基于多策略公共物品博弈的无人机集群弹药投放

doi:10.12305/j.issn.1001-506X.2026.07.19

摘要/Abstract

摘要：

为解决无人机集群分布式自主协同场景下的弹药投放优化问题，提出一种基于多策略公共品博弈模型的弹药投放方法。首先，提炼无人机集群弹药投放的核心需求，构建需求与公共物品演化博弈模型的映射关系。然后，建立多策略公共物品博弈模型，并优化改进愿景驱动动力学过程。最后，采用多主体建模方法搭建仿真框架，分析关键参数对集群合作水平及策略分布的影响，同时探究门限值对集群合作状态的调控作用。仿真结果表明，相较于传统单策略博弈模型多策略演化博弈有利于促进集群合作，通过调整门限值可有效调控集群合作水平与策略分布。所提方法可有效适配无人机集群分布式自主协同的作战需求，为无人机集群弹药投放决策提供可靠的理论支撑。

关键词: 公共物品博弈, 无人机集群, 弹药投放, 多策略

Abstract:

To address the optimization problem of ammunition deployment in the scenario of distributed autonomous collaboration of unmanned aerial vehicle （UAV） swarm, an ammunition deployment method based on a multi-strategy public goods game model is proposed. Firstly, the core requirements for UAV swarm ammunition deployment are extracted, and the mapping relationship between requirements and the public goods evolutionary game model is constructed. Secondly, a multi-strategy public goods game model is established, and the aspiration-driven dynamics process is optimized and improved. Finally, a simulation framework is built using the multi-agent modeling method to analyze the impact of key parameters on the swarm cooperation level and strategy distribution, while exploring the regulatory effect of threshold values on the swarm cooperation state. Simulation results show that compared with the traditional single-strategy game model, the multi-strategy evolutionary game is more conductive to promoting swarm cooperation, and the swarm cooperation level and strategy distribution can be effectively regulated by adjusting the threshold value. The proposed method can effectively adapt to the operational needs of distributed autonomous collaboration of UAV swarm and provide reliable theoretical support for UAV swarm ammunition deployment decisions.

Key words: public goods game, unmanned aerial vehicle swarm, ammunition deployment, multi-strategy

中图分类号:

TP 391

许贝佳, 刘学达, 禹明刚, 章乐贵. 基于多策略公共物品博弈的无人机集群弹药投放[J]. 系统工程与电子技术, 2026, 48(7): 2340-2351.

Beijia XU, Xueda LIU, Minggang YU, Legui ZHANG. Ammunition deployment of UAV swarm based on multi-strategy public goods game[J]. Systems Engineering and Electronics, 2026, 48(7): 2340-2351.

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参考文献 31

1	GILES K, GIAMMARCO K. A mission-based architecture for swarm unmanned systems[J]. Systems Engineering, 2019, 22 (3): 271- 281. doi: 10.1002/sys.21477
2	DATSKO D, NEKOVAR F, PENICKA R, et al. Energy-aware multi-UAV coverage mission planning with optimal speed of flight[J]. IEEE Robotics and Automation Letters, 2024, 9 (3): 2893- 2900. doi: 10.1109/LRA.2024.3358581
3	KHAWAJA W, GUVENC I, MATOLAK D W, et al. A survey of air-to-Ground propagation channel modeling for unmanned aerial vehicles[J]. IEEE Communications Surveys and Tutorials, 2019, 21 (3): 2361- 2391. doi: 10.1109/COMST.2019.2915069
4	ZHUGE S, HE Y W, CU X P, et al. Markerless motion capture for humans through a multi-uav system[J]. IEEE Trans. on Instrumentation and Measurement, 2024, 73, 5003112.
5	SHEN Y K, WEI C, SUN Y B, et al. Bird flocking inspired methods for multi-uav cooperative target search[J]. IEEE Trans. on Circuits and Systems II: Express Briefs, 2024, 71 (2): 702- 706.
6	CHEN Y B, YANG D, YU J Q. Multi-uav task assignment with parameter and time-sensitive uncertainties using modified two-part wolf pack search algorithm[J]. IEEE Trans. on Aerospace and Electronic Systems, 2018, 54 (6): 2853- 2872. doi: 10.1109/TAES.2018.2831138
7	王锋, 李凯璇, 朱子文, 等. 基于改进A*蚁群融合算法的路径规划研究[J]. 火力与指挥控制, 2024, 49 (1): 111- 117，123.
	WANG F, LI K X, ZHU Z W, et al. Research on path planning based on improved A*ant colony fusion algorithm[J]. Fire Control & Command Control, 2024, 49 (1): 111- 117，123.
8	黄峰, 李战武, 潘紫微, 等. 无人机群反舰作战动态目标弹药分配模型[J]. 安徽工业大学学报（自然科学版）, 2022, 39 (2): 196- 201，209.
	HUANG F, LI Z W, PAN Z W, et al. Dynamic target ammunition allocation model for UAV swarm anti-ship operations[J]. Journal of Anhui University of Technology （Natural Science Edition）, 2022, 39 (2): 196- 201，209.
9	刘学达, 何明, 禹明刚, 等. 基于公共物品博弈的无人机集群弹药分配方法[J]. 控制与决策, 2022, 37 (10): 2696- 2704.
	LIU X D, HE M, YU M G, et al. Ammunition allocation method for UAV swarms based on public goods game[J]. Control and Decision, 2022, 37 (10): 2696- 2704.
10	SMITH J M, PRICE G R. The logic of animal conflict[J]. Nature, 1973, 246 (5427): 15- 18. doi: 10.1038/246015a0
11	NOWAK M A, SIGMUND K. Evolution of indirect reciprocity[J]. Nature, 2005, 437 (6685): 1291- 1298.
12	TAKESUE H, OZAWA A, MORIKAWA S. Evolution of favoritism and group fairness in a co-evolving three-person ultimatum game[J]. Euro Physics Letters, 2017, 118 (4): 48002.
13	MILEN G, IVAN T, KATSUNORI S, et al. Evolution, robustness and generality of a team of simple agents with asymmetric morphology in predator-prey pursuit problem[J]. Information, 2019, 10 (2): 12- 14.
14	ZHANG H, LI Z. The evolution formation for multi-agent system[C]//Proc. of the Control Theory Professional Committee of Chinese Society of Automation, 2018.
15	NOWAK M A, SIGMUND K. Evolutionary dynamics of biological games[J]. Science, 2004, 303 (5659): 793- 799. doi: 10.1126/science.1093411
16	NOWAK M A. Evolving cooperation[J]. Journal of theoretical biology, 2012, 299, 1- 8. doi: 10.1016/j.jtbi.2012.01.014
17	JIAN J L, CHEN Y, LI Q N, et al. Decision-making method of multi-UAV cooperate air combat under uncertain environment[J]. IEEE Journal on Miniaturization for Air and Space Systems, 2024, 5 (3): 138- 148. doi: 10.1109/JMASS.2024.3378726
18	KUROE Y, IIMA H. Classes of dilemma problems and their multi-agent reinforcement learning method[J]. IEEE Access., 2024, 12, 107353- 107367. doi: 10.1109/ACCESS.2024.3438937
19	Nowak M A. Five rules for the evolution of cooperation[J]. Science, 2006, 314 (5805): 1560- 1563. doi: 10.1126/science.1133755
20	禹明刚, 何明, 张东戈, 等. 基于多元公共品演化博弈的无人作战集群策略占优条件[J]. 系统工程与电子技术, 2021, 43 (9): 2553- 2561.
	YU M G, HE M, ZHANG D G, et al. Strategy dominance conditions for unmanned combat swarms based on multivariate public goods evolutionary game[J]. Systems Engineering and Electronics, 2021, 43 (9): 2553- 2561.
21	SIGMUND K, DE S H, TRAULSEN A, et al. Social learning promotes institutions for governing the commons[J]. Nature, 2010, 466, 861- 863. doi: 10.1038/nature09203
22	ZHANG Y L, LI Y, CHEN X J, et al. Emergence of fairness behavior driven by reputation-based voluntary participation in evolutionary dictator games[J]. IEEE Trans. on Computational Social Systems, 2023, 11 (3): 3483- 3492.
23	RASHID M M, XIANG Y, UDDIN M P, et al. Trustworthy and fair federated learning via reputation-based consensus and adaptive incentives[J]. IEEE Trans. on Information Forensics and Security, 2025, 20, 2868- 2882. doi: 10.1109/TIFS.2025.3546841
24	XIN S, LI L, HU H X. Evolution of social power of stubborn individuals in cooperation-competition networks[C]//Proc. of the IEEE International Conference on Unmanned Systems, 2023.
25	XIA K. The characteristics of average abundance function of multi-player threshold public goods evolutionary game model under redistribution mechanism[J]. Applied Mathematics and Computation, 2021, 392, 125733. doi: 10.1016/j.amc.2020.125733
26	SANTOS M D, PINHEIRO F L, SANTOS F C, et al. Dynamics of N-person snowdrift games in structured populations[J]. Journal of Theoretical Biology, 2012, 315, 81- 86. doi: 10.1016/j.jtbi.2012.09.001
27	WANG X F, CHEN X J, GAO J, et al. Reputation-based mutual selection rule promotes cooperation in spatial threshold public goods games[J]. Chaos, Solitons & Fractals, 2013, 56, 181- 187.
28	LIN B X, ZHOU L, GAO Z, et al. Evolutionary dynamics of group cooperation on heterogeneous higher-order networks[J]. IEEE Trans. on Network Science and Engineerin, 2025, 12 (6): 4894- 4905. doi: 10.1109/TNSE.2025.3577657
29	XIE Z H, YU M G, HE M, et al. Evolution mechanism of unmanned cluster cooperation oriented toward strategy selection diversity[J]. Journal of Systems Engineering and Electronics, 2025, 36 (2): 462- 482. doi: 10.23919/JSEE.2025.000017
30	YU M G, HE M, ZHANG D G, et al. An approach to coordinated control of structured unmanned swarms based on evolutionary game[C]//Proc. of the IEEE International Conference on Unmanned Systems, 2020.
31	BAI J, CHANG X L, RICARDO J R, et al. Towards UAV-based MEC service chain resilience evaluation: a quantitative modeling approach[J]. IEEE Trans. on Vehicular Technology, 2023, 72 (4): 5181- 5194. doi: 10.1109/TVT.2022.3225564

无人机集群弹药投放概念	多策略公共物品博弈概念
负责攻击的无人机集群	结构种群
集群交互关系	环形拓扑
公共资源（无人机挂载的弹药）	公共品
单个无人机平台	个体
作为研究对象的无人机平台	焦点个体
无人机向集群贡献适量资源	合作策略
无人机向集群贡献过量资源	非合作策略
无人机在不同策略下获取的收益	收益
无人机基于获得的收益进行策略转换	博弈
多轮博弈下无人机策略占比动态变化	演化
多轮博弈后，占比稳定，博弈终止	演化稳定

军事需求下个体投弹量/枚	演化博弈中本金投入的策略集
$ \dfrac{{{B_i}}}{N} + (n - 1) $	$ \dfrac{0}{{n - 1}} $
$ \dfrac{{{B_i}}}{N} + (n - 2) $	$ \dfrac{1}{{n - 1}} $
	
$ \dfrac{{{B_i}}}{N} $	$ \dfrac{{n - 1}}{{n - 1}} $

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