Abstract-This paper presents a new sensor based global Path Planner 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 an extremely fast global planner operating on a simple sensor based environment modeling, while it operates at the sensor frequency. The main characteristics are speed and reliability, because the map dimensions are reduced to a unidimensional map and this map represents the safest areas in the environment for moving the robot.

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This paper presents a novel algorithm to solve the robot formation path planning problem working under uncertainty conditions such as errors the in robot's positions, errors when sensing obstacles or walls, etc. The proposed approach provides a solution based on a leaderfollowers architecture (real or virtual leaders) with a prescribed formation geometry that adapts dynamically to the environment. The algorithm described herein is able to provide safe, collision-free paths, avoiding obstacles and deforming the geometry of the formation when required by environmental conditions (e.g. narrow passages). To obtain a better approach to the problem of robot formation path planning the algorithm proposed includes uncertainties in obstacles' and robots' positions. The algorithm applies the Fast Marching Square (FM 2 ) method to the path planning of mobile robot formations, which has been proved to work quickly and efficiently. The FM 2 method is a path planning method with no local minima that provides smooth and safe trajectories to the robots creating a time function based on the properties of the propagation of the electromagnetic waves and depending on the environment conditions. This method allows to easily include the uncertainty reducing the computational cost significantly. The results presented here show that the proposed algorithm allows the formation to react to both static and dynamic obstacles with an easily changeable behavior.

This paper presents the application of the Voronoi Fast Marching (V F M ) method to the Control of Robot Formations. The V F M method uses the propagation of a wave (Fast Marching) operating on the world model to determine a motion plan over a viscosity map (similar to the refraction index in optics) extracted from the updated map model. The computational efficiency of the method allows the planner to operate at high rate sensor frequencies. This method allows us to maintain good response time and smooth and safe planned trajectories. The navigation function can be classified as a type of potential field, but it has no local minima, it is complete (it finds the solution path if it exists) and it has a complexity of order n (O(n)), where n is the number of cells in the environment map. The results presented in this paper show how the proposed method behaves with mobile robot formations and generates trajectories of good quality without problems of local minima when the formation encounters non-convex obstacles.

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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.