For the complete article check the link in the links section.
According to the mobile robot researchers and experts the best and smoothest transition curve to be used as a section of the path is the Eulers Spiral also known as Clothoid. During 19th century Arthur Talbot derived the equation of Clothoids to use as an easement curve for the purpose of avoiding the 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 will provide a linear change in the steering angle required by the driver to go through the turn. In other word for a car which is travelling on a Clothoid transition curve of the road there will be 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 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 studied here, and a design chart have been proposed to be used for finding the best suitable transition curve for different applications.