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路径约束条件下车辆行为的时空演化模型

潘登 郑应平

路径约束条件下车辆行为的时空演化模型

潘登, 郑应平
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  • 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.
    • 基金项目: 国家自然科学基金(批准号: 61174183)资助的课题.
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    Koutsopoulos H N, Farah H 2012 Transp. Res. Part. B 46 563

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    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]

  • 引用本文:
    Citation:
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  • 文章访问数:  1978
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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

路径约束条件下车辆行为的时空演化模型

  • 1. 同济大学电子与信息工程学院, 上海 201804
    基金项目: 

    国家自然科学基金(批准号: 61174183)资助的课题.

摘要: 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.

English Abstract

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