Biomedical Engineering Reference
In-Depth Information
1.0
0.5
0.0
0
.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-0.5
Time (Normalized)
-1.0
-1.5
q
1
q
2
-2.0
-2.5
FIGURE 4.4
Joint angle profiles.
15
10
τ
1
τ
2
5
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
-5
-10
Time (Normalized)
-15
FIGURE 4.5
Joint torque profiles.
3934 s, which is similar to that reported in
the literature (0.3945 s by
Furukawa [2002]
; 0.394 s by
Wang et al. [2005]
). The
optimality and feasibility tolerances are both set to the default value
The minimum travel time is
T
5
0
:
10
2
6
in
SNOPT. Different starting points were tried for the optimization and they all con-
verge to the same optimal solution, implying a global solution for the problem.
The convergence history of the cost function (the total travel time
T
) is plotted in
Figure 4.6
. It is noted that the SQP algorithm in SNOPT worked quite well and
optimal solutions were obtained in 1.07 CPU seconds on a 1.40-GHz PC.
ε
5
4.8
Arm lifting motion with load example
In this section, we shall use a simple introductory example to illustrate the capa-
bility of this method to address the lifting motion of a load with the arm.
The lifting motion of the two-link arm is studied by using a simple optimiza-
tion problem where we shall use an energy function as a human performance
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