一类考虑滑动摩擦力影响的追逃博弈问题

doi:10.15960/j.cnki.issn.1007-6093.2025.01.010

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (1): 114-126.doi: 10.15960/j.cnki.issn.1007-6093.2025.01.010

一类考虑滑动摩擦力影响的追逃博弈问题

侯敏¹, 于洋¹, 戴照鹏¹, 敬鲁晶¹, 高红伟¹^,²^,*()

1. 青岛大学数学与统计学院, 山东青岛 266071
2. 山东省应用数学研究所, 山东青岛 266071

收稿日期:2021-11-16 出版日期:2025-03-15 发布日期:2025-03-08
通讯作者: 高红伟 E-mail:gaohongwei@qdu.edu.cn
基金资助:
国家自然科学基金(72171126);国家自然科学基金(11872220);青岛大学“系统科学+”联合攻关项目(XT2024301)

A class of pursuit-evasion game problems considering the influence of sliding friction

Min HOU¹, Yang YU¹, Zhaopeng DAI¹, Lujing JING¹, Hongwei GAO¹^,²^,*()

1. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
2. Institute of Applied Mathematics of Shandong, Qingdao 266071, Shandong, China

Received:2021-11-16 Online:2025-03-15 Published:2025-03-08
Contact: Hongwei GAO E-mail:gaohongwei@qdu.edu.cn

摘要/Abstract

摘要：

本文以追逃博弈问题的经典模型之一——“homicidal chauffeur”博弈为基础, 考察汽车转弯时受滑动摩擦力影响的博弈问题的捕获区域。经典“homicidal chauffeur”博弈是基于足够粗糙的地面这一理想假设对汽车转弯时的速度进行处理的。然而在现实运动中, 地面粗糙程度不同会对转弯时汽车的速度造成不同的影响。本文建立模型对追逃过程中汽车速度给出全新的刻画, 求解最优策略, 分析与经典“homicidal chauffeur”博弈相比捕获区域的变化并阐述原因, 主要结论可用于陆地追逃、空战格斗等现实场景。

关键词: “homicidal chauffeur”博弈, 追逃微分博弈, 最优策略, 界栅

Abstract:

Based on the homicidal chauffeur game, one of the classic models of the pursuit-evasion game problem, this paper investigates the capture area of the game problem that is affected by the sliding friction when the car turns. The classic homicidal chauffeur game deals with the speed of a car turning a corner based on the ideal assumption of a sufficiently rough ground. However, in real sports, different ground roughness will have different effects on the speed of the car when cornering. In this paper, a model is established to give a new description of the speed of the car in the process of chasing and fleeing, to solve the optimal strategy, to analyze the changes in the capture area compared with the classic homicidal chauffeur game and to explain the reasons. The main conclusions can be used for land pursuit, space combat and other realistic scenes.

Key words: homicidal chauffeur game, pursuit-evasion differential games, optimal strategy, barrier

中图分类号:

O225

侯敏, 于洋, 戴照鹏, 敬鲁晶, 高红伟. 一类考虑滑动摩擦力影响的追逃博弈问题[J]. 运筹学学报（中英文）, 2025, 29(1): 114-126.

Min HOU, Yang YU, Zhaopeng DAI, Lujing JING, Hongwei GAO. A class of pursuit-evasion game problems considering the influence of sliding friction[J]. Operations Research Transactions, 2025, 29(1): 114-126.

图/表 7

图1

图2

图3

图4

图5

图6

图7

参考文献 15

1	Isaacs R. Games of Pursuit [R]. California: Santa Monica, RAND Report, 1951.
2	Isaacs R . Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization[M]. New York: John Wiley and Sons, 1965: 201- 230.
3	Breakwell J, Merz A. Toward a complete solution of the homicidal chauffeur game [C]//The 1st International Conference on the Theory and Application of Differential Games, 1969: Ⅲ-1-Ⅲ-5.
4	Merz A. The homicidal chauffeur\|a differential game [D]. California: Stanford University, 1971.
5	Marchal C. Analytical study of a case of the homicidal chauffeur game problem [C]//IFIP Technical Conference on Optimization Techniques, 1974: 472-481.
6	Patsko V , Turova V . Families of semipermeable curves in differential games with the homicidal chauffeur dynamics[J]. Automatica, 2004, 40 (12): 2059- 2068.
7	Lewin J , Breakwell J . The Surveillance-Evasion game of degree[J]. Journal of Optimization Theory and Applications, 1975, 16 (3-4): 339- 353. doi: 10.1007/BF01262940
8	Patsko V, Turova V. Numerical study of the homicidal chauffeur game [C]//Proceedings of the Eighth International Colloquium on Differential Equations, 2007: 363-371.
9	Patsko V, Turova V. Numerical investigation of the value function for the homicidal chauffeur problem with a more agile pursuer [M]//Bernhard P, Falcone M, Filar J, et al. Advances in Dynamic Games and Their Applications. Annals of the International Society of Dynamic Games. Boston: Birkhäuser Boston, 2009: 1-28.
10	Meir P , Sean C . The classical homicidal chauffeur game[J]. Dynamic Games and Applications, 2019, 9 (3): 800- 850. doi: 10.1007/s13235-018-0264-8
11	Patsko V, Turova V. Antony Merz and his works [M]//Dynamic Games and Applications, 2020, 10(1): 157-182.
12	Ruziboyev M . Evasion problem in the discrete-time version of the homicidal chauffeur game[J]. Journal of Applied Mathematics and Mechanics, 2008, 72 (6): 925- 929.
13	Oyler D, Girard A. Dominance regions in the homicidal chauffeur problem [C]//2016 American Control Conference, 2016: 2494-2499.
14	Basar T , Olsder G . Dynamic Noncooperative Game Theory[M]. New York: Academic Press, 1982: 423- 442.
15	Kleppner D , Kolenkow R . An Introduction to Mechanics[M]. England: Cambridge University Press, 2014.

[1]	高红伟, 孟斌斌, 刘剑, 戴照鹏. 群体追逃微分博弈[J]. 运筹学学报（中英文）, 2024, 28(3): 46-62.
[2]	罗乐, 唐应辉. 具有Min(N,D,V)-策略控制的M/G/1排队系统[J]. 运筹学学报, 2019, 23(2): 1-16.

一类考虑滑动摩擦力影响的追逃博弈问题

A class of pursuit-evasion game problems considering the influence of sliding friction

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 7

参考文献 15

相关文章 2

编辑推荐

Metrics

本文评价