Biomedical Engineering Reference
In-Depth Information
Table 3.3
Joint Weights for Discomfort
Joint Variables
Joint Weight
q
1
; ...; q
12
1
3
10
4
q
13
; q
14
1
3
10
8
q
15
; ...; q
21
1
With this normalization scheme, each term
ð
Δ
q
norm
i
2
Þ
acts as an individual
objective function and has values between zero and one.
Generally, this approach works well, but it often results in postures with joints
extended to their limits, and such postures can be uncomfortable. To rectify this
problem and to incorporate the final factor of discomfort (the discomfort associ-
ated with moving while joints are near their respective limits), specially designed
penalty terms are added to the discomfort function such that discomfort increases
significantly as joint values approach their limits. The final discomfort function is
given as follows:
G
X
DOF
i
5
1
½γ
i
ð
Δ
q
norm
1
f
Discomfort
ð
q
Þ
5
Þ
1
G
3
QU
i
1
G
3
QL
i
(3.13)
i
100
0
ð
q
i
2
5
:
q
i
Þ
QU
i
5
0
:
5 Sin
q
i
1
1
:
571
1
1
(3.14)
q
i
2
100
q
i
Þ
q
i
2
q
i
1
5
:
0
ð
q
i
2
:
:
QL
i
5
0
5 Sin
1
571
1
1
(3.15)
where G
QU is a penalty term associated with joint values that approach their
upper limits, and G
3
QL is a penalty term associated with joint values that
approach their lower limits;
3
γ
i
represents the weights defined in
Table 3.3
. Each
term varies between zero and G, as
q
i
Þ
vary between zero and one.
Figure 3.6
illustrates the curve for the following func-
tion, which represents the basic structure of the penalty terms
ð
q
i
2
q
i
Þ=ð
q
i
2
q
i
Þ
and
ð
q
i
2
q
i
Þ=ð
q
i
2
100
Q
5
ð
0
:
5Sin
ð
5
:
0r
1
:
571
Þ
1
1
Þ
(3.16)
1
r represents either
ð
q
i
2
q
i
Þ
.
Thus, as
Figure 3.6
illustrates, the penalty term has a value of zero until the
joint value reaches
q
i
Þ=ð
q
i
2
q
i
Þ
or
ð
q
i
2
q
i
Þ=ð
q
i
2
the upper or
lower 10% of
its
range, where either
ð
q
i
2
1. The curve for the penalty
term is differentiable and reaches its maximum of G
q
i
Þ=ð
q
i
2
q
i
Þ
#
0
:
1or
ð
q
i
2
q
i
Þ=ð
q
i
2
q
i
Þ
#
0
:
10
6
when r
1
0. The
5
3
5
final function in
Equation (3.13)
is multiplied by 1
=
G for the sake of presentation
Search WWH ::
Custom Search