带有时间与探测约束的“到达-回避”博弈

doi:10.7527/S1000-6893.2022.28215

Abstract

Abstract:

Based on the classic lifeline game， this paper proposes a novel kind of reach-avoid game with time limit and detection range of the players， due to the fact that the operating time of the aircraft is generally limited and the detectors equipped have limited detection range. Via analyzing all the possible neutral terminal state sets and the Hamiltonian of the game， the forms of the defender’s and the attacker’s optimal strategies are provided. Using the optimal strategies and the constraints of the players， we obtain the accurate solution to the barrier of the original game and prove the correctness of the results via numerical simulations. The barrier acquired separates the game space into two disjoint winning regions related to different players， which provides a quick way of judging the game’s outcomes and gives the theoretical foundation for the strategy formulation of the aircraft participating in the combat.

Key words: game theory, differential game of kind, "reach-avoid" game, time limit, detection range, barrier

CLC Number:

V249

Xi CHEN, Di YANG, Kang NIU, Jiaxun LI, Jianqiao YU. Reach-avoid game with time limit and detection range[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(17): 328215-328215.

Figures/Tables 15

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Table 1

Parameters of quadrotor UAV used in simulation

参数	数值
质量 $m$ /kg	2.0
升力系数 $k L$ /（kg·m）	2.715×10^-7
反扭矩系数 $k C$ /（kg·m²）	1.4×10^-8
力臂 $L ϕ$ /m	0.205
力臂 $L θ$ /m	0.205
转动惯量 $I x x$ /（kg·m²）	0.02
转动惯量 $I y y$ /（kg·m²）	0.02
转动惯量 $I z z$ /（kg·m²）	0.039 4

Table 1

Fig.12

Fig.13

Fig.14

References 26

1	ISAACS R. Differential games： A mathematical theory with applications to warfare and pursuit， control and optimization［M］. New York： Wiley， 1965
2	LIU Y C， CHEN X， ZHANG Y H， et al. Sample data game strategy for active rendezvous with disturbance rejection［J］. Aerospace Science and Technology， 2022， 121： 107358.
3	GARCIA E， CASBEER D W， FUCHS Z E， et al. Cooperative missile guidance for active defense of air vehicles［J］. IEEE Transactions on Aerospace and Electronic Systems， 2017， 54（2）： 706-721.
4	LIU F， DONG X W， LI Q D， et al. Robust multi-agent differential games with application to cooperative guidance［J］. Aerospace Science and Technology， 2021， 111： 106568.
5	YE D， SHI M M， SUN Z W. Satellite proximate pursuit-evasion game with different thrust configurations［J］. Aerospace Science and Technology， 2020， 99： 105715.
6	TANG X， YE D， HUANG L， et al. Pursuit-evasion game switching strategies for spacecraft with incomplete-information［J］. Aerospace Science and Technology， 2021， 119： 107112.
7	PACHTER M， VON MOLL A， GARCIA E， et al. Two-on-one pursuit［J］. Journal of Guidance， Control， and Dynamics， 2019， 42（7）： 1638-1644.
8	PACHTER M， GARCIA E， CASBEER D W. Toward a solution of the active target defense differential game［J］. Dynamic Games and Applications， 2019， 9（1）： 165-216.
9	王鑫，闫杰，孟廷伟. 高速目标分阶段博弈拦截制导策略［J］. 航空学报， 2022， 43（9）： 325598
	WANG X， YAN J， MENG T W. High-speed target multi-stage interception scheme based on game theory［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（9）： 325598 （in Chinese）.
10	SHAFERMAN V， SHIMA T. Cooperative differential games guidance laws for imposing a relative intercept angle［J］. Journal of Guidance， Control， and Dynamics， 2017， 40（10）： 2465-2480.
11	NOBAHARI H， NASROLLAHI S. A nonlinear robust model predictive differential game guidance algorithm based on the particle swarm optimization［J］. Journal of the Franklin Institute， 2020， 357（15）： 11042-11071.
12	毛柏源，李君龙，张锐，等. 拦截高速机动目标的捕获区及微分对策导引律［J］. 国防科技大学学报， 2021， 43（3）： 165-174.
	MAO B Y， LI J L， ZHANG R， et al. Capture zones and differential game guidance law for high-speed maneuvering target interception［J］. Journal of National University of Defense Technology， 2021， 43（3）： 165-174 （in Chinese）.
13	刘延芳，齐乃明，夏齐，等. 基于非线性模型的大气层内拦截弹微分对策制导律［J］. 航空学报， 2011， 32（7）： 1171-1179.
	LIU Y F， QI N M， XIA Q， et al. Differential game guidance law for endoatmospheric interceptor missiles based on nonlinear model［J］. Acta Aeronautica et Astronautica Sinica， 2011， 32（7）： 1171-1179 （in Chinese）.
14	王雨琪，宁国栋，王晓峰，等. 基于微分对策的临近空间飞行器机动突防策略［J］. 航空学报， 2020， 41（S2）： 724276.
	WANG Y Q， NING G D， WANG X F， et al. Maneuver penetration strategy for near space vehicle based on differential game［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（S2）： 724276 （in Chinese）.
15	GARCIA E， CASBEER D W， PACHTER M. Optimal strategies for a class of multi-player reach-avoid differential games in 3D space［J］. IEEE Robotics and Automation Letters， 2020， 5（3）： 4257-4264.
16	YAN R， SHI Z Y， ZHONG Y S. Reach-avoid games with two defenders and one attacker： An analytical approach［J］. IEEE Transactions on Cybernetics， 2019， 49（3）： 1035-1046.
17	ZHANG F， ZHA W Z. Evasion strategies of a three-player lifeline game［J］. Science China Information Sciences， 2018， 61（11）： 112206.
18	CHEN M， ZHOU Z Y， TOMLIN C J. Multiplayer reach-avoid games via low dimensional solutions and maximum matching［C］∥ 2014 American Control Conference. Piscataway： IEEE Press， 2014： 1444-1449.
19	CHEN M， ZHOU Z Y， TOMLIN C J. Multiplayer reach-avoid games via pairwise outcomes［J］. IEEE Transactions on Automatic Control， 2017， 62（3）： 1451-1457.
20	YAN R， SHI Z Y， ZHONG Y S. Task assignment for multiplayer reach–avoid games in convex domains via analytical barriers［J］. IEEE Transactions on Robotics， 2020， 36（1）： 107-124.
21	SHISHIKA D， KUMAR V. Local-game decomposition for multiplayer perimeter-defense problem［C］∥ 2018 IEEE Conference on Decision and Control （CDC）. Piscataway： IEEE Press， 2018： 2093-2100.
22	SHISHIKA D， PAULOS J， KUMAR V. Cooperative team strategies for multi-player perimeter-defense games［J］. IEEE Robotics and Automation Letters， 2020， 5（2）： 2738-2745.
23	SHISHIKA D， MAITY D， DOROTHY M. Partial information target defense game［C］∥ 2021 IEEE International Conference on Robotics and Automation （ICRA）. Piscataway： IEEE Press， 2021： 8111-8117.
24	YAN R， SHI Z Y， ZHONG Y S. Optimal strategies for the lifeline differential game with limited lifetime［J］. International Journal of Control， 2021， 94（8）： 2238-2251.
25	CHEN X， YU J Q. Reach-avoid games with two heterogeneous defenders and one attacker［J］. IET Control Theory & Applications， 2022， 16（3）： 301-317.
26	LIANG L， DENG F， PENG Z H， et al. A differential game for cooperative target defense［J］. Automatica， 2019， 102： 58-71.

[1]	Ming LU, Xueqin CHEN, Fan WU, Xibin CAO. Attitude maneuver control of spacecraft based on second⁃order fully actuated system under attitude constraints [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(1): 628958-628958.
[2]	Weilin NI, Yonghai WANG, Cong XU, Fenghua CHI, Haizhao LIANG. Cooperative game guidance method for hypersonic vehicles based on reinforcement learning [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729400-729400.
[3]	Yankuan LIU, Hang YUAN, Dinghe LI, Yujie FEI. Effect of thermal aging on mechanical properties of thermal barrier coatings interface and numerical calculation [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(20): 428507-428507.
[4]	Jiancheng ZHENG, Zhiguo QU, Xiansi TAN, Zhihuai LI, Gang ZHU, Chenlong YU. Design of search parameters for hypersonic target detection by phased array radar [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(16): 328124-328124.
[5]	MA Yu'e, YANG Meng, SUN Wenbo. Cracking behavior of thermal barrier coating after thermal shock based on perdynamic theory [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(6): 526587-526587.
[6]	LI Dingjun, YANG Liuyu, SUN Fan, JIANG Peng, CHEN Yiwen, WANG Tiejun. Effect of preheating temperature on formation of surface cracks in thermal barrier coating system [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(6): 526184-526184.
[7]	WANG Bin, WANG Haitao, WANG Yufeng, ZHANG Wenwu. Water-assisted laser scanning machining test of thermal barrier coating [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(4): 525353-525353.
[8]	XIA Pengcheng, LUO Jianjun, WANG Mingming, TAN Longyu. Coordinated stabilization control for dual-arm space robot capturing a non-cooperative target [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(2): 325398-325398.
[9]	LI Xinkai, ZHANG Hongli, FAN Wenhui. Prescribed performance control for morphing aerospace vehicle under mismatched disturbances [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(2): 325008-325008.
[10]	XIA Kailong, HE Qing, ZHANG Yusheng. Measurement method of turbine blade film aperture based on infrared thermal imaging and shrinkage law [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(12): 426271-426271.
[11]	SHANG Yong, FENG Yang, LIU Qiaomu, WANG Junwu, YANG Huijun, RU Yi, ZHANG Heng, ZHAO Wenyue, PEI Yanling, LI Shusuo, GONG Shengkai. Research and application of large scientific facility on high-temperature structural materials and coatings of aero-engine [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(10): 527481-527481.
[12]	YANG Shanjie, YAN Xudong, GUO Hongbo. Failure mechanism and protection strategy of thermal barrier coatings under CMAS attack [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(10): 527613-527613.
[13]	YAO Yudong, AI Yanting, SONG Chun, GUAN Peng, TIAN Jing. Prediction of dangerous point of thermal barrier coating by biaxial stress state analysis [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(1): 424937-424937.
[14]	GUO Lei, GAO Yuan, XIN Hui. Laser modification parameters optimization and structural design of thermal barrier coatings [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(7): 424114-424114.
[15]	WEI Dechen, ZHANG Guoxin, CHEN Yongbin, LIU Senyun. Effects of air-gap on temperature rise of high frequency AC-SDBD anti-icing and deicing actuator [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(6): 124195-124195.

Reach-avoid game with time limit and detection range

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 15

References 26

Related Articles 15

Recommended Articles

Metrics

Comments