Spatiotemporal evolution model of vehicular movement Behavior under path constraints

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.