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This paper presents the application to nonholonomic mobile robot path planning of our Voronoi fast marching (VFM) and FM2 methods, which represents our current progress on the design and analysis of these algorithms. The VFM and FM2 methods use the propagation of a wave (fast marching) operating on the world model, to determine a motion plan over a slowness map (similar to the refraction index in Optics) extracted from the updated map model. The computational efficiency of the method let the planner operate at high rate sensor frequencies. This method allow us to simplify the mobile robot or mobile manipulator architecture, while maintaining good response time and smooth and safe planned trajectories. This method can be classified inside the navigation functions (a type of potential fields) and it is complete (it finds the solution path if it exists) and of order n complexity (O(n)). The results presented in the paper show how the proposed method is faster than other existing path planning methods for non-holonomic (car like for example) mobile robots and generates trajectories of better quality .