基于有向刚性图论的多智能体编队控制研究

Recently, one of the main research topics considered for multiagent systems has been formation control, which finds wide applications in defence, space mission, industry, entertainment, etc. This project will characterize persistent (directed rigidity) graphs and provide fundamental results to design controllers for persistent formations. We plan to start with the study of distributed persistent formation merging, splitting and re-organization algorithms, and the design of generic distributed controllers that will preserve persistence; and then we will investigate the characterization of redundant persistent graphs and algorithms to generate such graphs, including K-vertex persistence and K-edge persistence; finally, we wish to abstract a certain performance objective for particular applications of persistent formations, and to design corresponding optimal (with respect to this performance objective) distributed formation controller and topology. The goal of this project is two fold. Firstly we want to advance the fundamental knowledge about persistent graph theory. Secondly we want to consider its application to multiagent systems, especially when failure of links between agents and/or loss of agents may happen and the system requires a level of redundancy; and this will certainly contribute to the theories of formation control of multiagent systems.

多智能体编队控制是当前多智能体系统研究的热点问题，在军事、航天、工业、娱乐等各个领域具有广泛的应用。本项目将围绕多智能体编队控制中基础性的有向刚性图论的性质及基于有向刚性图的编队控制律展开研究。项目将首先深入研究分布式的有向刚性图的合并、分裂和重组算法，并设计通用的保持有向刚性的分布式编队控制律；而后进一步研究冗余有向刚性图论的性质及生成算法，包括k-顶点有向刚性、k-边有向刚性等；最后结合综合了拓扑结构鲁棒性和编队实现代价的性能指标，设计最优的编队控制律及多智能体间的有向拓扑结构。项目期望一方面能够推动有向刚性图论的基础性研究，另一方面能够将研究的有向刚性图论应用于多智能体系统，特别是考虑边失效或者节点损毁等需要一定冗余的系统中，以推动多智能体编队控制理论的进一步发展。

多智能体编队控制是当前多智能体系统研究的热点问题，在军事、航天、工业、娱乐等各个领域具有广泛的应用。本项目围绕多智能体编队控制中基础性的有向刚性图论的性质及基于有向刚性图的编队控制律进行研究。深入研究分了布式的有向刚性图的合并、分裂和重组算法，并设计通用的保持有向刚性的分布式编队控制律、冗余有向刚性图论的性质及生成算法，包括 k-顶点有向刚性、k-边有向刚性等、综合了拓扑结构鲁棒性和编队实现代价的性能指标，设计最优的编队控制律及多智能体间的有向拓扑结构。该项目推动了有向刚性图论的基础性研究，将研究的有向刚性图论应用于多智能体系统，特别是考虑边失效或者节点损毁等需要一定冗余的系统中，进而推动了多智能体编队控制理论的进一步发展。本项目的研究获得了以下成果：1)深入研究并改进了 Laman 定理和 Henneberg 序列，并将其应用于分布式多智.能体系统和三维空间，实现了有向刚性图论的性质及生成、合并和重组等操作：2)对有向刚性矩阵性质进行研究，设计了通用的、保持有向刚性的分布式编队控率。3)对k-顶点有向刚性图和k-边有向刚性图的性质和生成算子进行研究4)结合编队拓扑结构的鲁棒性和编队实现的代价设计了指定指标下的最优编队控制律及对应的编队拓扑结构5)结合前述冗余有向刚性图论和通用控制律的研究，设计并推导具有最优性能的拓扑结构和控制方法