Better Road Design for Autonomous Vehicles Using Clothoids

Abstract

During the project for generating a mathematical algorithm for autonomous vehicles, a sample road which included different turns and scenarios was required. Studying different types of roads and their line equations Euler spirals, also known as Clothoids were found to be the best solution for designing new roads suitable for autonomous vehicles. During 19th century Arthur Talbot derived the equation of Clothoids to be used as an easement curve for the purpose of avoiding shock and disagreeable lurch of trains, due to instant change of direction. The Euler Spiral is a curve whose degree-of-curve increases directly with the distance along the curve from the start point of the spiral. This provides a linear change in the steering angle required by the driver to go through the turn. In other words for a car traveling on a Clothoid transition road curve there is no need for sudden changes in the steering angle of the wheels. The angle required starts from zero and increases to a maximum value and goes back to zero linearly. This provides a very comfortable ride for the passengers of the vehicle. The use of these curves for road design have been investigated, and a design chart have been proposed to be used for finding the best suitable transition curve for different applications.