Avoiding collisions in cucker-smale flocking models under group-hierarchical multileadership

Jonq Juang, Yu Hao Liang

研究成果: Article同行評審

10 引文 斯高帕斯(Scopus)

摘要

The Cucker-Smale (C-S) flocking model can be applied to design several mobile autonomous agent systems such as unmanned aerial vehicles and robot systems. In these applications, the problem of collision is usually a nonnegligible issue that should be addressed. In the literature, extra bonding/repulsive forces are added to solve the problem of collision. However, all the known results are limited to the symmetric coupling topology. In this paper, we address this problem under a group-hierarchical multileadership consisting of symmetric coupling topologies and the hierarchical leadership. We obtain the following three main results. First, we show that the augmented C-S model achieves asymptotic flocking provided, roughly, that the ratio between the rate of bounding force and communication rate is sufficiently large. Second, we prove that, for a given augmented C-S model, there exists a set of initial states, which can be explicitly described, such that their corresponding solutions maintain some minimum distance between them. Finally, we show that, for a given set of initial states, we can control the system so that its corresponding solution is collision free by suitably choosing bounding forces, which are independent of given initial states. This in turn suggests that the corresponding system can be collision free by having tolerance for error in their initial states.

原文American English
頁(從 - 到)531-550
頁數20
期刊SIAM Journal on Applied Mathematics
78
發行號1
DOIs
出版狀態Published - 1 1月 2018

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