Formation control of autonomous robots based on cooperative behavior

This paper considers the formation control problem for autonomous robots, where the target formation is specified as a minimally rigid formation. A distributed control law based on potential functions is derived from a directed sensor graph and relies on the graph matrices only. By methods of inverse optimality a certain class of sensor graphs is identified that is related to a cooperative behavior among the robots. These graphs are referred to as cooperative graphs, and undirected graphs, directed cycles, and directed open chain graphs can be identified as such graphs. Cooperative graphs admit a local stability result of the target formation together with a guaranteed region of attraction, that depends on the rigidity properties of the formation.