计算机科学 ›› 2021, Vol. 48 ›› Issue (6): 288-295.doi: 10.11896/jsjkx.201000137
黄鑫权, 刘爱军, 梁小虎, 王桁
HUANG Xin-quan, LIU Ai-jun, LIANG Xiao-hu, WANG Heng
摘要： 空中自组网(Flying Ad-Hoc Network,FANET)是支撑无人机集群系统(Unmanned Aerial Vehicle Swarm,UAV swarm)的关键技术,它由数量庞大且具有无线通信能力的小型无人机构成。FANET中的信标帧业务在实现集群一致性控制应用的过程中扮演着重要角色。然而,实际应用中FANET无线链路的不可靠性将会导致信标帧出现丢包现象,进而影响一致性控制算法的收敛速度(或收敛时间),即集群所有状态值趋于一致的快慢程度。从理论上分析一致性控制算法收敛性能与信标帧丢包率之间的解析关系,对一致性控制算法在未来FANET中的应用具有举足轻重的意义。针对上述研究背景,文中提出了一种基于随机有向图模型和矩阵论的收敛性能分析模型。该模型将每个周期内FANET中的信息流抽象为随机有向图,并采用指示矩阵来表示该随机有向图的拉普拉斯矩阵,有效地用矩阵多项式对一致性收敛过程进行建模。随后,基于矩阵运算和矩阵谱半径的相关知识,该模型给出了最终期望收敛值的解析表达式。利用该最终期望收敛值,所提模型定义了新的收敛速度量化方法。与现有收敛速度分析工作不同,文中通过评估所有节点的初始状态值收敛到期望收敛值的快慢来对收敛速度进行量化,而不是根据收敛到每个周期网络的平均状态值来进行量化。基于矩阵运算和矩阵谱半径相关知识,所提模型给出了该收敛速度与信标帧丢包率之间的耦合关系,并根据该耦合关系推导出了收敛时间的表达式。仿真结果表明,所提收敛性能分析模型能够准确地描述实际FANET中收敛速度随时间的变化情况。此外,该模型能够准确描述实际FANET中每条链路的平均丢包率、状态值初始分布以及无人机节点个数的变化趋势对收敛时间的影响。同时,相比现有收敛性能分析模型,所提模型得到的收敛性能曲线更接近实际FANET中的收敛性能曲线。
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