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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.
In complex geographic environment, the vehicle running track has the characteristics of three-dimensional space, and its constraint on vehicle behavior is obvious, which can be described in non-one-dimensional space and two-dimensional space.According to the abstract, Theory, the Serret-Frenet motion frame moving along the space curve is established by using geometric invariant parameters such as arc length, curvature and torsion. Then, the dynamic behavior of the Serret-Frenet frame with time-varying properties at any point on the space curve Mathematical description, and then establish the space-time evolution model of the vehicle behavior under the constraint of the path, and prove mathematically that the built space-time evolution model is suitable for the special case of the linear motion and the uniform circular motion of the vehicle (Serret-Frenet frame) Follow-up in a complex geographical environment on the traffic line vehicles following the car, lane change and other micro-behavior and macro-behavior of traffic flow, laid the theoretical foundation.