Biomedical Engineering Reference
In-Depth Information
wrist
d
r
1
r
2
hip
FIGURE 7.15
Self-avoidance constraint between the wrist and hip.
the leg rather than a quantitative relationship on the swing angles. The swing
angles are determined in the optimization process.
7.9.3.1.6
Self-avoidance
Self-avoidance is considered in this formulation to prevent penetration of the arm
in the body. A sphere-filling algorithm is used to formulate this constraint, as
shown in
Figure 7.15
:
T
(7.32)
where
r
1
is a constant radius to represent the wrist,
r
2
is another radius to repre-
sent the hip; and
d
is the distance between the wrist and hip.
dð
q
;
tÞ
2
r
1
2
r
2
$
;
t
0
0
#
#
7.9.3.2
Time-independent constraints
The following time-independent constraints are imposed on the optimization
problem.
7.9.3.2.1
Symmetry conditions
The gait simulation starts from the left heel strike and ends with the right heel strike.
The initial and final postures and velocities should satisfy the symmetry conditions
to generate continuous walking motion. These conditions are expressed as follows:
q
L
ð
0
Þ
2
q
R
ðTÞ
5
0
q
L
ð
0
Þ
2
_
_
q
R
ðTÞ
5
0
q
Sx
ð
0
Þ
2
q
Sx
ðTÞ
5
0
q
Sx
ð
0
Þ
2
_
_
q
Sx
ðTÞ
5
0
(7.33)
q
Sy
ð
0
Þ
1
q
Sy
ðTÞ
5
0
q
Sy
ð
0
Þ
1
_
_
q
Sy
ðTÞ
5
0
q
Sz
ð
0
Þ
1
_
_
q
Sz
ð
0
Þ
1
q
Sz
ðTÞ
5
0
q
Sz
ðTÞ
5
0
where subscripts
L
and
R
represent the DOFs of the leg, arm, and shoulder joints
which satisfy the symmetry conditions with the contra-lateral leg, arm and shoul-
der joints; the subscript
S
represents the DOFs of the spine, neck and global joints
which satisfy the symmetry conditions on themselves at the initial and final times;
x
,
y
,
z
are the global axes.
7.9.3.2.2
Ground clearance
To avoid foot drag motion, a ground clearance constraint is imposed during the
walking motion. Instead of controlling the maximum height of the swing leg, the
maximum knee flexion at mid-swing is used to formulate the ground clearance
constraint. Biomechanical experiments have shown that
the maximum knee
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