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412 Biomimetics: Biologically Inspired Technologies

4
3
5
x(t) ¼ x(0) þ (x(T f ) x(0))(10s 15s þ 6s ) (16:15)
where s ¼ t/T f.
Uno et al., on the other hand, proposed to take into account about the arm’s dynamics as a
constraint condition when performing optimal motion planning. Based on this idea, the minimum
joint torque–change criterion
ð
1 T f
T
J ¼ _ t t _t dt (16:16)
t
2 0
is presented (Uno et al., 1989a), which implies that human implicitly plans the PTP reaching
movements in the human body space based on the arm’s dynamic model. Here t is the combined
vector of the joint torques. They also expanded this model to a muscle model (Uno et al., 1989b)
and proposed the minimum muscle force change criterion to show that CNS may generate unique
hand trajectory by minimizing a global performance criterion of
ð
T f T
˙ ˙
J ¼ f f dt (16:17)
0
where f is the combined vector of the muscle forces.
Kawato et al. also presented a cascade neural network model that may be possible for the
nervous system to solve such a minimizing torque–change problem (Kawato et al., 1987; Miyamoto
et al., 1988).

16.3.2 Optimal Motion Formation under Environmental Constraints

Studies of above section considered only the simple PTP human arm movements in the free motion
space. However, how about the optimal criterion for the more complex constraint motions such as
opening a door, turning a steering wheel, rotating a coffee mill, et al.?
To ask this question, we performed experiments of crank rotation task. As shown in Figure 16.8,
rotating a crank requires only one degree of freedom force, however, we have to define the torques
for the two joints of the arm. This is also a force redundant problem.
At the same time, we have performed many optimum calculations for the different kinds of
criterions including the minimum jerk, minimum torque change, the minimum muscle force
change, the minimum end-effector’s interaction force change as well as our proposed criterion
to minimize the combination of end-effector’s interaction force change and muscle force change.

Figure 16.8 (See color insert following page 302) Experiments of human motion formation in crank rotation
tasks.