基于距离信息的追逃策略: 信念状态连续随机博弈

陈灵敏; 冯宇; 李永强

doi:10.16383/j.aas.c230018

基于距离信息的追逃策略: 信念状态连续随机博弈

doi: 10.16383/j.aas.c230018

1.
浙江工业大学信息工程学院杭州 313000

基金项目: 国家自然科学基金(61973276, 62073294), 浙江省自然科学基金(LZ21F030003)资助

详细信息

作者简介:
陈灵敏：浙江工业大学信息工程学院硕士研究生. 2020年获得绍兴文理学院学士学位. 主要研究方向为博弈论与机器学习在决策问题中的应用. E-mail: 2112003096@zjut.edu.cn

冯宇：浙江工业大学信息工程学院教授. 2011 年获得法国南特矿业大学博士学位. 主要研究方向为网络化控制系统, 分布式滤波, 不确定系统的鲁棒分析与控制, 以及博弈论与机器学习在决策问题中的应用. 本文通信作者. E-mail: yfeng@zjut.edu.cn

李永强：浙江工业大学信息工程学院副教授. 2014 年获得北京交通大学博士学位. 主要研究方向为强化学习, 非线性控制以及深度学习. E-mail: yqli@zjut.edu.cn

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出版历程
- 收稿日期: 2023-01-12
- 录用日期: 2023-04-04
- 网络出版日期: 2023-05-11
- 刊出日期: 2024-04-26

Distance Information Based Pursuit-evasion Strategy: Continuous Stochastic Game With Belief State

1.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 313000

Funds: Supported by National Natural Science Foundation of China (61973276, 62073294) and Natural Science Foundation of Zhejiang Province (LZ21F030003)

More Information

Author Bio:
CHEN Ling-Min　Master student at College of Information Engineering, Zhejiang University of Technology. She received her bachelor degree from Shaoxing University in 2020. Her research interest covers game theory and machine learning in decision-making

FENG Yu　Professor at College of Information Engineering, Zhejiang University of Technology. He received his Ph.D. degree from Ecole des Mines de Nantes in 2011. His research interest covers networked control systems, distributed filtering, and robust analysis and control for uncertainty systems, and applications of game theory and machine learning in decision-making. Corresponding author of this paper

LI Yong-Qiang　Associate professor at College of Information Engineering, Zhejiang University of Technology. He received his Ph.D. degree from Beijing Jiaotong University in 2014. His research interest covers reinforcement learning, nonlinear control and deep learning

摘要

摘要: 追逃问题的研究在对抗、追踪以及搜查等领域极具现实意义. 借助连续随机博弈与马尔科夫决策过程(Markov decision process, MDP), 研究使用测量距离求解多对一追逃问题的最优策略. 在此追逃问题中, 追捕群体仅领导者可测量与逃逸者间的相对距离, 而逃逸者具有全局视野. 追逃策略求解被分为追博弈与马尔科夫决策两个过程. 在求解追捕策略时, 通过分割环境引入信念区域状态以估计逃逸者位置, 同时使用测量距离对信念区域状态进行修正, 构建起基于信念区域状态的连续随机追博弈, 并借助不动点定理证明了博弈平稳纳什均衡策略的存在性. 在求解逃逸策略时, 逃逸者根据全局信息建立混合状态下的马尔科夫决策过程及相应的最优贝尔曼方程. 同时给出了基于强化学习的平稳追逃策略求解算法, 并通过案例验证了该算法的有效性.
- 追逃问题 /
- 信念区域状态 /
- 连续随机博弈 /
- 马尔科夫决策过程 /
- 强化学习
Abstract: The pursuit-evasion problem is of great importance in the fields of confrontation, tracking and searching. In this paper, we are focused on the study of optimal strategies for solving the multi-pursuits and single-evader problem with only measured distances within the framework of continuous stochastic game and Markov decision process (MDP). In such problem, only the leader of pursuits can measure its relative distance with respect to the evader, while the evader has a global view. The strategies of the pursuits and evader are established via two steps: The pursuit game and the MDP. For the pursuits＇ strategy, the belief region state is introduced by partitioning the environment to estimate the evader＇s position, and the belief region state is further corrected by using the measured distances. A continuous stochastic pursuit game is then formed based on the belief region state, and the existence of stationary Nash equilibrium strategies is shown through the fixed-point theorem. For the evader＇s strategy, an MDP with the global states is established and the underlying optimal Bellman equation is devised. Moreover, a reinforcement learning based algorithm is presented for stationary pursuit-evasion strategies computation, and an example is also included to exhibit the effectiveness of the current method.
- Pursuit-evasion problem /
- belief region state /
- continuous stochastic game /
- Markov decision process (MDP) /
- reinforcement learning

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图 1 追逃问题环境

Fig. 1 Environment of pursuit-evasion problem

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图 2 (a) $ L $个区域; (b) 追捕群体的划分

Fig. 2 (a) $ L $ regions; (b) Division of pursuit group

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图 3 警戒区域

Fig. 3 Warning area

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图 4 第$ m $个区域

Fig. 4 The $m\text{-}{\rm{th}}$ area

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图 5 预测距离

Fig. 5 Prediction distance

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图 6 地图尺寸

Fig. 6 Size of map

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图 7 追博弈中追捕群体的收益

Fig. 7 Pursuits＇ reward in the pursuit game

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图 8 MDP中逃逸者的收益

Fig. 8 Evader＇s reward in MDP

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图 9 算法测试过程

Fig. 9 Algorithm testing process

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图 10 追捕群体与逃逸者的运动轨迹图

Fig. 10 Trajectories of pursuits and evader

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表 1 结果对比

Table 1 Result comparison

算法	捕捉平均步数	捕捉成功率
本文算法	41	95%
本文算法(未修正)	43	87%
MAPPO^[40]	88	59%
MASAC^[41]	85	61%
MADDPG^[42]	99	56%
几何估计追捕^[33]	78	72%
基于三角定位追捕^[34]	61	94%
至少一人全局视野追捕^[23]	62	85%
自动追踪追捕^[36]	82	71%
自适应切换追捕^[37]	65	66%
随机策略	152	10%

下载: 导出CSV

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