A General Rhythmic Pattern Generation Architecture for Legged Locomotion - Advancing Artificial Intelligence Through Biological Process Applications - page 211

There is a timing relation between the pair of
flexor and extensor for the different locomotion
speeds. As a cockroach escapes more swiftly,
the duty factor for the firing duration of the
cockroach's extensor (corresponding to stance)
will decrease drastically, while the firing duration
of its flexor (corresponding to swing) remains
basically unchanged, which is consistent with
biological observations (Pearson, 1976) . This
insight indicates that hexapod speed is determined
largely by the extensor firing, i.e., the time dura-
tion of a leg contacting the ground.
The state transition of each leg and the corre-
sponding phase relations among different legs are
important to simulate the gait model. The phase
circulation can be represented by the circulation
of OBB modules. In the case of a cockroach's
fast-speed gait, simple SER-based OBBs can be
applied to initiate oscillation and coordinate the
movement of the six legs (see Figure 3c). In order
to formulate more complex metachronal move-
ment, an appropriate OBB configuration in the
pattern circulation (Figure 4) is chosen for each
of six legs, respectively, according to the corre-
sponding phase relationship presented in Figure
3a. The coordinated patterns of the cockroach's
metachronal gait can thus be generated by different
SMER-based OBB modules in their appropriate

configurations. This process is generalisable to
modelling the other gaits. An example of how a
possible scheme of firing circulation patterns of
building blocks can simulate the activity envelope
of a pair of flexor and extensor motor neurons is
shown in Figure 5.
It is widely recognised that animal's locomo-
tion behaviour is a continuous-time procedure. So
far our gait analysis only samples some typical
time instant from these continuous, high-dimen-
sional waveforms where the number of dimensions
is equal to the number of legs. The samples are the
snapshots with at least one leg supporting ground
substantially and, ignoring all other snapshots
which may contribute little for the model retrieval.
Given that a kind of high pass filter characteristic
is a common property observed in every real
neuron (Bässler, 1986; Matsuoka, 1987), we
believe that the sampled time instants can lead
to smooth, continuous waveforms for driving
motor behaviours since the filtering property
can be naturally implemented by the hysteretic
phenomena of mechanical oscillation.
After a building block is constructed for
either a flexor or an extensor neuron, it is clear
that there are two sampling time instants in one
leg's locomotion period representing the firing
of the flexor and extensor, respectively. It is the

Figure 4. One possible scheme of firing circulation patterns of building blocks. (a) Four possible
configurations for medium-speed gait; ri = 1, rj = 3. (b) Six possible configurations for slow-speed
(metachronal) gait; ri = 1, rj = 5.