Autonomous Collaboration Mechanism of UAV Cluster Based on Public Goods Game

doi:10.12382/bgxb.2023.0811

Abstract

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

CLC Number:

V249

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.

Figures/Tables 15

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

Fig.2 UAV’s operational capability indicator system

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

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

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

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

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

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

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

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

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

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

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

Fig.10 Variation of evolutionarily stable round with various factors

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

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

Fig.12 Evolution of state distribution for UAV cluster

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