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410 Biomimetics: Biologically Inspired Technologies

y (m )
T 2 T 3
0.5

O
S
0.3

0.1 T 1 T 4

0.1 0.3 0.5
x (m )

2 D.O.F. Robot
Figure 16.6 Diffusion-based spatial generalization of the optimal control. Here S is an initial position and
T 1 to T 4 are four terminal positions for which we already have the optimal controls. We can then obtain the
semioptimal controls from S to any terminal positions such as O without solving the complex two-point boundary
value problems.

are already obtained, then, by using diffusion-based algorithm, we can obtain all semioptimal
control solutions for all the initial and terminal conditions within a bounded work space as shown in
Figure 16.7 without solving the nonlinear two-point boundary value problem.
Our approach greatly reduces the computational cost. In addition, since the diffusion-based
learning process is completely parallel distributed, it only requires local interaction between the
nodes of a learning network (a lattice) and therefore can be realized by the modern integrated circuit
technology easily.
Recent neuron scientific discoveries show that, nitric oxide (NO), a gas that diffuses between
neuron cells locally, can modulate the local synaptic plasticity and thus plays an important rule in
motor learning and generalization (Yanagihara and Kondo, 1996). We expect that our diffusion-
based learning theory may provide some mathematical understanding of the function of NO in the
neural information processing and motor learning.

16.3 OPTIMAL MOTION FORMATION

In the previous section, we described on how to solve the sensory-motor organization from the
redundant sensory space input to the motor control output. In this section, we consider the optimal
motion formation problem for the arm to move from one position to another in the task space.

16.3.1 Optimal Free Motion Formation

For a simple human arm’s point-to-point (PTP) reaching movement in free motion space, it is found
experimentally that the path of human arm tends to be straight, and the velocity profile of the arm
trajectory is smooth and bell-shaped (Morasso, 1981; Abend et al., 1982). These invariant features
give us hints about the internal representation of motor control in the central nervous system (CNS).
One of the main approaches adopted in computational neuroscience is to account for these
invariant features via optimization theory. Specifically, Flash and Hogan (1985) proposed the
minimum jerk criterion