基于公共品博弈的无人机集群自主协同机制

doi:10.12382/bgxb.2023.0811

摘要/Abstract

摘要：

无人机集群自主协同作战是未来战争的重要作战样式,自主协同机制研究有利于揭示无人机集群协同形成与演化规律,为无人机集群作战应用提供理论支撑。首先构建无人机集群信息交互网络,定义基于拓扑势的无人机交互等级。通过分析无人机集群自主协同与演化博弈的映射关系,建立基于公共品博弈的无人机集群演化博弈模型,设计基于交互等级的无人机集群总体期望收益函数、平均期望收益函数和愿景更新动态策略更新机制。利用马尔可夫链定量描述无人机集群演化过程,并理论推导了表征无人机集群演化博弈平稳分布的平均丰度函数。通过仿真验证基于公共品博弈的无人机集群自主协同机制的可行性和有效性,并分析选择强度、交互收益系数、增益因子与愿景水平等参数变化对无人机集群协同行为的影响,为无人机集群自主协同参数调控设计提供理论支持。研究结果表明:所提自主协同机制相较于提供点机制、惩罚机制能更大程度促进无人机集群合作涌现,为无人机集群自主协同理论向作战应用提供技术支持。

关键词: 无人机集群, 自主协同, 演化博弈, 公共品博弈

Abstract:

Autonomous cooperative combat of UAV cluster is an important combat mode in future wars. The study on autonomous collaboration mechanism of UAV cluster is conducive to reveal the formation and evolution pattern of its cooperation for providing the theoretical support for its application in combat. Firstly, an autonomous collaboration information interaction network for UAV cluster is constructed, and the UAV interaction levels based on topological potential are defined. An UAV cluster evolutionary game model based on the public goods game is established by analyzing the mapping relationship between autonomous cooperation of UAV cluster and evolutionary game, and the overall expected gain function, average expected gain function and improved aspiration dynamic strategy based on UAV interaction levels are proposed. Then, the evolution process of UAV cluster is quantitatively described by Markov chain, and the average abundance function which characterizes the evolutionarily stable distribution of UAV cluster is deduced theoretically. Finally, the feasibility and effectiveness of the autonomous collaboration mechanism of UAV cluster based on public goods game are verified by simulation, and the influences of the changes in the selection intensity, interaction gain factor, enhancement factor and aspiration level on the collaboration of UAV cluster are analyzed, which provides the theoretical support for autonomous cooperative parameter regulation design of UAV cluster. The results show that the proposed autonomous collaboration mechanism can promote the emergence of UAV cluster cooperation to a greater extent than the point and punishment mechanisms, and provide technical support for UAV cluster autonomous collaboration theory to be applied to combat.

Key words: UAV cluster, autonomous collaboration, evolutionary game, public goods game

中图分类号:

V249

毕文豪, 王炤晰, 吴伟, 张安. 基于公共品博弈的无人机集群自主协同机制[J]. 兵工学报, 2023, 44(11): 3407-3421.

BI Wenhao, WANG Zhaoxi, WU Wei, ZHANG An. Autonomous Collaboration Mechanism of UAV Cluster Based on Public Goods Game[J]. Acta Armamentarii, 2023, 44(11): 3407-3421.

图/表 15

图1 无人机集群自主协同信息交互网络示意图

Fig.1 Schematic diagram of autonomous collaboration information interaction network for UAV cluster

图2 无人机作战能力指标体系

Fig.2 UAV’s operational capability indicator system

图3 无人机集群自主协同与演化博弈映射关系

Fig.3 Mapping relationship between autonomous cooperation of UAV cluster and evolutionary game

表1 概念映射关系

Table 1 Concept mapping

无人机集群自主协同	公共品博弈	变量表示
无人机集群	结构化种群	G=(V,E)
燃油、武器、通信、干扰等资源	公共品
无人机个体	参与者	v_i,i=1,2,3,…,N
所有无人机当前选择策略构成的集合	策略集合	S(t)
无人机个体愿意向集群贡献资源	合作	C
无人机个体选择搭便车行为	背叛	D
不同策略下集群回馈给个体的作战效能	期望收益	$E v i$ (t)
无人机根据收益进行策略调整	策略更新
选择不同策略的无人机在集群中占比变化	演化
多轮博弈后占比稳定在一定范围内	演化稳定

表1 概念映射关系

Table 1 Concept mapping

无人机集群自主协同	公共品博弈	变量表示
无人机集群	结构化种群	G=(V,E)
燃油、武器、通信、干扰等资源	公共品
无人机个体	参与者	v_i,i=1,2,3,…,N
所有无人机当前选择策略构成的集合	策略集合	S(t)
无人机个体愿意向集群贡献资源	合作	C
无人机个体选择搭便车行为	背叛	D
不同策略下集群回馈给个体的作战效能	期望收益	$E v i$ (t)
无人机根据收益进行策略调整	策略更新
选择不同策略的无人机在集群中占比变化	演化
多轮博弈后占比稳定在一定范围内	演化稳定

图4 基于无人机交互等级的收益发放模式示意图

Fig.4 Schematic diagram of revenue disbursement model based on UAV interaction levels

图5 异构无人机集群自主协同信息交互网络

Fig.5 Autonomous collaboration information interaction network for heterogeneous UAV cluster

表2 无人机的交互等级取值

Table 2 Interaction levels of UAV cluster

无人机v_j	侦察能力S			决策能力M			打击能力A			保障能力F			属性指标 m(v_j)	交互等级 ψ(v_j)
无人机v_j	S₁	S₂	S₃	M₁	M₂	M₃	A₁	A₂	A₃	F₁	F₂	F₃	属性指标 m(v_j)	交互等级 ψ(v_j)
UA $V r_r a d 1$	0.92	0.92	0.98	0.12	0.23	0.15	0.25	0.10	0.19	0.78	0.86	0.75	0.77	1.59
UA $V r_r a d 2$	0.92	0.92	0.98	0.12	0.23	0.15	0.25	0.10	0.19	0.78	0.86	0.75	0.77	2.25
UA $V r_r a d 3$	0.92	0.92	0.98	0.12	0.23	0.15	0.25	0.10	0.19	0.78	0.86	0.75	0.77	2.78
UA $V r_i n f 1$	0.90	0.86	0.85	0.11	0.26	0.13	0.15	0.10	0.18	0.70	0.85	0.71	0.71	1.94
UA $V r_i n f 2$	0.90	0.86	0.85	0.11	0.26	0.13	0.15	0.10	0.18	0.70	0.85	0.71	0.71	1.26
UA $V r, a 1$	0.75	0.72	0.68	0.32	0.35	0.24	0.74	0.82	0.75	0.75	0.74	0.83	0.68	1.03
UA $V a 1$	0.42	0.70	0.51	0.21	0.32	0.26	0.91	0.93	0.92	0.82	0.70	0.85	0.58	0.82
UA $V a 2$	0.42	0.70	0.51	0.21	0.32	0.26	0.91	0.93	0.92	0.82	0.70	0.85	0.58	0.86

表2 无人机的交互等级取值

Table 2 Interaction levels of UAV cluster

无人机v_j	侦察能力S			决策能力M			打击能力A			保障能力F			属性指标 m(v_j)	交互等级 ψ(v_j)
无人机v_j	S₁	S₂	S₃	M₁	M₂	M₃	A₁	A₂	A₃	F₁	F₂	F₃	属性指标 m(v_j)	交互等级 ψ(v_j)
UA $V r_r a d 1$	0.92	0.92	0.98	0.12	0.23	0.15	0.25	0.10	0.19	0.78	0.86	0.75	0.77	1.59
UA $V r_r a d 2$	0.92	0.92	0.98	0.12	0.23	0.15	0.25	0.10	0.19	0.78	0.86	0.75	0.77	2.25
UA $V r_r a d 3$	0.92	0.92	0.98	0.12	0.23	0.15	0.25	0.10	0.19	0.78	0.86	0.75	0.77	2.78
UA $V r_i n f 1$	0.90	0.86	0.85	0.11	0.26	0.13	0.15	0.10	0.18	0.70	0.85	0.71	0.71	1.94
UA $V r_i n f 2$	0.90	0.86	0.85	0.11	0.26	0.13	0.15	0.10	0.18	0.70	0.85	0.71	0.71	1.26
UA $V r, a 1$	0.75	0.72	0.68	0.32	0.35	0.24	0.74	0.82	0.75	0.75	0.74	0.83	0.68	1.03
UA $V a 1$	0.42	0.70	0.51	0.21	0.32	0.26	0.91	0.93	0.92	0.82	0.70	0.85	0.58	0.82
UA $V a 2$	0.42	0.70	0.51	0.21	0.32	0.26	0.91	0.93	0.92	0.82	0.70	0.85	0.58	0.86

图6 交互收益系数与选择强度共同调控下平均丰度函数的变化趋势图

Fig.6 Variation of average abundance function with interaction gain factor and selection intensity

图7 成本与选择强度共同调控下平均丰度函数的变化趋势图

Fig.7 Variation of average abundance function with cost and selection intensity

图8 增益因子与选择强度共同调控下平均丰度函数的变化趋势图

Fig.8 Variation of average abundance function with enhancement factor and selection intensity

图9 愿景水平与选择强度共同调控下平均丰度函数的变化趋势图

Fig.9 Variation of average abundance function with aspiration level and selection intensity

图10 演化稳定轮次随各种参数变化图

Fig.10 Variation of evolutionarily stable round with various factors

表3 其他合作演化机制的参数条件

Table 3 Parameters of other cooperative evolutionary mechanisms

合作演化机制	仿真参数条件
本文所提机制	ω=0.3、ϑ=0.5、r=0.3、c=1、α=2
提供点机制	提供点T=1
惩罚机制	惩罚代价γ=0.2、惩罚概率a=0.6、惩罚系数β=2
奖励机制	奖励概率ap=0.2、公共额外奖励apT=1

图11 不同机制下合作水平与期望效益函数演变情况

Fig.11 Evolution of cooperation level and expected benefit functions under different cooperative evolutionary mechanisms

图12 无人机集群状态分布概率演化图

Fig.12 Evolution of state distribution for UAV cluster

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