Model of passing a turn by a vehicle

The car turning model is considered, in particular at an X-shaped intersection with an arbitrary intersection angle of the tracks. The conditions and restrictions that are imposed when the car enters a turn are analyzed. It is shown that, when the car moves from straight to curved sections, angular accelerations acting relative to its vertical axis have a significant influence on the redistribution of the forces of interaction between the wheels and the road surface and, accordingly, on the stability and controllability of the car. The analysis of motion trajectories, which consist of conjugate rectilinear and curvilinear sections and are described by the equations of a circle, a parabola, and a hyperbolic cosine, is provided. It is shown that choosing a trajectory according to the law of parabola and hyperbolic cosine slightly reduces the turning radius of the car, but significantly reduces the curvature gradient in the conjugation zone and, accordingly, reduces angular accelerations and increases the resistance of the car to rotation relative to the vertical axis. For a smooth transition from a straight path to a curved one, a special logistic dependency was used to connect (stitch) different sections of the route. This made it possible to describe the trajectory of the car by a smooth function, the first and second derivatives of which are also smooth functions. For the selection of the trajectory of passing turns with a slight curvature of the route, a dependence in the form of a fourth-degree polynomial, the curvature of which at the point of conjugation is equal to zero, is proposed, which ensures a smooth transition from a straight to a curved section and ensures passing a turn with minimal dynamic loads. The developed model allows you to design the trajectory of turning for various types of intersections in real time and can be used to build dynamic models of car movement along given trajectories, as well as to build simulators for unmanned vehicles.