路径约束条件下车辆行为的时空演化模型

潘登; 郑应平

doi:10.7498/aps.64.078902

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.

关键词:

Abstract

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.

Keywords:

作者及机构信息

潘登,
郑应平

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.

Authors and contacts

1.
School of Electronic & Information Engineering, Tongji University, Shanghai 201804, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61174183).

参考文献

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施引文献

[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 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 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 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]

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