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Biologically Inspired Robotics
output. Therefore, we can conclude that the mathematical model reflects
the response properties of the primary afferent-to-cuneate neuron junction
well. Because it is able to do so for two widely different inputs (manual
skin stimulation that evokes a primary afferent spike response lasting 50
ms and electrical skin stimulation that evokes a spike response lasting for
0.1 ms), it promises to be able to account for the response properties over a
wide range of inputs and perhaps covering the majority of the physiological range of inputs.
As an illustration of model variability, Figure  14.6 shows the impulse
response corresponding to electrical skin stimulation for the ARX model.
It is evident that these models do not capture the cuneate neuron firing
mechanics in response to electrical stimulation as the PEM model did. These
empirical mathematical models are of the form
• ARX:
A z y = B z u
( )
( )
+ w
k
k
k
• OE:
B z
( )
y =
u + w
k
k
k
F z
( )
Figure  14.7 shows the Bode diagram of the PEM model. Interestingly, the
diagram shows deriving properties for a large part of the spectrum with
–20
0
20
40
6 0
Time (ms)
–0.15
–0.1
–0.05
0
0.05
0.1
0.15
0.2
Spikes
8 0
FIGURE 14.6
Impulse response for the ARX model.