Vehicle Kinematics and Its Application to Highway Design

Abstract

This paper presents a mathematical model for computing the path of any one point on a wheeled vehicle, which may be a bus, an articulated truck, or a wheeled robot, and the steering angle necessary for a reference point to travel a specified curve. This problem arises in applications that require determination of the swept space of a vehicle and in the automatic control of a mobile robot while the reference point on the vehicle moves along a specified path. The mathematical model is applicable to any dimension of a rigid vehicle or vehicle combination. It can be shown that the widely used Western Highway Institute (WHI) formula for highway design is a special case of the mathematical model presented in this paper. Based on this model, some inherent characteristics of wheeled vehicles, such as curvature, radius of instantaneous rotation of a point on the vehicle, and their relationship; and the independence of vehicle's orientation angle, steering angle, curvature, and radius of instantaneous rotation to its velocity, are also analyzed. The analytic solutions of two typical motions, circular and straight-line motions, have been developed, and the comparison of the simulation results with the existing standards has been conducted.