This paper researched into some methods for generating min-weighted rigid graphs and min-weighted persistent graphs.Rigidity and persistence are currently used in various studies on coordination and control of autonomous multi-agent formations.To minimize the communication complexity of formations and reduce energy consumption,this paper introduces the rigidity matrix and presents three algorithms for generating min-weighted rigid and min weighted persistent graphs.First,the existence of a min-weighted rigid graph is proved by using the rigidity matrix,and algorithm 1 is presented to generate the min-weighted rigid graphs.Second,the algorithm 2 based on the rigidity matrix is presented to direct the edges of min-weighted rigid graphs to generate min-weighted persistent graphs.Third,the formations with range constraints are considered,and algorithm 3 is presented to find whether a framework can form a min-weighted persistent formation.Finally,some simulations are given to show the efficiency of our research.
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