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Simplicity. The decentralized control strategy to be implemented on each
agent is often simple and require a low computational eort. Moreover, very
often many control schemes do not require the identication of the neighbors
and rather rely on a simpler sensing of some relevant variables (e.g. position,
velocity, etc.).
Robustness. The absence of a central coordination unit and the exploitation
of a reduced communication scheme allow the system to keep working even in
case of failure of one or more agents. Moreover, the problem of the existence of
a single vulnerable point (i.e., the coordination unit) is not present.
Scalability. The control eort is independent of the number of agents.
Limited communication. As the communication between agents is per-
formed mostly locally (i.e. within a neighborhood), many real-world appli-
cations with communication constraints can be dealt with. Moreover, the au-
tonomous character of the control laws often allows to cope with limited and/or
uncertain communication, or with nite delays [Paley et al. (2008); Fiorelli et al.
(2006); Moreau (2005)].
Although very often the control law aboard the single agent seems \simple", the
approaches towards the construction of a system and control theory of coordinated
motion involves several advanced mathematical tools. A rigorous formalization of
the framework is necessary, at least to:
model the phenomena involved;
code the motion coordination tasks;
design the distributed control strategy;
prove the correctness and convergence of the strategy;
assess the overall performance of the control strategy.
With this in view, many approaches have been considered. Justh and Krish-
naprasad (2004) exploit the Lie group theory to set up a framework for the analysis
of the motion of a planar formation, emphasizing the fact that the conguration
space of the vehicles consists of N copies of the group SE(2) (where N is the num-
ber of vehicles). The Frenet-Serret equations of motion are used to describe the
evolution of both position and orientation of a vehicle moving at unit speed under
a steering control. Based on this model, an eective framework for the analysis and
control of the formation motion has been developed in which each moving agent is
modeled with an oscillator. The control problem is in fact paralleled with a problem
of synchronization of a network of oscillators, which is another fascinating topic of
complex system science [Strogatz (2000, 2003)]. For a review of this approach we
address the reader to [Paley et al. (2007)] and to the references in there.
Another interesting approach has been introduced in [Bullo et al. (2008);
Mart nez et al. (2007)], which essentially exploits tools from computational ge-
ometry, such as the notion of proximity graph. Several coordination tasks, such as
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