Xsens MTi Series, User Manual And Technical Documentation

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MTi and MTx User Manual and Tech. Doc., © 2005, Xsens Technologies B.V.
MT0100P.E
11
rotation matrix norm is always equal to one (1) and a rotation
R
GS
followed by the inverse
rotation
R
SG
naturally yields the identity matrix
I
3 .
The rotation matrix,
R
GS
, can be interpreted in terms of quaternions;
or in terms of Euler-angles;
As defined here
R
GS
, rotates a vector in the sensor co-ordinate system (
S
) to the global
reference system (
G
):
It follows naturally that,
R
SG
rotates a vector in the global reference co-ordinate system (
G
) to
the sensor co-ordinate system (
S
).
For the rotation matrix (DCM) output mode it is defined that:
Here, also the row-order/col-order is defined.
R
GS
= R
Z
Ã
R
Y
µ
R
X
Á
=
2
4
cosà ¡ sin à 0
sin à cosà 0
0 0 1
3
5
2
4
cosµ 0 sin µ
0 1 0
¡ sin µ 0 cosµ
3
5
2
4
1 0 0
0 cosÁ ¡ sin Á
0 sin Á
cosÁ
3
5
=
2
4
cosµcosà sin Ásin µcosà ¡ cosÁsin à cosÁsin µcosà + sin Ásin Ã
cosµsin à sin Ásin µsin à + cosÁcosà cosÁsin µsin à ¡ sin ÁcosÃ
¡ sin µ sin Ácosµ cosÁcosµ
3
5
R
G S
=
2
4
a d g
b e h
c f
i
3
5 =
2
4
R
11
R
12
R
13
R
21
R
22
R
23
R
31
R
32
R
33
3
5
x
G
= R
G S
x
S
= (R
SG
)
T
x
S
R
G S
R
SG
= I
3
k R k= 1
R
SG
=
2
4
a b c
d e f
g h
i
3
5
R
G S
=
2
4
q
2
0
+ q
2
1
¡ q
2
2
¡ q
2
3
2q
1
q
2
¡ 2q
0
q
3
2q
0
q
2
+ 2q
1
q
3
2q
0
q
3
+ 2q
1
q
2
q
2
0
¡ q
2
1
+ q
2
2
¡ q
2
3
2q
2
q
3
¡ 2q
0
q
1
2q
1
q
3
¡ 2q
0
q
2
2q
2
q
3
+ 2q
0
q
1
q
2
0
¡ q
2
1
¡ q
2
2
+ q
2
3
3
5
=
2
4
2q
2
0
+ 2q
2
1
¡ 1 2q
1
q
2
¡ 2q
0
q
3
2q
1
q
3
+ 2q
0
q
2
2q
1
q
2
+ 2q
0
q
3
2q
2
0
+ 2q
2
2
¡ 1 2q
2
q
3
¡ 2q
0
q
1
2q
1
q
3
¡ 2q
0
q
2
2q
2
q
3
+ 2q
0
q
1
2q
2
0
+ 2q
2
3
¡ 1
3
5