# Rigid Graph Theory for Vision-Based Formation Control in Heterogeneous Robot Networks

## Tony Grubman

Formation control systems enable networks of robots to move together
in a fixed geometric configuration. This allows the network to operate
autonomously, with all robots working together to achieve a global
objective. Rigid graph theory is a powerful mathematical tool that can
be used to construct formation control systems with provable
stability. The network of robots is modelled as a graph embedded in
space, with the length of each edge actively controlled by the
robots.
In order for the robots to control their position, they must
first have some capability of sensing the distance to each of their
neighbours. In many configurations, the identity of each neighbour is
also essential to determine. A camera-based identification and
tracking system that performs this necessary sensing was devised and
implemented. The syste involves a circular sequence of colours
around the perimeter of each robot. To maximise the number of possible robots while guaranteeing that they still can be identified, a combinatorial model of the
colouring process was created. Interesting links were found to cycle
decompositions of de Bruijn graphs, and several existence results were
proved using a combination of Galois field algebra and combinatorics
of words. The mathematical constructions that led to these results were developed.

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Department of Electrical and Computer Systems Engineering, Monash University, Melbourne, Australia
Last modified: Tue Oct 28 15:14:15 EST 2014 by Ahmet Sekercioglu