April 2016
Intermediate to advanced
552 pages
17h 2m
English
Content preview from Bio-Inspired Computing and Networking
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Bio-Inspired Computing and Networking
Base reference
system
Position trackers
(x
2
, y
2
, z
2
)
(x
1
, y
1
, z
1
)
z
0
x
0
q
2
q
4
q
3
q
1
y
0
Figure 11.1 The user moves his arm in the 3D space. Two position tracker
measurements are used for computing the four joint angles. The tracker base
reference system is placed on the shoulder.
q
1
= arctan 2
±y
1
, x
1
q
2
= arctan 2
±
x
2
1
+y
2
1
, z
1
q
3
= arctan 2
(
±B
3
, B
1
)
q
4
= arctan 2
±
B
2
1
+B
2
3
, −B
2
−L
1
(11.1)
where
B
1
= x
2
cos
q
1
cos
q
2
+y
2
sin
q
1
cos
q
2
−z
2
sin
q
2
B
2
=−x
2
cos
q
1
sin
q
2
−y
2
sin
q
1
sin
q
2
−z
2
cos
q
2
B
3
=−x
2
sin
q
1
+y
2
cos
q
1
(11.2)
where L
1
is the length of the upper arm. The length of the upper arm can be
computed from the distance of the
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