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This paper presents the application of the Voronoi Fast Marching (V FM) method to the Control of Robot Formations. The V FM method uses the propagation of a wave (Fast Marching) operating on the world model to de- termine a motion plan over a viscosity map (similar to the refraction index in optics) extracted from the updated map model. The computational effciency 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 classiffed as a type of potential field, but it has no local minima, it is complete (it finds the solu- tion 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.
robot formation motion planning; formation control; fast marching