The mathematical theory for autonomous vehicles, which was initially developed for 4 Wheel steering vehicles was formulated to work for 2 wheel steering vehicles as well. This was the first step towards making the theory closer to practice. Then a sample road using clothoids as the transition curve was generated. Clothoid was used as the best transition curve according to the literature for mobile robots trajectory generation. This study ended up in development of a design chart which could be used for better road design. The sample road is used to find the kinematic steering angles required by the vehicle to stay on the road. The kinematic steering angles work well only at very low forward velocities. The dynamic differential equations of motion of the vehicle needed to be solved to make the study of motion of the vehicle possible in higher velocities. During high forward velocity travelling some factors will cause the vehicle to move on a road different to the desired path of motion. The sample road generated proved that the traditional method of solving differential equations of motion was not very effective especially in the case of complicated mathematical paths of motion. That is why a new method was sought for, which resulted in the generation of the Steady-State Dynamic Steering method. This method provides an alternative way of studying the dynamics of motion of a vehicle, which is proved to be much faster and less complicated than the traditional method. At the end the new method was, put in to test by trying different vehicle travelling manoeuvres. After validation of the new method it was used mathematically to take control of a car to travel a sample desired path of motion autonomously by using the mathematical theory of autonomous vehicles.
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