This paper is concerned with the maintenance of rigid formations
of mobile autonomous agents. A key element in all future
multi-agent systems will be the role of sensor and communication
networks as an integral part of coordination. Network topologies
are critically important for autonomous systems involving mobile
underwater, ground and air vehicles and for sensor networks. This
paper focuses on developing techniques and strategies for the
analysis and design of sensor and network topologies required
to achieve a rigid formation for cooperative tasks. Energy
efficiency and communication bandwidth are critically important
in formations of mobile autonomous agents, and hence strategies
that make efficient use of power and energy are beneficial.
Therefore, we develop topologies for providing sensing and
communications with the minimum number of links, and propose
methods requiring the minimum number of changes in the set
of links in dynamic missions and maneuvers, including agent
departure from a rigid formation, splitting a rigid formation
and merging rigid sub-formations. To do this in a systematic
manner, it is necessary to develop a framework for modeling
agent formations that characterizes the sensing and
communication links needed to maintain the formations. The
challenge is that a comprehensive theory of such topologies
of formations with sensing and communication limitations is
in the earliest stage of development. Central to the development
of these techniques and strategies will be the use of tools from
rigidity theory, and graph theory.