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The fundamental vision of modern nano-robotics is a swarm of
micro-robots, which is capable of performing tasks that are not
possible with either a single micro-robot, or even with a small
group of micro-robots. Using principles of artificial physics and
self-organization for the control algorithms of such a swarm of
micro-robots, it is expected, that the swarm controlled in such a
way shows self-organized behavior similar to the self-organization
phenomena occurring in many biological or ecological systems like
ant tribes, bee colonies and other insect aggregations or flocking
birds and shoals. There are many potential benefits of such a system
including greater flexibility and adaptability to the environment,
robustness to failures, compensation of breakdowns from one or
several units, etc.
In this work we describe a basic mathematical approach for modeling
of the swarm behavior and for developing the control software of
individual micro-robots. The approach is based on laws of artificial
physics and coupled hybrid automata. Designing the interaction
patterns between robots, we are able to achieve the desired
self-organized behavior. For the modeling of these interactions we
use so-called virtual power functions (also known as social powers).
Depending on the complexity of the considered swarm scenarios,
specific classes of hybrid automata, namely degenerated, standard or
hierarchical ones, are used. In the last case complex swarm
scenarios are implemented using the concept of hierarchical
self-organization. According to this concept, the whole system
consists of a hierarchy of subsystems. The most simple subsystems
(atomic entities, robots) build simple formations via a usual
self-organization process. In the presented approach these simple
formations are chains of robots with a pre-defined or variable
length. Then the simple formations operate as entities (non-atomic
self-organized entities) and build more complex formations via a
self-organization process on the next hierarchy level.
Theoretically, the number of the self-organization levels in a
hierarchical self-organization process is not restricted, however in
our approach we restrict it firstly to two levels. This restriction
is sufficient in order to demonstrate the applicability of the
presented concept and can be extended in future work.
The application of the presented approach is demonstrated by example
scenarios with several complexity levels. Additionally, some
techniques for the investigation of the self-organization phenomena,
applied from the fields of coupled map lattices and hybrid systems,
are discussed.
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