Voronoi diagram and fast marching applied to path planning

Abstract

Abstract-This paper presents a new Path Planning method which operates in two steps. In the first step the safest areas in the environment are extracted by means of a Voronoi diagram. In the second step Fast Marching Method is applied to the Voronoi extracted areas in order to obtain the shortest path. In this way the trajectory obtained is the shortest between the safe possible ones. This two step method combines speed and reliability, because the map dimensions is reduced to a unidimensional map and this map represents the safest areas in the environment for moving the robot.

Distributed Motion Planning for Ground Objects Using a Network of Robotic Ceiling Cameras

“…The potential field is computed using the wave front expansion with skeleton on a uniform cell partitioning of the 2D map of the environment. This solution first spreads the potential over a subset of the free space, called skeleton, which corresponds to the Voronoi diagram [3,5,12]; then, the potential is computed in the rest of the map. The potential descent from the start to the final configuration is performed using A * [6].…”

SLAM and Exploration using Differential Evolution and Fast Marching

“…This problem has been dealt with by Latombe (14), and the resulting navigation function is called NF2. The Voronoi Method also tries to follow a maximum clearance map (6). To generate a safe path, it is necessary to add a component that repels the robot away from obstacles.…”

“…On one hand, the trajectories tend to go close to the Voronoi skeleton because of the optimal conditions of this area for robot motion (6). An attractive potential used to plan a trajectory bring robots too close to obstacles as shown in fig.…”

General Path Planning Methodology for Leader-Follower Robot Formations

“…This problem has been addressed by Latombe [14], and the resulting navigation function is called . The Voronoi method also tries to follow a maximum clearance map [15]. To obtain a safe path, it is necessary to add a component that repels the robot from obstacles, as proposed by Khatib [16].…”