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基于讨价还价博弈机制的B-IHCA*多机器人路径规划算法

张凯翔 毛剑琳 向凤红 宣志玮

张凯翔, 毛剑琳, 向凤红, 宣志玮. 基于讨价还价博弈机制的B-IHCA*多机器人路径规划算法. 自动化学报, 2020, 46(13): 1−15 doi: 10.16383/j.aas.c220065
引用本文: 张凯翔, 毛剑琳, 向凤红, 宣志玮. 基于讨价还价博弈机制的B-IHCA*多机器人路径规划算法. 自动化学报, 2020, 46(13): 1−15 doi: 10.16383/j.aas.c220065
Zhang Kai-Xiang, Mao Jian-Lin, Xiang Feng-Hong, Xuan Zhi-Wei. B-ihca*, a bargaining game based multi-agent path finding algorithm. Acta Automatica Sinica, 2020, 46(13): 1−15 doi: 10.16383/j.aas.c220065
Citation: Zhang Kai-Xiang, Mao Jian-Lin, Xiang Feng-Hong, Xuan Zhi-Wei. B-ihca*, a bargaining game based multi-agent path finding algorithm. Acta Automatica Sinica, 2020, 46(13): 1−15 doi: 10.16383/j.aas.c220065

基于讨价还价博弈机制的B-IHCA*多机器人路径规划算法

doi: 10.16383/j.aas.c220065
基金项目: 云南省重点研发计划项目(202002AC080001), 国家自然科学基金(62263017)资助
详细信息
    作者简介:

    张凯翔:昆明理工大学机电工程学院博士研究生. 主要研究方向为移动机器人路径规划. E-mail: Kaixiangzhang35@163.com

    毛剑琳:昆明理工大学信息工程与自动化学院教授. 主要研究方向为通信网络资源分配与协议优化, 智能优化与调度算法, 多机器人系统协同控制研究. 本文通信作者. E-mail: jlmao@kmust.edu.cn

    向凤红:昆明理工大学信息工程与自动化学院教授. 主要研究方向为智能控制理论与应用, 计算机网络控制系统. E-mail: xiangfh5447@sina.com

    宣志玮:昆明理工大学信息工程与自动化学院硕士研究生. 主要研究方向为移动机器人路径规划. E-mail: rangxuan@foxmail.com

B-IHCA*, a Bargaining Game Based Multi-agent Path Finding Algorithm

Funds: Supported by Provincial Major Research Program of Yunnan (202002AC080001) and National Natural Science Foundation of China (62263017)
More Information
    Author Bio:

    ZHANG Kai-Xiang Ph.D. candidate at the Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology. His main research interest is mobile robot path planning

    MAO Jian-Lin Professor at the Faculty of Information Engineering and Automation, Kunming University of Science and Technology. Her research interest covers communication network resource allocation and protocol optimization, intelligent optimization and scheduling algorithm, and cooperative control of multi-agent systems. Corresponding author of this paper

    XIANG Feng-Hong Professor at the Faculty of Information Engineering and Automation, Kunming University of Science and Technology. His research interest covers intelligent control theory and its applications, control system of computer network

    XUAN Zhi-Wei Master student at the Faculty of Information Engineering and Automation, Kunming University of Science and Technology. His main research interest is mobile robot path planning

  • 摘要: 针对密集场景中大规模冲突导致多机器人路径规划(Multi-agent path finding, MAPF) 成功率低的问题, 引入讨价还价博弈机制并以层级协作A* (Hierarchical cooperative A*, HCA*) 算法为内核, 提出一种基于讨价还价博弈机制的改进层级协作A* (Bargaining game based improving HCA*, B-IHCA*) 算法. 首先, 在HCA*算法基础上, 对导致路径无解的冲突双方或多方进行讨价还价博弈. 由高优先级机器人先出价, 当低优先级机器人在该条件下无法求解时, 则其将不接受该出价, 并通过降约束求解方式进行还价. 再由其他冲突方对此做进一步还价, 直至各冲突方都能协调得到可接受的路径方案. 其次, 为避免原始HCA*算法由于高优先级的阻碍陷于过长或反复无效搜索状态, 在底层A*搜索环节加入了熔断机制. 通过熔断机制与讨价还价博弈相配合可在提升路径求解成功率的同时兼顾路径代价. 研究结果表明, 所提算法在密集场景大规模机器人路径规划问题上较现有算法求解成功率更高, 求解时间更短, 路径代价得到改善, 验证了算法的有效性.
  • 图  1  MAPF问题描述

    Fig.  1  MAPF problem description

    图  2  one-shot类型MAPF问题的终点占位现象

    Fig.  2  Goal occupations in one-shot MAPF problem

    图  3  拥塞问题示例

    Fig.  3  Example of congestion problem

    图  4  约束表使用与更新

    Fig.  4  Use and update of constraint tables

    图  5  密集场景中典型封堵问题

    Fig.  5  Typical blocking problems in dense scenarios

    图  6  讨价还价博弈基本思路

    Fig.  6  Basic example of bargaining game process

    图  7  单点多封堵求解过程

    Fig.  7  Solving process of the single-site and multi-blocking

    图  8  多点多封堵问题降约束个体二次规划

    Fig.  8  Replanning of reduced constraint individuals for the multi-site and multi-blocking

    图  9  HCA*底层算法低效搜索状态

    Fig.  9  Inefficient searching in underlying of HCA*

    图  10  $ 8 \times 8$地图[11]及任务设置

    Fig.  10  $ 8 \times 8$ map[11] and its tasks

    图  11  大规模随机任务实验地图

    Fig.  11  Maps for large scale randomized tasks

    图  12  各算法测试成功率及求解时间离散分布统计

    Fig.  12  Statistics on success rate and solution time of the tested algorithms

    图  13  4类地图最高数量B-IHCA*算法求解路径图

    Fig.  13  Path scheme of B-IHCA* algorithm for four tested maps in case of the highest number of robots

    表  1  单点单封堵类型路径规划结果

    Table  1  Solution of the single-site and single-blocking

    机器人路径具体方案
    ${a_1}$${p_{1,1}}$[(3, 2), (3, 2), (3, 1), (3, 2), (4, 2)]
    ${a_2}$${p_{2,1}}$[(1, 2), (2, 2), (3, 2), (4, 2), (5, 2)]
    下载: 导出CSV

    表  2  单点多封堵类型路径规划结果

    Table  2  Solution of the single-site and multi-blocking

    机器人路径具体方案
    ${a_1}$${p_{1,1}}$[(3, 3), (3, 2), (3, 3), (3, 2), (3, 3), (3, 3), (3, 3), (3, 3), (3, 4), (3, 3), (4, 3)]
    ${a_2}$${p_{2,1}}$[(2, 3), (3, 3), (4, 3), (5, 3), (5, 4), (6, 4)]
    ${a_3}$${p_{3,1}}$[(1, 2), (1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (5, 2), (5, 1)]
    ${a_4}$${p_{4,1}}$[(5, 2), (5, 3), (5, 3), (5, 2), (5, 3), (5, 4), (5, 3), (4, 3), (3, 3), (3, 2), (3, 1), (2, 1)]
    下载: 导出CSV

    表  3  多点多封堵类型路径规划结果

    Table  3  Solution of the multi-site and multi-blocking

    机器人路径具体方案
    ${a_1}$${p_{1,1}}$[(3, 3), (3, 3), (3, 4), (3, 4), (3, 4), (3, 4), (3, 3), (4, 3)]
    ${a_2}$${p_{2,1}}$[(1, 2), (1, 3), (2, 3), (3, 3), (3, 2), (3, 3), (4, 3), (5, 3)]
    ${a_3}$${p_{3,1}}$[(1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (5, 2)]
    ${a_4}$${p_{4,1}}$[(1, 1), (1, 2), (1, 3), (2, 3), (3, 3),
    (4, 3), (5, 3), (5, 4), (6, 4)]
    下载: 导出CSV

    表  4  不同$N_{\rm{robot}}$规模对应的求解限制时间

    Table  4  Time limits for different sizes of $N_{\rm{robot}}$

    机器人数(个)$0 < {N_{\rm{robot}}} \le 50$$50 < {N_{\rm{robot}}} \le 100$${N_{\rm{robot}}} > 100$
    限制时间(秒)150300500
    下载: 导出CSV

    表  5  实验I参数设置

    Table  5  Parameters for experiment I

    地图类型$N_{\rm{robot}}$$\alpha (\% )$$\beta (\% )$$\omega $${R_L}$
    $8 \times 8$ grid1023.437520.408236000
    下载: 导出CSV

    表  6  实验I求解结果

    Table  6  Results of experiment I

    算法路径总代价(步)求解时间(秒)
    HCA*NANA
    CBSNANA
    CBS-DS62132.0
    WdSIPP($w = 1.01$)NANA
    WdSIPP($w = 1.75$)NANA
    B-IHCA*730.1
    下载: 导出CSV

    表  7  B-IHCA*求解过程路径与冲突信息

    Table  7  Path and conflict information during the solving process of B-IHCA*

    求解阶段信息类型信息值
    顺序求解全约束路径${p_{1,0}},{p_{2,0}},{p_{5.0}},{p_{6.0}},{p_{7,0}},{p_{9,0}},{p_{10,0}}$
    欠约束路径$p_{3,0}^u,p_{4,0}^u,p_{8,0}^u$
    零约束路径$\varnothing $
    冲突机器人$({a_2},{a_3}),({a_2},{a_4}),({a_5},{a_8})$
    全约束路径${p_{1,1}}$, ${p_{2,1}}$, ${p_{3,1}}$, ${p_{4,1}}$, ${p_{5,1}}$,
    ${p_{6,1}}$, ${p_{7,1}}$, ${p_{8,1}}$, ${p_{9,1}}$, ${p_{10,1}}$
    讨价还价欠约束路径$\varnothing $
    第1轮零约束路径$\varnothing $
    冲突机器人$\varnothing $
    下载: 导出CSV

    表  8  实验II参数设置A

    Table  8  Part A of the parameters for Experiment II

    地图类型$\alpha (\%)$$R_L$
    $20 \times 20$ blocked-10地图9.750010000
    $20 \times 20$ random-15地图15.000015000
    $32 \times 32$ blocked-20地图19.921915000
    $32 \times 32$ room地图33.398415000
    下载: 导出CSV

    表  9  实验II参数设置B

    Table  9  Part B of the parameters for Experiment II

    $20 \times 20$ blocked-10地图$20 \times 20$ random-15地图$32 \times 32$ blocked-20地图$32 \times 32$ room地图
    $N_{\rm{robot}}$$\beta (\%)$$\omega $$N_{\rm{robot}}$$\beta (\%)$$\omega $$N_{\rm{robot}}$$\beta (\%)$$\omega $$N_{\rm{robot}}$$\beta (\%)$$\omega $
    205.54022154.41182303.65854101.46634
    4011.08034308.82355506.09765202.93265
    6016.620564513.23536708.53666304.39886
    8022.160766017.647169010.97566405.86518
    10027.700877522.0588811013.41468507.331410
    12033.241089026.47061013015.853710608.797712
    下载: 导出CSV

    表  10  算法路径质量统计

    Table  10  Path cost statistics of the tested algorithms

    地图类型$N_{\rm{robot}}$公共算例数平均总代价(步)平均求解轮数
    CBSCBS-DSHCA*WdSIPP (1.01)WdSIPP (1.75)B-IHCA*公共算例非公共算例
    $20 \times 20$ blocked-102013263.1267.1273.0275.8281.5267.21.541.43
    4017NANA603.8604.9622.1591.91.411.67
    6019NANA933.2928.2969.5926.31.322.00
    8010NANA1340.91347.71392.31327.81.402.00
    1006NANA1731.31744.21820.71731.31.002.62
    $20 \times 20$ random-151518209.1211.1219.1220.1224.4213.71.501.00
    3018NANA473.0472.8488.2470.21.332.50
    4515NANA745.2745.1771.3737.51.272.25
    6011NANA1076.81072.31115.21055.91.912.22
    759NANA1391.21390.41437.41386.71.332.09
    $32 \times 32$ blocked-20306618.3626.2630.0655.7623.71.171.29
    5018NANA1237.21342.91311.61234.01.111.50
    7017NANA1781.51778.61881.81763.01.412.50
    9014NANA2396.92383.52538.52368.11.642.80
    1109NANA3010.33008.63190.32981.81.892.33
    1306NANA3596.33555.53757.73558.51.672.70
    $32 \times 32$ room1017248.7249.9253.1254.6264.2252.51.061.67
    206550.5566.5563.7585.8558.21.501.62
    3015NANA841.1838.5874.7830.81.402.00
    4014NANA1188.31174.51208.91175.61.431.83
    5011NANA1536.31528.31573.71512.41.912.43
    606NANA1891.51892.81949.71881.21.672.83
    下载: 导出CSV
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  • 收稿日期:  2022-01-25
  • 录用日期:  2022-09-09
  • 网络出版日期:  2022-11-02

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