Automatic generation of optimally rigid formations using decentralized methods

In this paper, decentralized methods of optimally rigid graphs generation for formation control are researched. The notion of optimally rigid graph is first defined in this paper to describe a special kind of rigid graphs. The optimally rigid graphs can be used to decrease the topology complexity of graphs while maintaining their shapes. To minimize the communication complexity of formations, we study the theory of optimally rigid formation generation. First, four important propositions are presented to demonstrate the feasibility of using a decentralized method to generate optimally rigid graphs. Then, a formation algorithm for multi-agent systems based on these propositions is proposed. At last, some simulation examples are given to show the efficiency of the proposed algorithm.