An Optimal Path for an Autonomous Vehicle: A Nonparametric Approach

The objective of this study is to find the best trajectory for an autonomous vehicle which has to move from point A to point B in the minimum distance possible while avoiding all fixed obstacles between these points. Moreover, we assume that there is a safe distance r to be kept between the vehicle and the obstacles at all times. Also, the maneuverability of the vehicle is not easy, that is it cannot make abrupt turns and the trajectory has to follow a smooth curve. Obviously, if there are no obstacles, the best route is a straight line between A and B. In this work we propose a nonparametric method of finding the best path. If there is measurement error, a consistent stochastic estimator is proposed in the sense that as the number of observations increase the stochastic trajectory converges to the deterministic one.