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The ! parameter, which weights the inuence of the individual criterion of mo-
tion over the social one (see Eq. (17.7)) is of least importance if the proportion
of informed individuals is small or large. On the contrary, at intermediate levels
it is strongly correlated with the coordination capability.
Moreover, in [Couzin et al. (2005)], the case in which there exist two groups of
informed individual with two dierent preferential directions is also investigated.
Simulation results highlighted that if the number of components of the two groups
is equal, the group behavior depends on the discrepancy between the two preferred
directions: if this dierence is small, the collective moves along the average direction
of all informed individuals. As the dierence increases, the naive individuals choose
at random one of the two preferential directions. On the other hand, if the number
of components of the two informed groups is dierent, the collective tends to assume
the direction of motion of the larger informed group.
Besides being a suitable model for describing phenomena from animal world,
Couzin's model has been taken as a source of inspiration to implement decentral-
ized control schemes for pools of mobile robots [Buscarino et al. (2007)]. In fact, in
this model many interesting issues for decentralized control are raised. In particu-
lar, the individual control law is simple and includes the avoidance task, which is
fundamental for the control of a robot team. Moreover, only sensing of neighbors
is needed, not identication. That is, a robot does not need to know if a sensed
neighbor is an informed individual or not. On the contrary, it only has to sense its
neighbor's position and velocity.
In the following Section we will highlight the networked nature of these models
and present our results on the application of collective motion models and complex
network theory to the problem of motion coordination.
17.3. Applying Complex Network Theory to Coordination Models
When, as in most motion coordination models, many autonomous units act on the
basis of a set of rules requiring the knowledge of the state of neighboring units, a
way to describe interactions is needed. The most used tool to do this is a graph,
in which nodes represent agents and links represent interactions between them.
Therefore, concepts and tools from graph and network theory can be exploited to
study the properties of the interaction graph, and consequently to investigate the
system behavior.
Some approaches tend to simplify the theoretical framework by considering a
network of interactions which does not change in time (the simplest case of which is
the all-to-all coupling [Sepulchre et al. (2007)]), even though, in general, as agents
move their neighborhoods change over time and the related interaction graph is
time-variant [Jadbabaie et al. (2003); Buscarino et al. (2006, 2007); Sepulchre et al.
(2008)]. Time-variant networks are a powerful modelling and analysis tool which use
is not strictly limited to motion coordination problems. For instance, such networks
