  In this paper we propose an application of adaptive synchronization of chaos
to detect changes in the topology of a mobile robotic network. We assume that
the network may evolve in time due to the relative motion of the mobile robots
and due to unknown environmental conditions, such as the presence of obstacles
in the environment. We consider that each robotic agent is equipped with a
chaotic oscillator whose state is propagated to the other robots through
wireless communication, with the goal of synchronizing the oscillators. We
introduce an adaptive strategy that each agent independently implements to: (i)
estimate the net coupling of all the oscillators in its neighborhood and (ii)
synchronize the state of the oscillators onto the same time evolution. We show
that by using this strategy, synchronization can be attained and changes in the
network topology can be detected. We go one step forward and consider the
possibility of using this information to control the mobile network. We show
the potential applicability of our technique to the problem of maintaining a
formation between a set of mobile platforms, which operate in an inhomogeneous
and uncertain environment. We discuss the importance of using chaotic
oscillators and validate our methodology by numerical simulations.
