An iterative graph generation method for motion coordination of mobile robotic networks

This paper presents a crystal-grid graph generation method for construction of the communication topology of a mobile robotic network. The notion of edge degree of undirected graphs is defined and the structure properties of crystal-grid graphs are discussed. The method firstly makes a complete graph of three nodes as the base graph, and then builds a sequence of intermediate graphs by adding other nodes iteratively until the final graph defined on all nodes is attained. In this procedure, the addition of new nodes and edges satisfies the constraints induced by the properties of crystal-grid graphs. Finally, the simulation results verify the effectiveness of the algorithm and its adaptability to different initial configurations of mobile robotic networks.