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Article(id=1200070652662215120, tenantId=1146029695717560320, journalId=1189918454225211397, issueId=1200070648174314131, articleNumber=null, orderNo=null, doi=10.20104/j.cnki.1674-6546.20240087, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=null, receivedDateStr=null, revisedDate=1713888000000, revisedDateStr=2024-04-24, acceptedDate=null, acceptedDateStr=null, onlineDate=1764048739829, onlineDateStr=2025-11-25, pubDate=1728921600000, pubDateStr=2024-10-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1764048739829, onlineIssueDateStr=2025-11-25, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1764048739829, creator=13701087609, updateTime=1764048739829, updator=13701087609, issue=Issue{id=1200070648174314131, tenantId=1146029695717560320, journalId=1189918454225211397, year='2024', volume='', issue='10', pageStart='1', pageEnd='48', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1764048738759, creator=13701087609, updateTime=1764049409565, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1200073461822488711, tenantId=1146029695717560320, journalId=1189918454225211397, issueId=1200070648174314131, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1200073461822488712, tenantId=1146029695717560320, journalId=1189918454225211397, issueId=1200070648174314131, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=31, endPage=36, ext={EN=ArticleExt(id=1200070652888707540, articleId=1200070652662215120, tenantId=1146029695717560320, journalId=1189918454225211397, language=EN, title=Research on Intelligent Vehicle Path Planning Based on Improved RRT-Connect Algorithm, columnId=null, journalTitle=Automotive Engineer, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In addressing the issues of suboptimal solutions and poor exploration performance in narrow passages of intelligent car path planning using the Rapidly-exploring Random Tree-Connect (RRT-Connect) algorithm, this paper improves the RRT-Connect algorithm in expansion strategy and path smoothing based on an analysis of the basic principle of the RRT-Connect algorithm. Firstly, in terms of expansion strategy, a probability bias method is introduced to screen random points, and an expansion method based on artificial potential fields is used to shorten paths and reduce computation time. Secondly, regarding path smoothing, a third-order B-spline curve is introduced to optimize the path and generate a smooth path, ensuring that the path meet the dynamic characteristics of intelligent cars. Finally, the superiority of the improved RRT-Connect algorithm is demonstrated through comparative simulation. The results show that in environments with simple obstacles, complex obstacles and narrow paths, the average time and path length of the improved RRT-Connect algorithm are superior to those of the traditional RRT-Connect algorithm.

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针对智能汽车路径规划中双向快速扩展随机树（RRT-Connect）算法获得的路径不是最优解和狭小通道探索性能较差的问题，在分析RRT-Connect算法基本原理的基础上，对其在扩展策略和路径平滑等方面进行了改进。首先，引入概率偏向法对选取的随机点进行筛选，并基于人工势场进行扩展，以缩短路径和计算时间，然后，引入三次B样条曲线对路径进行优化，生成光滑路径，保证路径满足智能汽车的动力学特性，最后，通过仿真验证改进RRT-Connect算法的性能，结果表明，在简单障碍物、复杂障碍物和狭窄路径环境下，改进的RRT-Connect算法的平均路径长度和平均耗时均优于传统RRT-Connect算法。

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算法 平均路径长度/mm 平均耗时/s
RRT-Connect 637.2 2.09
改进RRT-Connect 545.5 1.09
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简单障碍物环境下2种算法性能对比结果

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算法 平均路径长度/mm 平均耗时/s
RRT-Connect 637.2 2.09
改进RRT-Connect 545.5 1.09
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地图环境 算法 平均路径长度/mm 平均耗时
/s
多障碍物 RRT-Connect 1 892 7.90
改进RRT-Connect 1 616 3.14
狭窄路径 RRT-Connect 1 183 4.16
改进RRT-Connect 1 167 2.80
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复杂障碍物和狭窄路径环境下2种算法性能对比结果

, figureFileSmall=null, figureFileBig=null, tableContent=
地图环境 算法 平均路径长度/mm 平均耗时
/s
多障碍物 RRT-Connect 1 892 7.90
改进RRT-Connect 1 616 3.14
狭窄路径 RRT-Connect 1 183 4.16
改进RRT-Connect 1 167 2.80
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基于改进双向快速扩展随机树算法的智能汽车路径规划研究*
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张明月 1, 2 , 王军 1
汽车工程师 | 2024,(10): 31-36
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汽车工程师 | 2024, (10): 31-36
基于改进双向快速扩展随机树算法的智能汽车路径规划研究*
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张明月1, 2, 王军1
作者信息
  • 1 中国矿业大学， 徐州 221008
  • 2 青岛科技大学， 青岛 266061
Research on Intelligent Vehicle Path Planning Based on Improved RRT-Connect Algorithm
Mingyue Zhang1, 2, Jun Wang1
Affiliations
  • 1 China University of Mining and Technology, Xuzhou 221008
  • 2 Qingdao University of Science and Technology, Qingdao 266061
出版时间: 2024-10-15 doi: 10.20104/j.cnki.1674-6546.20240087
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摘要
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针对智能汽车路径规划中双向快速扩展随机树（RRT-Connect）算法获得的路径不是最优解和狭小通道探索性能较差的问题，在分析RRT-Connect算法基本原理的基础上，对其在扩展策略和路径平滑等方面进行了改进。首先，引入概率偏向法对选取的随机点进行筛选，并基于人工势场进行扩展，以缩短路径和计算时间，然后，引入三次B样条曲线对路径进行优化，生成光滑路径，保证路径满足智能汽车的动力学特性，最后，通过仿真验证改进RRT-Connect算法的性能，结果表明，在简单障碍物、复杂障碍物和狭窄路径环境下，改进的RRT-Connect算法的平均路径长度和平均耗时均优于传统RRT-Connect算法。

路径规划  /  快速扩展随机树  /  概率偏向法  /  人工势场

In addressing the issues of suboptimal solutions and poor exploration performance in narrow passages of intelligent car path planning using the Rapidly-exploring Random Tree-Connect (RRT-Connect) algorithm, this paper improves the RRT-Connect algorithm in expansion strategy and path smoothing based on an analysis of the basic principle of the RRT-Connect algorithm. Firstly, in terms of expansion strategy, a probability bias method is introduced to screen random points, and an expansion method based on artificial potential fields is used to shorten paths and reduce computation time. Secondly, regarding path smoothing, a third-order B-spline curve is introduced to optimize the path and generate a smooth path, ensuring that the path meet the dynamic characteristics of intelligent cars. Finally, the superiority of the improved RRT-Connect algorithm is demonstrated through comparative simulation. The results show that in environments with simple obstacles, complex obstacles and narrow paths, the average time and path length of the improved RRT-Connect algorithm are superior to those of the traditional RRT-Connect algorithm.

Path planning  /  Rapidly-exploring Random Tree (RRT)  /  Probability bias method  /  Artificial potential fields
张明月, 王军. 基于改进双向快速扩展随机树算法的智能汽车路径规划研究*. 汽车工程师, 2024 , (10) : 31 -36 . DOI: 10.20104/j.cnki.1674-6546.20240087
Mingyue Zhang, Jun Wang. Research on Intelligent Vehicle Path Planning Based on Improved RRT-Connect Algorithm[J]. Automotive Engineer, 2024 , (10) : 31 -36 . DOI: 10.20104/j.cnki.1674-6546.20240087
正文
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1 前言
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在不同场景下，智能汽车面临的环境各不相同。为了应对多样化的场景应用需求，避免发生碰撞，许多学者提出了不同的路径规划算法和相应的改进算法。目前，常见的路径规划方法主要有迪杰斯特拉（Dijkstra）算法[1]、A*算法[2]、遗传算法[3]、蚁群算法[4]、概率路线图法（Probabilistic Roadmap Method，PRM）[5]、快速扩展随机树（Rapidly-exploring Random Tree，RRT）算法[6]等。很多传统的路径规划算法存在运算时间过长、路径规划较为复杂等问题。
其中，RRT算法[6-7]由于采样逻辑简单、易于使用等原因，在机器人领域得到了广泛应用，但该算法存在规划路线过于复杂、路径过长等弊端。为解决RRT算法在狭窄路段效率不佳的问题，Kuffner提出了双向快速扩展随机树（Rapidly-exploring Random Tree-Connect，RRT-Connect）算法[8-9]，规划效率大幅提升。Karaman等提出了RRT*算法[10-11]，以解决RRT算法路径规划复杂和陷入局部最优的问题。Gammell等在RRT*算法基础上进行优化，提出了Informed-RRT*算法[12-13]，通过引入新的状态子集对算法本身的采样空间进行简化。
本文基于扩展策略和路径平滑等方法对RRT-Connect算法进行改进，引入概率偏向法筛选随机点，并基于人工势场进行扩展，采用三次B样条曲线优化并生成光滑路径，最后通过MATLAB仿真验证改进算法在不同环境下的具体表现。
2 改进RRT-Connect算法的构建
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2.1 基本RRT算法与RRT-Connect算法
RRT算法的主要思想是以路径规划的起点作为根节点，然后通过随机采样的方式增加叶节点，并不断生长成一个随机扩展树，随机树中某一个叶节点到达目标点附近区域时，将两点相连即可获得从起点位置到目标点位置的路径。传统RRT算法在延伸的过程中专注于局部最优，往往忽略整体最优，导致规划路线存在过于复杂和路径过长等弊端。
RRT-Connect采用了一种贪婪的双向扩展的随机树算法[14]，即在RRT算法随机生成采样点并向其延伸的基础上，使起始点Xinit和目标点Xgoal同时生长，并且在每次扩展的过程中，两棵树都尝试直接向对方父节点方向延伸。在扩展延伸过程中引入了启发算法，使随机树可以通过环境因素自动调节步长，提高双树搜索效率、缩短搜索时间和路径，RRT算法和RRT-Connect算法的路径优化仿真对比如图1所示。但由于RRT-Connect算法未能从根本上改进RRT随机取样带来的弊端，其在不同环境下的工作效率提升效果不够稳定。同时，算法扩展具有很强的随机性，使其在多障碍的复杂环境下难以找到合适的扩展方向。
2.2 基于概率偏向法的随机点筛选优化方法
本文引入概率偏向法对选取的随机点进行筛选。该算法在取点时加入随机数阈值[15]：当某次选取的随机数大于设定的随机数阈值时，则在地图中随机选取2个随机点Xrand，并对Xrand与目标点Xgoal之间的直线距离进行比较，取与目标点Xgoal距离近的点作为此次扩展所用的随机点Xrand；当选取的随机数小于设定的阈值时，则将此次选取的随机点Xrand更改为算法运行时的目标点Xgoal。通过阈值的设定引导RRT-Connect算法的扩展方向，加快算法的收敛速度，并对最终路径进行优化，以达到缩短路径长度的目的。
2.3 基于人工势场的扩展方式改进
利用人工势场法的思想[16]对新节点的扩展方式进行改进，即通过在环境中添加引力点对扩展点进行吸引，进而加速算法收敛。常用的扩展公式为：
${X}_{new}={X}_{near}+s\left(\frac{{X}_{rand}-{X}_{near}}{‖{X}_{rand}-{X}_{near}‖}\right)$
式中：Xnew为新节点，Xnear为最近点，s为扩展步长。
本文在此基础上加入目标点Xgoal对新节点Xnew的引力，公式调整为：
${X}_{new}={X}_{near}+s\left(\frac{{X}_{rand}-{X}_{near}}{‖{X}_{rand}-{X}_{near}‖}+k\frac{{X}_{goal}-{X}_{near}}{‖{X}_{goal}-{X}_{near}‖}\right)$
式中：k为引力系数，用于控制Xgoal对Xnew的引力。
若由最近点Xnear向新节点Xnew扩展过程中未触碰到障碍物，则正常扩展，否则通过减小k对障碍物进行规避。
2.4 基于三次B样条曲线的路径优化
RRT-Connect算法在得到有效的可行路径后，往往无法进一步优化，导致最终路径与最优路径仍存在差距。针对此问题，利用三次B样条曲线对最终路径进行平滑处理，以缩短路径长度。
B样条曲线可以保证曲线的每一段都是平滑的，且在有限阶内连续可导，保证了B样条基函数可以通过局部支撑达到全局支撑。三次B样条曲线函数Pi(t)为[17-18]：
$\begin{array}{l}{P}_{i}\left(t\right)=\sum _{j=0}^{3}{B}_{j,3}\left(t\right){C}_{i+j}\\ \begin{array}{cc}& \end{array}=\frac{1}{6}\left[\begin{array}{cccc}{t}^{3}& {t}^{2}& t& 1\end{array}\right]\left[\begin{array}{cccc}-1& 3& -3& 1\\ 3& -6& 3& 0\\ -3& 0& 3& 0\\ 1& 4& 1& 0\end{array}\right]\left[\begin{array}{c}{C}_{i}\\ {C}_{i+1}\\ {C}_{i+2}\\ {C}_{i+3}\end{array}\right]\end{array}$
式中：t∈[0,1]为参数，Ci+j为第i段曲线中的第j个控制点，Bj,3(t)为三次B样条曲线第j个控制点的基函数。
3 改进RRT-Connect算法仿真验证
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为了验证改进RRT-Connect算法在不同环境下的路径规划效果，本文在MATLAB中分别构建存在简单障碍物、复杂障碍物和仅有狭窄路径的环境地图，地图大小均为1 000 mm×1 000 mm，设置步长为20 mm、改进RRT-Connect算法的引力系数为1.3、概率阈值为0.2，进行路径规划仿真。
3.1 简单障碍物环境下的性能验证
本文设置的简单障碍物环境及RRT-Connect算法与改进RRT-Connect算法的路径规划仿真对比结果如图2所示。由图2可知，RRT-Connect和改进RRT-Connect算法的路径长度分别为567 mm和532 mm。由图2c可以看出，经过三次B样条处理后，生成的最终路径更优。同时，RRT-Connect和改进RRT-Connect算法的运行时间分别为1.300 s和0.747 s，改进RRT-Connect算法用时更短。
图3所示为多次仿真获得的算法路径长度和需要的运行时间，可以看出，改进RRT-Connect算法具有更好的路径稳定性。表1所示为改进RRT-Connect算法与RRT-Connect算法的性能对比结果，可以明显看出，改进RRT-Connect在所得路径长度和运行时间方面明显优于传统的RRT-Connect算法，效率更高。
3.2 复杂障碍物和狭窄路径环境下的性能验证
分别在多障碍物的复杂环境和狭窄路径环境下进行仿真分析，结果如图4、图5所示。并取20次仿真后的平均值作为路径长度和算法耗时的最终数据，如表2所示。由图4可知，多障碍物环境下，改进的RRT-Connect算法规划的路径更短、更平滑，由表2可知，其平均路径长度为1 616 mm，平均耗时3.14 s，优于RRT-Connect算法。
结合图5和表2数据，在狭窄路径环境下，使用改进RRT-Connect算法，平均路径长度为1 167 mm，平均耗时2.8 s，由图4和图5结合表2的数据对比，表明改进RRT-Connect算法有效缩短了路径长度和运行时间。
不同环境下的仿真结果表明，各环境下改进RRT-Connect算法生成的最终路径明显优于RRT-Connect算法，且改进RRT-Connect算法的平均耗时相差较小，即算法的路径规划效率受环境影响较小，更适合在复杂路况条件下应用。
4 结束语
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本文对RRT-Connect算法在扩展策略和路径平滑等方面进行改进，并利用MATLAB对改进算法和原算法在不同环境下的性能表现进行了对比分析，从生成路径的长度、路径规划耗时方面验证了改进算法的性能。结果表明，相较于RRT-Connect算法，改进算法生成的路径和平均耗时更短。
本文所做的工作未能覆盖智能汽车的真实运行环境，未来需进一步开展实际工况和多动态障碍物条件下的系统路径规划算法研究。
基金
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  • *山东省自然科学基金项目(ZR2021QF031)
  • 中国博士后科学基金项目(2023M743757)
文献
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2024年第卷第10期
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doi: 10.20104/j.cnki.1674-6546.20240087
  • 首发时间：2025-11-25
  • 出版时间：2024-10-15
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  • 修回日期：2024-04-24
基金
*山东省自然科学基金项目(ZR2021QF031)
中国博士后科学基金项目(2023M743757)
作者信息
    1 中国矿业大学， 徐州 221008
    2 青岛科技大学， 青岛 266061
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