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Article(id=1212795572545835909, tenantId=1146029695717560320, journalId=1189645257101713411, issueId=1212795571727946626, articleNumber=null, orderNo=null, doi=10.19822/j.cnki.1671-6329.20220113, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=null, receivedDateStr=null, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1767082597146, onlineDateStr=2025-12-30, pubDate=1672848000000, pubDateStr=2023-01-05, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1767082597146, onlineIssueDateStr=2025-12-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1767082597146, creator=13701087609, updateTime=1767082597146, updator=13701087609, issue=Issue{id=1212795571727946626, tenantId=1146029695717560320, journalId=1189645257101713411, year='2023', volume='', issue='1', pageStart='1', pageEnd='62', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1767082596952, creator=13701087609, updateTime=1767503658793, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1214561633142231144, tenantId=1146029695717560320, journalId=1189645257101713411, issueId=1212795571727946626, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1214561633142231145, tenantId=1146029695717560320, journalId=1189645257101713411, issueId=1212795571727946626, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=39, endPage=46, ext={EN=ArticleExt(id=1212795572839437194, articleId=1212795572545835909, tenantId=1146029695717560320, journalId=1189645257101713411, language=EN, title=Research on Trajectory Planning Based on CiteSpace, columnId=1212795572503892868, journalTitle=Automotive Digest, columnName=Special Issue on Technologies of NEV, runingTitle=null, highlight=null, articleAbstract=

While the development of autonomous driving technology is progressing rapidly, trajectory planning, as an essential part of its decision planning module, has received a lot of attention from scholars. A graphical analysis of trajectory planning research through the CiteSpace bibliometric tool provides some convenience and reference for relevant researchers. The literature of trajectory planning journals included in the Web Of Science(WOS) core collection since 2010 is used as a sample for visualization and analysis, and the overview of trajectory planning research is introduced through bibliometric analysis, and shows the thematic lineage and research hotspots of trajectory planning through keyword co-occurrence analysis and burst detection.

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自动驾驶技术发展飞速进步的同时，轨迹规划作为其决策规划模块中必不可少的一部分，得到广大学者的重点关注，通过CiteSpace文献计量工具对轨迹规划研究进行图谱分析可为相关研究人员提供一些便利与参考。以2010年以来WOS核心合集收录的轨迹规划期刊文献为样本进行可视化分析，通过文献统计分析介绍轨迹规划研究的概况，并通过关键词共现分析与突发性检测展现轨迹规划的主题脉络与研究热点。

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期刊名称 发文量
/篇·年-1		 5年平均影响因子
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 424 7.252 9
IEEE ACCESS 17 835 3.670 8
IEEE TRANSACTIONS ON INTELLIGENT VEHICLES 472 6.492 5
IEEE ROBOTICS AND AUTOMATION LETTERS 894 3.855 9
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 1 420 5.428 6
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轨迹规划研究发文量与被引频次

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期刊名称 发文量
/篇·年-1		 5年平均影响因子
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 424 7.252 9
IEEE ACCESS 17 835 3.670 8
IEEE TRANSACTIONS ON INTELLIGENT VEHICLES 472 6.492 5
IEEE ROBOTICS AND AUTOMATION LETTERS 894 3.855 9
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 1 420 5.428 6
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国家 发文量/篇 中介中心性 起始年份/年
中国 210 0.45 2011
美国 133 0.65 2010
韩国 36 0.03 2012
德国 36 0.01 2012
英国 36 0.23 2012
加拿大 33 0.20 2012
西班牙 27 0.14 2012
法国 21 0.26 2010
澳大利亚 16 0.10 2011
瑞典 14 0.05 2016
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轨迹规划领域发文量前10国家

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国家 发文量/篇 中介中心性 起始年份/年
中国 210 0.45 2011
美国 133 0.65 2010
韩国 36 0.03 2012
德国 36 0.01 2012
英国 36 0.23 2012
加拿大 33 0.20 2012
西班牙 27 0.14 2012
法国 21 0.26 2010
澳大利亚 16 0.10 2011
瑞典 14 0.05 2016
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序号 文献题名 被引频次/次 作者（单位） 发表
年份/年
1 A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles 624 Paden Brian
(University of California Berkeley)		 2016
2 A Review of Motion Planning Techniques for Automated Vehicles 546 Gonzalez David
(Inria Paris Rocquencourt)		 2016
3 Making Bertha Drive-An Autonomous Journey on a Historic Route 462 Ziegler Julius
(FZI Res Ctr Informat Technolony)		 2014
4 A Survey of Motion Planning Algorithms from the Perspective of Autonomous UAV Guidance 418 Goerzen Chad
(San Jose State University)		 2010
5 Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions 347 Katrakazas Christos
(National Technical University of Athens)		 2015
6 Algorithms for collision-free navigation of mobile robots in complex cluttered environments: a survey 265 Hoy Michael
(Nanyang Technological University)		 2015
7 A review on improving the autonomy of unmanned surface vehicles through intelligent collision avoidance manoeuvres 213 Campbell Sable
( Queens University Belfast)		 2012
8 Cooperative Intersection Management: A Survey 212 Chen Lei
(Viktoria Swedish ICT)		 2016
9 Maneuver-Based Trajectory Planning for Highly Autonomous Vehicles on Real Road With Traffic and Driver Interaction 168 Glaser Sebastien
(Queensland University of Technology)		 2010
10 Local Path Planning for Off-oad Autonomous Driving With Avoidance of Static Obstacles 167 Chu Keonyup
( Hanyang University)		 2012
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国际轨迹规划研究高被引文献

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序号 文献题名 被引频次/次 作者（单位） 发表
年份/年
1 A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles 624 Paden Brian
(University of California Berkeley)		 2016
2 A Review of Motion Planning Techniques for Automated Vehicles 546 Gonzalez David
(Inria Paris Rocquencourt)		 2016
3 Making Bertha Drive-An Autonomous Journey on a Historic Route 462 Ziegler Julius
(FZI Res Ctr Informat Technolony)		 2014
4 A Survey of Motion Planning Algorithms from the Perspective of Autonomous UAV Guidance 418 Goerzen Chad
(San Jose State University)		 2010
5 Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions 347 Katrakazas Christos
(National Technical University of Athens)		 2015
6 Algorithms for collision-free navigation of mobile robots in complex cluttered environments: a survey 265 Hoy Michael
(Nanyang Technological University)		 2015
7 A review on improving the autonomy of unmanned surface vehicles through intelligent collision avoidance manoeuvres 213 Campbell Sable
( Queens University Belfast)		 2012
8 Cooperative Intersection Management: A Survey 212 Chen Lei
(Viktoria Swedish ICT)		 2016
9 Maneuver-Based Trajectory Planning for Highly Autonomous Vehicles on Real Road With Traffic and Driver Interaction 168 Glaser Sebastien
(Queensland University of Technology)		 2010
10 Local Path Planning for Off-oad Autonomous Driving With Avoidance of Static Obstacles 167 Chu Keonyup
( Hanyang University)		 2012
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关键词 频次/次 中介中心性 年份/年
Autonomous vehicle 313 0.16 2010
Trajectory planning 310 0.27 2010
Collision avoidance 104 0.04 2010
Model 83 0.08 2013
Algorithm 71 0.31 2011
Optimal control 62 0.05 2016
Autonomous driving 59 0.05 2011
System 55 0.1 2012
Model predictive control 53 0.38 2011
Mobile robot 52 0.14 2012
Autonomous navigation 51 0.4 2013
Trajectory tracking 45 0.06 2019
Vehicle dynamics 33 0.09 2017
Trajectory optimization 23 0.02 2013
Decision making 62 0.05 2016
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国内外轨迹规划研究高频关键词

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关键词 频次/次 中介中心性 年份/年
Autonomous vehicle 313 0.16 2010
Trajectory planning 310 0.27 2010
Collision avoidance 104 0.04 2010
Model 83 0.08 2013
Algorithm 71 0.31 2011
Optimal control 62 0.05 2016
Autonomous driving 59 0.05 2011
System 55 0.1 2012
Model predictive control 53 0.38 2011
Mobile robot 52 0.14 2012
Autonomous navigation 51 0.4 2013
Trajectory tracking 45 0.06 2019
Vehicle dynamics 33 0.09 2017
Trajectory optimization 23 0.02 2013
Decision making 62 0.05 2016
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聚类标签 篇数/篇 剪影度 活跃年份/年
Model predictive control 124 0.948 2016
Trajectory prediction 116 0.976 2017
Heuristic algorithms 132 0.882 2020
Automated driving 230 0.912 2016
Trajectory tracking 143 0.904 2017
Nonholonomic constraints 99 0.879 2015
Autonomous navigation 87 0.964 2016
Machine vision 57 0.851 2017
Optimal control 207 0.869 2016
Target pursuit 161 0.971 2015
Data models 72 0.793 2020
Behavior selection 86 1 2016
Model predictive control 62 0.937 2020
Trajectory prediction 333 0.953 2013
Heuristic algorithms 347 0.966 2015
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WOS时间线聚类主要信息

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聚类标签 篇数/篇 剪影度 活跃年份/年
Model predictive control 124 0.948 2016
Trajectory prediction 116 0.976 2017
Heuristic algorithms 132 0.882 2020
Automated driving 230 0.912 2016
Trajectory tracking 143 0.904 2017
Nonholonomic constraints 99 0.879 2015
Autonomous navigation 87 0.964 2016
Machine vision 57 0.851 2017
Optimal control 207 0.869 2016
Target pursuit 161 0.971 2015
Data models 72 0.793 2020
Behavior selection 86 1 2016
Model predictive control 62 0.937 2020
Trajectory prediction 333 0.953 2013
Heuristic algorithms 347 0.966 2015
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关键词 突现度 时间/年
Dynamic window approach 1.72 2010—2015
Mobile robot 1.75 2011—2016
Generation 2.37 2012—2018
Environment 4.01 2014—2018
Curvature 1.97 2015—2018
Algorithm 3.12 2016—2019
Electric vehicle 1.9 2018—2019
Road safety 2.87 2019—2020
Predictive control 1.98 2019—2020
Machine learning 2.12 2020—2022
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轨迹规划领域关键词突现

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关键词 突现度 时间/年
Dynamic window approach 1.72 2010—2015
Mobile robot 1.75 2011—2016
Generation 2.37 2012—2018
Environment 4.01 2014—2018
Curvature 1.97 2015—2018
Algorithm 3.12 2016—2019
Electric vehicle 1.9 2018—2019
Road safety 2.87 2019—2020
Predictive control 1.98 2019—2020
Machine learning 2.12 2020—2022
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基于CiteSpace的轨迹规划研究
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靳慧
汽车文摘 | 新能源汽车技术专题 2023,(1): 39-46
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汽车文摘 | 新能源汽车技术专题 2023, (1): 39-46
基于CiteSpace的轨迹规划研究
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靳慧
作者信息
  • 重庆交通大学机电与车辆工程学院， 重庆 400074
Research on Trajectory Planning Based on CiteSpace
Hui Jin
Affiliations
  • School of Mechatronics and Vehicle Engineering, Chongqing Jiaotong University, Chongqing 400074
出版时间: 2023-01-05 doi: 10.19822/j.cnki.1671-6329.20220113
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摘要
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自动驾驶技术发展飞速进步的同时，轨迹规划作为其决策规划模块中必不可少的一部分，得到广大学者的重点关注，通过CiteSpace文献计量工具对轨迹规划研究进行图谱分析可为相关研究人员提供一些便利与参考。以2010年以来WOS核心合集收录的轨迹规划期刊文献为样本进行可视化分析，通过文献统计分析介绍轨迹规划研究的概况，并通过关键词共现分析与突发性检测展现轨迹规划的主题脉络与研究热点。

轨迹规划  /  研究脉络  /  文献计量分析  /  CiteSpace

While the development of autonomous driving technology is progressing rapidly, trajectory planning, as an essential part of its decision planning module, has received a lot of attention from scholars. A graphical analysis of trajectory planning research through the CiteSpace bibliometric tool provides some convenience and reference for relevant researchers. The literature of trajectory planning journals included in the Web Of Science(WOS) core collection since 2010 is used as a sample for visualization and analysis, and the overview of trajectory planning research is introduced through bibliometric analysis, and shows the thematic lineage and research hotspots of trajectory planning through keyword co-occurrence analysis and burst detection.

Trajectory planning  /  Research lineage  /  Bibliometric analysis  /  CiteSpace
靳慧. 基于CiteSpace的轨迹规划研究. 汽车文摘, 2023 , (1) : 39 -46 . DOI: 10.19822/j.cnki.1671-6329.20220113
Hui Jin. Research on Trajectory Planning Based on CiteSpace[J]. Automotive Digest, 2023 , (1) : 39 -46 . DOI: 10.19822/j.cnki.1671-6329.20220113
正文
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缩略语
WOS Web Of Science
GSTCN Graph-based Spatial Temporal Convolutional
Network
ILQR Linaer Ouadratic Ragulator
1 前言
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随着5G时代的到来，自动驾驶获得了日新月异的发展。自动驾驶汽车的发展离不开自动驾驶系统的设计。从功能角度划分，一般的自动驾驶系统主要分为感知、决策规划和控制3个功能模块[1]。其中，决策规划模块根据感知模块接收的信息，决定自动驾驶车辆的驾驶行为与运动路线，并输出控制模块所需的动作指令。因此，决策规划模块是自动驾驶系统不可或缺的一部分，将直接影响其功能性。其中轨迹规划是决策规划模块的基础组成与技术核心，在行驶过程中轨迹规划模块负责生成满足车辆运动学与动力学约束、碰撞约束和驾驶环境与交通法规等时空约束条件的连接车辆起点与终点的轨迹信息，同时该轨迹信息也要满足车辆在行驶过程中的安全性与舒适性等要求。因此，轨迹规划研究是决策规划模块的重要组成，是自动驾驶系统研究的重点内容。本文将通过文献计量分析的方式对现有的轨迹规划研究进行总结分析。
通过对现有的文献进行统计分析，不仅可以了解现有的研究脉络，清楚相关研究的知识演进过程，还能够以一种宏观的角度把握现有的知识架构。对轨迹规划领域的知识进行图谱分析不仅为现有研究提供一种新的视角，还能清晰展现当前研究中的科研进展与技术积累，在帮助相关研究人员在当前研究基础上的进一步探索，同时为新接触轨迹规划领域的人提供一些便利。
2 研究方法与数据来源
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CiteSpace是用于研究科学文献发展趋势的一种可视化分析工具，其通过相关领域文献的正文以及参考文献所构成的知识图谱网络，展现该领域的知识整体架构变化与研究脉络进展。通过CiteSpace得出的知识图谱以节点与连线的方式展现，节点大小与颜色反映相关分析对象（作者、机构、关键词、被引文献等)出现的频次与年份，连线的粗细程度则展现了相关节点的联系强度，如合作关系强度与共被引强度等[2]。本文以WOS核心数据库作为数据源（CNKI数据库中关于自动驾驶轨迹规划的期刊文献相对较少（167篇），分析结果参考性较低，故未选择）。在WOS中限定数据库为“Web of Science核心合集”，语种为“英语”，文献类型限定为“Article OR Review”，检索时间设置为“所有年份（1985—2022）”，剔除会议录论文后，最终检索有效文献为575篇。检索时间节点为2022年5月4日。
本文将按照“文献统计分析→研究主题脉络→研究热点分析”的研究思路对WOS 核心合集中有关自动驾驶轨迹规划的研究成果进行文献计量和可视化分析。首先，从年度发文量、期刊来源、研究机构3方面对研究现状进行统计分析，展现轨迹规划研究的整体概况；其次，通过关键词聚类分析与关键词共现网络等功能对文献进行图谱分析，探究轨迹规划领域的研究脉络；最后，通过关键词与引文突现展现轨迹规划领域的研究热点更替，来呈现轨迹规划研究的趋势变化。
3 文献统计分析
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3.1 发文量与期刊统计
3.1.1 发文量统计
从文献发文量变化可以看出轨迹规划研究的发展状况，由图1可以看出，有关轨迹规划研究的文献多集中于2010—2022年之间，在2010—2017年之间轨迹规划研究的发文量增长速度缓慢，自2017始，有关轨迹规划的研究开始蓬勃发展，这与2017年自动驾驶行业的迅速发展有着必然联系。
3.1.2 期刊统计
发文量靠前的期刊一定程度上反映了该期刊在轨迹规划领域的学术影响力，相关研究人员可以通过该期刊寻找本领域有价值的学术论文。本文统计了轨迹规划领域发文量前5的期刊（表1）。
3.2 国家、机构合作网络分析
3.2.1 国家合作网络分析
CiteSpace的国家合作网络中可以直观地看出某个国家在轨迹规划研究领域中的学术影响力。图谱网络中的节点大小反映了该国学者在轨迹规划领域的发文量；节点处的年轮颜色代表文献出现时间的早晚，年轮中心代表时间较早；每圈年轮的厚度代表该年的文献数量。
从图2中可以明显看出，中国与美国在轨迹规划方向的发文量远超于其他国家，代表中国的节点略大于美国，节点中心颜色较为深且外围年轮厚度明显超过代表美国的节点，由此可以看出，中国对轨迹规划的研究时间相对晚于美国，但发文量要大于美国；从连线数量角度来看，中美两国与国际间的交流远超于其他国家之间的交流，美国与其他国家的连线密度相对高于中国；从连线的粗细程度来看，各国之间的连线都相对较细且平均，表明各国之间的交流程度并不紧密。
通过统计2010—2022年间轨迹规划领域发文量前10的国家（表2），可以看出各国在轨迹规划领域的总体概况。中介中心性即某一节点担任其他节点的中介作用程度。结合图2与表2分析，除韩国、德国与瑞典之外的国家的中介中心性都大于0.1，表明这些国家与其他国家的合作过程中起到了一定的中介作用。从表2可以明显看出中国的中介中心性（0.45）低于美国（0.65），但2者的中介中心性都远高于其他国家，说明中国与美国在轨迹规划的国际交流合作中起到了巨大的承接作用。
3.2.2 机构合作网络分析
通过对WOS核心合集中的机构在2010—2022年中的发文量与合作关系进行图谱分析，可以了解轨迹规划领域中各机构的研究状况与合作关系。对发文量较多的机构进行共现分析，可以清晰展现轨迹规划领域中的核心研究力量，发现其中的“巨人”，有利于相关研究人员有的放矢的寻找轨迹规划的研究成果。
通过机构合作网络，可以发现在轨迹规划领域内学术影响力较大的一些机构，可以通过这些机构进行发现与了解轨迹规划的技术成果与研究动态。如图3所示，中国在轨迹规划研究方面学术影响力较大的机构有吉林大学、北京理工大学、清华大学、同济大学、中国科学院、浙江大学、同济大学、长安大学与重庆大学。国外在轨迹规划研究方面学术影响力大的机构有加利福尼亚大学、滑铁卢大学、加州大学伯克利分校、克兰菲尔德大学、汉阳大学、南洋理工大学、慕尼黑工业大学和密歇根大学等机构。可以发现，国内与国际间的主要研究机构基本为高校，其他类型机构较少，主要研究力量略显单薄，这是因为工业界在轨迹规划领域中的研究成果不一定以学术论文的方式展现，也可能体现为专利或产品，因此无法通过科学文献分析的方法完全展现轨迹规划研究的技术成果与研究动态。从研究的规模与深度来看，轨迹规划的研究仍处于探索阶段，产学研一体的局面尚未完成，因此轨迹规划的研究还有很大的发展空间与进步余地。
3.3 高被引文献
从所导出的数据中筛选出国内外2010—2022年轨迹规划研究被引量前10的文献（表3），文献的被引频次反映了该文献在轨迹规划领域的学术价值影响力，可以通过高被引文献了解轨迹规划领域的主体研究方向和研究内容以及常用的研究方法。从时间范围来看，国际高被引文献的发表时间相对较早，多数文献集中于2014—2016年之间，2014之前的高被引文献相对较少，2016之后的文献还缺乏一定的时间积累；从文献研究内容来看，国际高被引文献中包含轨迹规划算法综述（4篇）、自动驾驶系统（1篇）、轨迹规划算法（4篇）以及其他内容；从国际高被引文献的作者来看，暂时还未有中国学者在内，说明我国的轨迹规划研究还未有突破性进展。从发表机构来看，多数高被引文献集中于大学等研究机构，来自于工业界的相关科研机构的文献相对较少，具有一定的差异性。
4 轨迹规划研究脉络
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4.1 主题脉络
关键词是文献内容的总结与提炼，通过对得到的大量轨迹规划文献数据进行关键词共现分析，可以展现轨迹规划研究的主要研究内容，笔者将通过对关键词的频次分析与聚类分析呈现轨迹规划研究的主题脉络。
4.1.1 关键词频次分析
运用CiteSpace软件对相关数据进行关键词共现分析，得到关键词的频次统计数据，将出现频次最高的前15个关键词罗列在表4中。以频次和中心度作为关键要素判断该关键词的重要性，频次反映关键词的影响程度，中心性则体现关键词之间的关联程度。从表4中可以看出，除自动驾驶车辆、轨迹规划、自动驾驶等基础关键词外，国际规划规划研究领域的研究重点大概可以分为2类：一类是自动驾驶车辆轨迹的功能性研究，包括防碰撞研究、自主导航与轨迹跟踪等方面；另一类则是关注于轨迹本身的研究，包括最优控制方法、系统、算法、模型预测控制、车辆动力学与轨迹优化研究等方面。关键词中出现移动机器人是因为自动驾驶车辆可以认为是满足道路与环境约束条件的一种特殊移动机器人，这是因为2者不仅在环境信息感知识别、目标决策规划与动作指令控制这3个核心技术方面有很多相通之处，同样2者在操纵稳定性、舒适性与经济性等性能上有着类似的要求。
4.1.2 关键词聚类分析
聚类分析是一种探索性数据挖掘技术[3]，可以对特定领域中的专有术语或背景分类进行标识与探析，将所收集到的数据通过一定的算法转变为多个结构化集群，突出相关知识领域的主题分布与组织结构，从而直观地展现该领域研究的主题脉络。本文将通过简单介绍聚类标签所代表的各个子领域的演变过程和研究进展来展现轨迹规划领域的研究概况。
本文对2010—2022年之间轨迹规划领域中每年被引最多的50篇文献进行共被引分析，得到国际轨迹规划领域的聚类信息，如表5所示。表5总共展示了14个聚类，从研究规模上看，轨迹优化、自动驾驶车辆、自动驾驶、最优控制、模型预测控制等子领域的发文量较多；从剪影度来看，行为选择、模型预测控制、轨迹预测、自动驾驶、轨迹跟踪与自主导航等子领域的值要高于其他聚类标签；从活跃年份上看，早期研究多集中在自动驾驶车辆、非完整约束、目标跟踪与轨迹优化等子领域，2018—2019之间未有活跃的研究子领域，启发式算法、数据模型与协同控制是2020至今活跃的研究热点。综合聚类文献规模、活跃年份与剪影度等因素，笔者将视角聚焦于模型预测控制、自动驾驶、最优控制、自动驾驶车辆和轨迹优化等子领域的重点文献，从时间维度上分析轨迹规划各子领域研究的主题脉络。
（1）模型预测控制研究脉络分析
模型预测控制子领域包含124篇相关文献，该聚类下的主要节点为：‘模型预测控制’。从时间线来看，模型预测控制于2012年引入到轨迹规划领域中，之后与该子领域的所有关键词产生交集；除此之外，该标签下除模型预测控制之外不存在其他大的节点，因此模型预测控制是该聚类的决定性因素。模型预测控制可以理解为一种在有限时间范围内通过递归的方式求解的优化问题，同时能够在求解的过程中实时更新并且满足规划过程的所需环境约束。Berry等[4]将模型预测控制方法应用于轨迹规划框架以应对自动驾驶车辆运动过程中复杂多变的环境，通过将传统的模型预测控制问题的输出和控制元素分隔成不同的层，从而降低局部运动轨迹优化的复杂性，使求解速度更快，预测时域增加。Hoy等[5]综述了自动驾驶车辆在有障碍的未知环境的导航技术，尤其是基于模型预测控制与滑模控制方法的避免碰撞的导航技术。Nilsson等[6]提出一种换道算法，该算法能够确定适当的换道间隙与时间通过判断是否存在一个允许目标车辆能够安全执行换道的纵向轨迹。并实车验证了该算法生成安全、平稳轨迹的实时能力。除模型预测控制方法之外，动态窗口法与博弈论等理论方法也应用于该聚类研究领域。
（2）自动驾驶研究脉络分析
自动驾驶子领域包含230篇相关文献，从图中可以明显看出，该聚类主要由2个节点组成，分别为‘模型’（2013年出现）和‘自动驾驶’（2016年出现）。在模型节点中，各学者通过不同的模型实现满足各种约束条件的轨迹规划任务。Wei等[7]基于时空状态网格设计了一种动态编程模型以用于优化纵向轨迹，同时在Newell’s的简化汽车跟踪模型中引入随时间变化的车队反应时间的变量用以反映各种程度的V2X的通信连接。通过调整车队中头车的速度与车队反应时间，所提出的优化模型能够有效控制整个车队的轨迹实现多车轨迹的联合优化；Yang等[8]提出了一种包括变道起点确定模块、轨迹决策模块和轨迹生成模块的动态变道轨迹规划模型，即考虑车辆在实际运动过程中的状态时变化的轨迹规划模型，并通过仿真实验验证了该模型的有效性；Suh等[9]制定了一个满足组合预测（概率性和确定性）约束的随机模型来获得理想的转向角和纵向加速，实现自动驾驶车辆在复杂驾驶环境下的变道轨迹规划。并通过MATLAB/Simulink联合仿真验证了该算法可以在保证安全的同时处理复杂的变道情况。
在自动驾驶节点中，Chen等[10]介绍了轨迹规划在复杂环境下自动驾驶将要面临的挑战，提出了一种迭代线性二次调节器（Linaer Quadratic Regulator, ILQR）的改进方法：用受限地带二次调节器来解决非线性系统动力学和一般形式约束的最优控制问题，并通过仿真实例该方法的性能；Hubmann等[11]将这种不确定性因素表述为一个部分可观测的马尔科夫决策过程，将对未来预测准确性的估计变化融入到最优控制中，从而对其他车辆的交互式概率模型所产生的未来轨迹进行优化。同时他们从算法的收敛性、不同不确定因素的影响、复杂状况（无信号）交叉路口的在线模拟3个方面对所提出的方法进行验证；Kiran等[12]提出了一个自动驾驶任务的分类方法，并且总结了应用于自动驾驶领域的深度强化学习算法；Sheng等[13]设计了一个基于图的空间-时间卷积网络（Graph-Based Spatial-Temporal Convolutional Network, GSTCN），通过利用历史轨迹预测所有相邻车辆的未来轨迹分布，同时提出了一个加权邻接矩阵来描述车辆之间相互影响的强度，并从预测误差、模型大小和计算速度3个方面验证了该方案的性能；Lienke等[14]提出了一种用于面对复杂交通环境的环境表示方法，通过对周围交通车辆的轨迹预测和自车轨迹的规划实现对其他车辆未来运动的准确快速估计完成自动驾驶的预测性驾驶。
（3）最优控制研究脉络分析
最优控制子领域包含207篇相关文献，同样该聚类主要由2个节点组成，分别为‘防碰撞’（2010年出现）和‘最优控制’（2011年出现）。防碰撞是轨迹规划问题的基本要求，Chu等[15]提出了一种为具有静态避障功能的越野自动驾驶车辆实时规划路径的算法，该算法将由预定义的航点产生的候选轨迹转换为直角坐标系，并使用障碍物数据进行评估。通过考虑轨迹安全成本、曲率连续性和轨迹一致性确定一条最优轨迹；Chen等[16]对非信号交叉路口的合作方法（时间段和空间保留、轨迹规划和虚拟交通灯）进行探讨，并关注了处理不确定因素的车辆碰撞警告和避免方法和避免行人碰撞的方法；Guo等[17]提出了一种基于模型预测控制方法的同步轨迹规划方法和跟踪控制器来解决自动驾驶车辆的防碰撞问题，并在有无约束2种情况下进行veDYNA-Simulink联合仿真验证了其防碰撞性能；Zhang等[18]利用凸优化的强对偶性将不可微调的防撞约束条件重新表述为平滑的可微调的约束，使其适用于一般的障碍物和受控物体。并且将该方法与传统轨迹生成算法中的符号距离相联系应用于一般的导航与轨迹规划任务。
最优控制即建立精确的问题模型并寻找高效的求解方法，求解方法适用范围以及求解时间限制制约了模型的精度，一般而言模型精度越高则求解速率随之下降。近年来随着计算能力的进步与处理器的高速发展，最优控制方法由于对模型和约束条件的直观表达将得到快速发展。Wu等[19]通过建立车辆运动学模型，结合动态约束和终点及防撞约束将自主停车的轨迹规划问题被转化为一个最优控制问题，通过MATLAB/Simulink仿真验证该方法的有效性；Cichella[20]将最优运动规划问题表述为连续时间最优控制问题，并使用伯恩斯坦多项式在离散化环境中对其解决方案进行近似，通过这种方法使自动驾驶车辆在复杂环境和多车任务中实时生成安全运行的轨迹；Xu等[21]在曲线坐标系中建立质点车辆动力学模型，使用最优控制方法生成一个接近人类自然驾驶行为的轨迹，提升自动驾驶乘员的安全感与舒适性。
由表5可知，除上述3个聚类之外，聚类结果最明显的还有自动驾驶车辆与轨迹优化2个子领域，产生如此结果的原因是2聚类的主体即节点‘自动驾驶车辆’与‘轨迹优化’，这2个节点在轨迹规划领域的发文量与影响力巨大，并且自动驾驶车辆与轨迹优化是轨迹规划问题的必要关联，自动驾驶车辆是轨迹规划任务的载体，轨迹规划任务的实现离不开轨迹优化研究的发展，因此轨迹规划研究相关文献都会涉及这2个领域的研究，故而聚类效果明显。Badue等[22]调查了自DAPPA挑战赛起来开发的自动驾驶汽车，介绍了自动驾驶系统的典型架构，详细介绍了圣埃斯皮里图联邦大学开发的自动驾驶汽车IARA，并且回顾了关于自动驾驶汽车感知与决策2个领域的研究。
4.2 研究热点
关键词突现即某一关键词在不同的时间段内数量骤增、词频速率加大，是学界当下的热点话题，关键词突现的变化趋势反映了特定领域的研究动态以及发展趋势，关键词的突现度体现了该关键词的学术关注程度。本文通过对样本数据进行关键词突发性检测，展示轨迹规划研究的研究热点与知识演进状况，将提取的2010—2022年间突现关键词按时间发展进行排列（表6）。
从关键词突现结果来看，早期的研究热点有动态窗口法、移动机器人与路径生成，并且这3者的突现时间最长，研究人员对移动机器人的持续关注是因为自动驾驶系统的核心技术(环境感知、决策控制与执行控制)与移动机器人极大的关联参考性；从突现强度来看，环境约束、算法、道路安全与路径生成的突现强度最高，特别是环境，这是由于自动驾驶车辆不仅要在简单的结构化场景中安全运行，还要面对非结构环境、动态环境、无信号环境、恶劣天气环境等单个或混合复杂环境的考验，因此对驾驶环境的研究是实现自动驾驶的必要条件；突现强度其次的关键词为算法，自动驾驶系统的设计与运行离不开环境感知模块、规划决策模块和执行控制模块，这些模块的运行与求解离不开算法的执行，因此对算法结构、求解速度、泛化能力等的研究是众多学者的重要目标。
从表6可以看出，近些年轨迹规划研究的热点有道路安全、预测控制与机器学习3方面。从道路安全方面来看，自动驾驶在提高道路通行能力与降低交通事故方面等方面有很好的应用前景，但近些年频发的自动驾驶事故则说明当下的自动驾驶技术还有相当大的研究空间；就预测控制而言，通过对自动驾驶车辆的环境与周围车辆进行合理的预测(驾驶意图预测、驾驶行为预测、行人预测等)可以为车辆规划安全可行的满足舒适性、行驶效率的最优轨迹；将机器学习与轨迹规划相结合可以有效改善规划结果，提高对周围车辆未来轨迹和驾驶行为的预测精度，生成安全高效的可行轨迹，同时机器学习在自动驾驶的车道线检测、目标检测与目标跟踪有相当大的应用前景。
5 总结与展望
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本文以WOS核心合集中2010—2022年间的轨迹规划领域的期刊文献为样本，通过CiteSpace软件对样本数据进行图谱分析为读者展示轨迹规划研究的主题脉络与发展趋势。首先分别从发文量、国家与机构合作网络进行统计，对轨迹规划研究的概况做了简单介绍，同时列举了前10篇高被引文献。继而通过关键词的频次分析与聚类分析对轨迹规划研究的主题脉络做了简单介绍，并且通过关键词的突发性检测为读者展现轨迹规划研究热点的发展演进。通过对轨迹规划研究的热点演进分析，发现学界对轨迹规划的研究，由轨迹本身的生成与优化逐渐转变为单个因素的细化、深入研究，以及多种方法的融合创新，同时对轨迹的研究不仅局限于技术层面，同时也将环境变化、政策法规、行人等因素考虑在内。
随着自动驾驶逐步进入人们的日常出行，道路的车辆将是不同等级的自动驾驶车辆、人工驾驶车辆混合行驶的状况，同时车辆也将面对复杂多变的驾驶环境，这将为轨迹规划研究带来极大的挑战；就轨迹研究本身而言，目前通用的车辆模型并不能切实地反映车辆的运行状态，同时规划所采用算法的泛化能力还有待提高，以应对不同的驾驶工况。
本文借助CiteSpace的图谱分析功能对轨迹规划研究的主题脉络、研究热点演进进行了简单介绍，但该领域的研究是多学科专业融合的共同创新发展，受限于笔者的综合学术水平，本文并未对轨迹规划的主题内容和知识要点进行详尽分析。这将是后续研究需要提升进步的方向。
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doi: 10.19822/j.cnki.1671-6329.20220113
  • 首发时间：2025-12-30
  • 出版时间：2023-01-05
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    重庆交通大学机电与车辆工程学院， 重庆 400074
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