coordinate system

between FT sensor and IMU. As the translational shift of the IMU can be

neglected, the transform only consists of a rotational matrix.

Due to the system setup (cf. Fig.
6.6
), we have a coarse knowledge of the

orientation of IMU and FT sensor:

e
FT
x
e
A
z

ð
6
:
6
Þ

e
FT
y
e
A
y

ð
6
:
7
Þ

e
FT
z
e
A
z

ð
6
:
8
Þ

where e denotes the corresponding unit vector. Figure
6.7
illustrates this rela-

tionship with recorded force and acceleration measurements. Also the cosine fits

for each modality are shown. Consequently, we know that a rotation of approxi-

mately 90

around the y-axis is needed to transform accelerations into the FT-

sensor

coordinate

frame.

Furthermore,

the

remaining

phase

angles

must

be

adapted, resulting in the following equation:

FT
T
IMU
R
z
ð
0
Þ
R
x
ð
0
Þ
R
y
ð
p

2

Þ;

ð
6
:
9
Þ

where R
y
describes a rotation around the y-axis, R
z
and R
x
around z- and x-axis,

respectively.

Using the phase angles b
l
, the equation can now be refined as:

FT
T
IMU
¼
R
z
ð
b
F
z
b
A
x
Þ
R
x
ð
b
F
x
b
A
z
Þ
R
y
ð
p

2
ð
b
F
y
b
A
y
ÞÞ:

ð
6
:
10
Þ

Note that the Eqs.
6.9
and
6.10
can be easily adapted to any other system setup.

The rotational matrices must be changed in accordance with the specific setup.

Additionally, we are applying the calibration matrix
FT
T
V
which converts the

voltage readings from the FT sensor into forces and torques. As a result, we

employ

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