Under certain assumptions described below, a kinematic model for the lateral motion of a vehicle can be developed. Such a model provides a mathematical description of the vehicle motion without considering the forces that affect the motion. The equations of motion are based purely on geometric relationships governing the system.
Consider a bicycle model of the vehicle as shown in Figure 2-3 (Wang and Qi, 2001). In the bicycle model, the two left and right front wheels are represented by one single wheel at point A. Similarly the rear wheels are represented by one central rear wheel at point B. The steering angles for the front and rear wheels are represented by Jf and 4 respectively. The model is derived assuming both front and rear wheels can be steered. For front-wheel-only steering, the rear steering angle 6,. can be set to zero. The center of gravity (c.g.) of the vehicle is at point C. The distances of points A and B from the c.g. of the vehicle are l and C, respectively. The wheelbase of the vehicle is L = C + C ,