A General Rhythmic Pattern Generation Architecture for Legged Locomotion - Advancing Artificial Intelligence Through Biological Process Applications - page 205

differential equations (ODE), which may also be
an autonomous system.
In other words, a complex biological pattern
generator system such as the CPGs can be sim-
plified and implemented in a phenomenological
model which uses the concrete ANN network
dynamics.

and deadlock, or saying, these CPG models can
operate without undesired problems.
These PDP algorithms give a potentially op-
timal solution to Edsger Dijkstra's paradigmatic
dining philosophers problem (Dijkstra, 1971),
which is a canonical resource-sharing problem.
They were devised on the assumption that the
target systems were under the heavy load and
neighbourhood-constrained environment, i.e.,
processes are constantly demanding access to all
shared-resources, and neighbouring processes in
the system must alternate in their turns to operate.
These scheduling mechanisms were proved having
the potential to provide the greatest concurrency
among scheduling schemes with neighbourhood-
constrained feature, while it is also capable of
avoiding traditional problems as deadlock and
starvation.
Based on the aforementioned PDP algorithms,
we present a novel structural approach to the mod-
elling the complex behavioural dynamics with a
new concept of oscillatory building blocks (OBB)
(Yang & França, 2003; França & Yang, 2000).
Through appropriate selection and organisation
of appropriately configured OBB modules, dif-
ferent gait patterns can be achieved for producing
complicated rhythmic outputs, retrieving realistic
locomotion prototypes and facilitating the VLSI
circuit synthesis in an efficient, uniform, and
systematic framework. In addition to the formal
introduction of the new concepts of OBB building
blocks and OBB networks, we will also show their
applications in simulating various gait patterns of
hexapod animals and demonstrate the efficiency
of using an OBB network to mimic some func-
tionalities of the CPG models.

Implementing Artificial CPGs as
Neighbourhood-Constrained
Systems

From a philosophical point-of-view, one could see
that the world is full of neighbourhood-constrained
systems. Considering our case of CPGs consist-
ing of purely inhibitory connections, which is
essentially a neighbourhood-constrained system,
the traditional research method is to investigate
an ordinary differential equation (ODE) or par-
tial differential equation (PDE) of the concerned
variables over a time course for all neurons.
Nevertheless, it may be difficult to construct an
ODE/PDE group representing a complicated CPG
architecture with various periodic solutions for
various locomotion patterns. Therefore, qualita-
tive dynamical analysis may be a simpler strategy
than quantitative numerical approach.
However, because of the complexity of the
neuronal locomotor system, accurate math-
ematical descriptions or even detailed qualitative
analysis are usually impossible. Thus , one has
to make use of simplifications to describe the
observed phenomena. As an alternative, a series
of novel PDP fundamentals and algorithms,
namely scheduling by edge reversal (SER) and its
generalisation, scheduling by multi-edge reversal
(SMER) (Barbosa & Gafni, 1989; Barbosa, 1996;
França, 1994), have been found to be especially
efficient in treating topologically representable
CPGs. By adopting a self-timing scheme which
is a key technique underlying the SER approach,
large-scale CPG systems can be constructed eas-
ily and naturally, with immunity of starvation

PREvIEW OF FUNDAMENTALS

After a brief introduction to the state of the art of
neurolocomotion, we describe SER and SMER
algorithms and show their potential as a theoretical
background for our pattern generation strategy.