搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

路径约束条件下车辆行为的时空演化模型

潘登 郑应平

引用本文:
Citation:

路径约束条件下车辆行为的时空演化模型

潘登, 郑应平

Spatiotemporal evolution model of vehicular movement Behavior under path constraints

Pan Deng, Zheng Ying-Ping
PDF
导出引用
  • 复杂地理环境下车辆运行线路具有空间三维特征, 它对车辆行为的约束是显然的, 非一维空间和二维空间所能描述. 将复杂地理环境下车辆运行线路抽象为空间曲线, 引入微分几何理论, 利用弧长、曲率和挠率等几何不变量参数建立沿空间曲线运动的Serret-Frenet活动标架; 然后, 对空间曲线上任意一点处Serret-Frenet标架具有时变属性的动态行为进行数学描述, 进而建立路径约束条件下车辆行为的时空演化模型, 并在数学上严格证明了所建时空演化模型适用于车辆(Serret-Frenet标架)直线运行和做匀速圆周运动的特殊情形. 为后续复杂地理环境中交通线路上的车辆跟驰、变道等微观行为和交通流宏观行为研究, 奠定了理论基础.
    The path of vehicle movement in a complex geographical environment has the 3D space feature, which is evidently the constraint for vehicular movement behaviors and cannot be described in one-dimensional or two-dimensional space. But the path of vehicle movement in a complex geographical environment can be abstracted into a space curve. By introducing theories in differential geometry, we can build a Serret-Frenet frame moving along this space curve with the geometric invariants of arc length, curvature, and torsion. And then, we can give a mathematical description to the dynamic behavior of the Serret-Frenet frame with the time-varying property at an arbitrary point of space curve. Finally, the spatiotemporal evolution model of the vehicle movement behaviors under the path constraint conditions is established and is rigidly proven in mathematics to be suitable for the longitudinal movement and uniform circular motion of a vehicle (in Serret-Frenet frame). It will lay the theoretical foundation for the future study of vehicular movement behaviors on the transport line in a complex geographical environment, including vehicular microscopic behaviors such as the vehicle following operation, lane changing, as well as the vehicular macroscopic behavior in traffic flows.
    • 基金项目: 国家自然科学基金(批准号: 61174183)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61174183).
    [1]

    Tomer E, Safonov L, Havlin S 2000 Phys. Rev. Lett. 84 382

    [2]

    Koutsopoulos H N, Farah H 2012 Transp. Res. Part. B 46 563

    [3]

    Naito Y, Nagatani T 2011 Phys. Lett. A 375 1319

    [4]

    Naito Y, Nagatani T 2012 Physica A 391 1626

    [5]

    Zheng Z D 2014 Transp. Res. Part B 60 16

    [6]

    Lee H Y, Lee H W, Kim D 1998 Phys. Rev. Lett. 81 1130

    [7]

    Mitarai N, Nakanishi H 2000 Phys. Rev. Lett. 85 1766

    [8]

    Peng G H, Sun D H, He H P 2009 Chin. Phys. B 18 468

    [9]

    Zheng L, Ma S F, Zhong S Q 2011 Chin. Phys. B 20 088701

    [10]

    Peng G H, Cai X H, Liu C Q 2011 Phys. Lett. A 375 3973

    [11]

    Sugiyama N, Nagatani T 2012 Phys. Lett. A 376 1803

    [12]

    Tang T Q, Wang Y P, Yang X B, Wu Y H 2012 Nonlinear Dynam. 70 1397

    [13]

    Jetto K, Ez-Zahraouy H, Benyoussef A 2012 Chin. Phys. B 21 118901

    [14]

    Gupta A K, Sharma S 2012 Chin. Phys. B 21 015201

    [15]

    Kamal M A S, Imura J, Hayakawa T, Ohata A, Aihara K 2014 IEEE Trans. Intell. Transp. Syst. 15 878

    [16]

    Ploeg J, Shukla D P, van de Wouw N, Nijmeijer H 2014 IEEE Trans. Intell. Transp. Syst. 15 854

    [17]

    Davis L C 2014 Physica A 405 128

    [18]

    Laval J A, Leclercq L 2013 Transp. Res. Part B 52 17

    [19]

    Ren D B, Zhang J Y, Zhang J M, Cui S M 2011 Sci. China Ser. E 54 630

    [20]

    Zhang L D, Jia L, Zhu W X 2012 Acta Phys. Sin. 61 074501 (in Chinese) [张立东, 贾磊, 朱文兴 2012 物理学报 61 074501]

    [21]

    Guo L, Huang X H, Ge P S 2013 Journal of Jilin University (Engineering and Technology Edition) 43 323 (in Chinese) [郭烈, 黄晓慧, 葛平淑2013 吉林大学学报 (工学版) 43 323]

    [22]

    Ren D B, Zhang J M, Wang C 2014 Acta Phys. Sin. 63 078902 (in Chinese) [任殿波, 张京明, 王聪 2014 物理学报 63 078902]

    [23]

    He Z C, Sun W B, Zhang L C, Xu F F, Zhuang L J 2013 Acta Phys. Sin. 62 168901 (in Chinese) [何兆成, 孙文博, 张力成, 许菲菲, 庄立坚 2013 物理学报 62 168901]

    [24]

    Saffarian M, de Winter J C F, Happee R 2013 IEEE Trans. Human-Mach. Syst. 43 8

    [25]

    Wang J Q, Zhang L, Zhang D Z, Li K Q 2013 IEEE Trans. Intell. Transp. Syst. 14 1

    [26]

    Borhaug E, Pavlov A, Pettersen K Y 2008 Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, Dec. 9-11, 2008 p4984

    [27]

    Ghommam J, Mnif F, Benali A 2009 J. Dyn. Syst.-T. Asme. 131 021006

    [28]

    Sasongko R A, Sembiring J, Muhammad H, Mulyanto T 2011 Proceedings of the 8th Asian Control Conference, Kaohsiung, Taiwan, May 15-18, 2011 p1259

    [29]

    Moe S, Caharija W, Pettersen K Y, Schjolberg I 2014 American Control Conference, Portland, Oregon, USA, June 4-6, 2014 p3856

    [30]

    Burger M, Pettersen K Y 2010 The 49th IEEE Conference on Decision and Control, Atlanta, GA, USA, December 15-17, 2010 p7159

    [31]

    Aggoune W, Morarescu I C, Niculescu S I 2011 Mathematical Reports 13 217

    [32]

    Ali Z, Popov A A, Charles G 2013 Vehicle Syst. Dyn. 51 943

    [33]

    Kim Y C, Yun K H, Min K D 2014 Vehicle Syst. Dyn. 52 456

    [34]

    Pan D, Zheng Y 2014 IET Intell. Trans. SY. 8 232

    [35]

    Xiao L Y, Gao F 2010 Vehicle Syst. Dyn. 48 1167

    [36]

    Davis L C 2012 Phys. Lett. A 376 2658

    [37]

    Lee M H, Park H G, Lee, S H, Yoon K S, Lee K S 2013 Int. J. Precis. Eng. Man. 14 373

    [38]

    Bifulco G N, Pariota L, Simonelli F, Di Pace R 2013 Transp. Res. Part C 29 156

    [39]

    Wang M, Daamen W, Hoogendoorn S, van Arem B 2014 IET Intell. Trans. SY. 8 77

    [40]

    Chen W H 2006 Differential Geometry (Beijing: Peking University Press) pp23-32 (in Chinese) [陈维桓2006微分几何(北京: 北京大学出版社)第23–32页]

    [41]

    Su B Q, Hua Y J, Xin Y L 2010 Introduction to Practical Differential Geometry (Beijing: Science Press) pp10-27 (in Chinese) [苏步青, 华宣积, 忻元龙2010实用微分几何引论(北京: 科学出版社)第10–27页]

  • [1]

    Tomer E, Safonov L, Havlin S 2000 Phys. Rev. Lett. 84 382

    [2]

    Koutsopoulos H N, Farah H 2012 Transp. Res. Part. B 46 563

    [3]

    Naito Y, Nagatani T 2011 Phys. Lett. A 375 1319

    [4]

    Naito Y, Nagatani T 2012 Physica A 391 1626

    [5]

    Zheng Z D 2014 Transp. Res. Part B 60 16

    [6]

    Lee H Y, Lee H W, Kim D 1998 Phys. Rev. Lett. 81 1130

    [7]

    Mitarai N, Nakanishi H 2000 Phys. Rev. Lett. 85 1766

    [8]

    Peng G H, Sun D H, He H P 2009 Chin. Phys. B 18 468

    [9]

    Zheng L, Ma S F, Zhong S Q 2011 Chin. Phys. B 20 088701

    [10]

    Peng G H, Cai X H, Liu C Q 2011 Phys. Lett. A 375 3973

    [11]

    Sugiyama N, Nagatani T 2012 Phys. Lett. A 376 1803

    [12]

    Tang T Q, Wang Y P, Yang X B, Wu Y H 2012 Nonlinear Dynam. 70 1397

    [13]

    Jetto K, Ez-Zahraouy H, Benyoussef A 2012 Chin. Phys. B 21 118901

    [14]

    Gupta A K, Sharma S 2012 Chin. Phys. B 21 015201

    [15]

    Kamal M A S, Imura J, Hayakawa T, Ohata A, Aihara K 2014 IEEE Trans. Intell. Transp. Syst. 15 878

    [16]

    Ploeg J, Shukla D P, van de Wouw N, Nijmeijer H 2014 IEEE Trans. Intell. Transp. Syst. 15 854

    [17]

    Davis L C 2014 Physica A 405 128

    [18]

    Laval J A, Leclercq L 2013 Transp. Res. Part B 52 17

    [19]

    Ren D B, Zhang J Y, Zhang J M, Cui S M 2011 Sci. China Ser. E 54 630

    [20]

    Zhang L D, Jia L, Zhu W X 2012 Acta Phys. Sin. 61 074501 (in Chinese) [张立东, 贾磊, 朱文兴 2012 物理学报 61 074501]

    [21]

    Guo L, Huang X H, Ge P S 2013 Journal of Jilin University (Engineering and Technology Edition) 43 323 (in Chinese) [郭烈, 黄晓慧, 葛平淑2013 吉林大学学报 (工学版) 43 323]

    [22]

    Ren D B, Zhang J M, Wang C 2014 Acta Phys. Sin. 63 078902 (in Chinese) [任殿波, 张京明, 王聪 2014 物理学报 63 078902]

    [23]

    He Z C, Sun W B, Zhang L C, Xu F F, Zhuang L J 2013 Acta Phys. Sin. 62 168901 (in Chinese) [何兆成, 孙文博, 张力成, 许菲菲, 庄立坚 2013 物理学报 62 168901]

    [24]

    Saffarian M, de Winter J C F, Happee R 2013 IEEE Trans. Human-Mach. Syst. 43 8

    [25]

    Wang J Q, Zhang L, Zhang D Z, Li K Q 2013 IEEE Trans. Intell. Transp. Syst. 14 1

    [26]

    Borhaug E, Pavlov A, Pettersen K Y 2008 Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, Dec. 9-11, 2008 p4984

    [27]

    Ghommam J, Mnif F, Benali A 2009 J. Dyn. Syst.-T. Asme. 131 021006

    [28]

    Sasongko R A, Sembiring J, Muhammad H, Mulyanto T 2011 Proceedings of the 8th Asian Control Conference, Kaohsiung, Taiwan, May 15-18, 2011 p1259

    [29]

    Moe S, Caharija W, Pettersen K Y, Schjolberg I 2014 American Control Conference, Portland, Oregon, USA, June 4-6, 2014 p3856

    [30]

    Burger M, Pettersen K Y 2010 The 49th IEEE Conference on Decision and Control, Atlanta, GA, USA, December 15-17, 2010 p7159

    [31]

    Aggoune W, Morarescu I C, Niculescu S I 2011 Mathematical Reports 13 217

    [32]

    Ali Z, Popov A A, Charles G 2013 Vehicle Syst. Dyn. 51 943

    [33]

    Kim Y C, Yun K H, Min K D 2014 Vehicle Syst. Dyn. 52 456

    [34]

    Pan D, Zheng Y 2014 IET Intell. Trans. SY. 8 232

    [35]

    Xiao L Y, Gao F 2010 Vehicle Syst. Dyn. 48 1167

    [36]

    Davis L C 2012 Phys. Lett. A 376 2658

    [37]

    Lee M H, Park H G, Lee, S H, Yoon K S, Lee K S 2013 Int. J. Precis. Eng. Man. 14 373

    [38]

    Bifulco G N, Pariota L, Simonelli F, Di Pace R 2013 Transp. Res. Part C 29 156

    [39]

    Wang M, Daamen W, Hoogendoorn S, van Arem B 2014 IET Intell. Trans. SY. 8 77

    [40]

    Chen W H 2006 Differential Geometry (Beijing: Peking University Press) pp23-32 (in Chinese) [陈维桓2006微分几何(北京: 北京大学出版社)第23–32页]

    [41]

    Su B Q, Hua Y J, Xin Y L 2010 Introduction to Practical Differential Geometry (Beijing: Science Press) pp10-27 (in Chinese) [苏步青, 华宣积, 忻元龙2010实用微分几何引论(北京: 科学出版社)第10–27页]

  • [1] 戴碧涛, 谭索怡, 陈洒然, 蔡梦思, 秦烁, 吕欣. 基于手机大数据的中国人口迁徙模式及疫情影响研究. 物理学报, 2021, 70(6): 068903. doi: 10.7498/aps.70.20202084
    [2] 吕鑫. 相干与路径信息. 物理学报, 2020, 69(7): 070301. doi: 10.7498/aps.69.20191084
    [3] 万海容, 郝艳捧, 房强, 苏恒炜, 阳林, 李立浧. 大气压氦气介质阻挡放电单-多柱演化动力学. 物理学报, 2020, 69(14): 145203. doi: 10.7498/aps.69.20200473
    [4] 李丞, 高勋, 刘潞, 林景全. 磁场约束下激光诱导等离子体光谱强度演化研究. 物理学报, 2014, 63(14): 145203. doi: 10.7498/aps.63.145203
    [5] 董宇蔚, 蔡世民, 尚明生. 电子商务中人类活动的标度行为实证研究. 物理学报, 2013, 62(2): 028901. doi: 10.7498/aps.62.028901
    [6] 王荣, 吴莹, 刘少宝. 随机中毒对神经元网络时空动力学行为的影响. 物理学报, 2013, 62(22): 220504. doi: 10.7498/aps.62.220504
    [7] 何兆成, 孙文博, 张力成, 许菲菲, 庄立坚. 瓶颈处车辆横纵向行为建模与分析. 物理学报, 2013, 62(16): 168901. doi: 10.7498/aps.62.168901
    [8] 李文慧, 忽满利, 马志博, 种兰祥, 万云. LiNbO3晶体中屏蔽光伏孤子自偏转的时空演化与可控因素. 物理学报, 2012, 61(2): 020201. doi: 10.7498/aps.61.020201
    [9] 邹建龙, 沈瑶, 马西奎. 终端含NMOS反相器传输线系统中的时空复杂行为分析. 物理学报, 2012, 61(17): 170514. doi: 10.7498/aps.61.170514
    [10] 严雄伟, 於海武, 曹丁象, 李明中, 郑建刚, 蒋东镔, 蒋新颖, 段文涛, 王明哲. 重频Yb:YAG片状激光器电光调Q时空演化模拟计算和实验研究. 物理学报, 2009, 58(8): 5798-5804. doi: 10.7498/aps.58.5798
    [11] 邓敏艺, 施 娟, 李华兵, 孔令江, 刘慕仁. 用晶格玻尔兹曼方法研究螺旋波的产生机制和演化行为. 物理学报, 2007, 56(4): 2012-2017. doi: 10.7498/aps.56.2012
    [12] 杨吉军, 徐可为. 生长初期Ta膜的表面动态演化行为. 物理学报, 2007, 56(10): 6023-6027. doi: 10.7498/aps.56.6023
    [13] 余晓敏, 梁国栋, 钟艳花. 极化激元系统时间演化的量子涨落特性和非经典统计行为. 物理学报, 2006, 55(5): 2128-2137. doi: 10.7498/aps.55.2128
    [14] 张 林, 孔红艳, 杨国健. 约束阱中受激发原子的集体反弹效应所导致的自组织行为. 物理学报, 2006, 55(10): 5122-5128. doi: 10.7498/aps.55.5122
    [15] 郑春阳, 刘占军, 李纪伟, 张爱清, 裴文兵. 无碰撞等离子体中电子束流不稳定性的时空演化研究. 物理学报, 2005, 54(5): 2138-2146. doi: 10.7498/aps.54.2138
    [16] 张远涛, 王德真, 王艳辉. 大气压介质阻挡丝状放电时空演化数值模拟. 物理学报, 2005, 54(10): 4808-4815. doi: 10.7498/aps.54.4808
    [17] 刘成森, 王德真. 空心圆管端点附近等离子体源离子注入过程中鞘层的时空演化. 物理学报, 2003, 52(1): 109-114. doi: 10.7498/aps.52.109
    [18] 薛郁, 董力耘, 袁以武, 戴世强. 考虑车辆相对运动速度的交通流演化过程的数值模拟. 物理学报, 2002, 51(3): 492-496. doi: 10.7498/aps.51.492
    [19] 贺智勇, 靳根明, 李祖玉, 段利敏, 戴光曦, 吴和宇, 张保国, 文万信, 漆玉金, 罗清政, 王宏伟, 王素芳. 25MeV/u40Ar+197Au反应中高激发热核的时空演化. 物理学报, 1998, 47(6): 916-921. doi: 10.7498/aps.47.916
    [20] 丁祥茂, 王延申, 侯伯宇. 活动标架系下以O(3)非线性σ模型Lax-pair矩阵的Poisson-Lie结构. 物理学报, 1994, 43(1): 1-6. doi: 10.7498/aps.43.1
计量
  • 文章访问数:  4820
  • PDF下载量:  309
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-08-28
  • 修回日期:  2014-11-06
  • 刊出日期:  2015-04-05

/

返回文章
返回