On the Path Curvature of Vehicles

In recent years, there has been much discussion concerning the development of control enhancement methods for vehicles. Furthermore, path planning for robotic and autonomous vehicles has received significant attention. In each of these areas, vehicles can easily arrive in configurations involving large sideslip angles due to high inertial loads, etc. In such instances, it is essential that the relationship between vehicle accelerations and path curvature is well understood. This paper applies basic kinematics to relate the accelerations of the vehicle body centered coordinate system to the path curvature. In doing so, we hope to illustrate the necessity to accurately consider vehicle kinematics in such applications as path planning for autonomous vehicles.