Automatic generation of minimally persistent formations using rigidity matrix

In this paper, the methods for generating minimally rigid formations and minimally persistent formations, is studied by using the rigidity matrix. Based on the properties of rigidity matrix, three algorithms are proposed. Firstly, the algorithm 1 is designed to generate the minimally rigid graphs in r-Dimension (r=2,3,ldrldrldr) workspace through some operations to the rigidity matrix; Secondly, the formations with range constraints are considered, and the algorithm 2 is presented to judge the minimally rigid feasibility of a formation; thirdly, the algorithm 3 gives some operations to direct the edges of minimally rigid graphs to generate minimally persistent graphs. At last, some simulations are provided to show the efficiency of our research.