Log of the inverse of the Distance Transform and Fast Marching applied to Path Planning

This paper presents a new path planning method based in the inverse of the logarithm of the distance transform and in the fast marching method. The distance transform of an image gives a grey scale that is darker near the obstacles and walls and more clear far from them and it is calculated via Voronoi diagram. The logarithm of the inverse of the distance transform imitates the repulsive electric potential from walls and obstacles. This method is very fast and reliable and the trajectories are similar to the human trajectories: smooth and not very close to obstacles and walls