A Comparative Study of Smoothing a Vehicle s Trajectory which is Calculated by an Evolutionary Algorithm

Abstract

Determining a vehicle’s trajectory is a complex and hard to solve type problem in the literature and it is identified as a NP-Hard optimization problem which is studied in different engineering disciplines such as computer, electrical and industrial engineering. It has been observed that such complex problems can be solved by using various approaches and lots of them are focused on the usage of Evolutionary Algorithms especially in case of a large number of controls points which are needed to be visited. Although these algorithms provide near optimal solutions, in the real world, vehicles are not able to follow this determined path (trajectory) without any deviation. Because vehicles are moving objects and each one moves with a certain speed. Therefore it is impossible for a vehicle to make a sharp turn after visiting control points. These vehicles need to make smoothed turns over these points. Therefore there will be a certain difference between the calculated path and the real path. It is needed to determine the real path by using necessary mathematical solutions for smoothing these paths. To ensure the motion continuity of vehicles, they need to follow paths determined according to a certain criterion. In this study, the most common smoothing methods which are used to ensure these continuities (Bezier, B-Spline and Dubins) have been compared and it is aimed to show the different approaches in an application area of path planning problems as a comparative study.