路径约束条件下车辆行为的时空演化模型  

Spatiotemporal evolution model of vehicular movement behavior under path constraints

作　　者：潘登[1] 郑应平[1] 

机构地区：[1]同济大学电子与信息工程学院,上海201804

出　　处：《物理学报》2015年第7期408-413,共6页Acta Physica Sinica

基　　金：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.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.

关 键 词：车辆行为 时空演化 路径约束 Serret-Frenet活动标架 

分 类 号：U491[交通运输工程—交通运输规划与管理]