Abstract 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.
Received: 13 December 2008
Revised: 31 December 2008
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation for
Distinguished Young Scholars of China (Grant No 60525303), the
National Natural Science Foundation of China (Grant No 60704009) and
Doctor Fund of Yanshan University (Grant No B203).
Cite this article:
Luo Xiao-Yuan(罗小元), Li Shao-Bao(李绍宝), and Guan Xin-Ping(关新平) Automatic generation of min-weighted persistent formations 2009 Chin. Phys. B 18 3104
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
