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In this paper, a new methodology to build compact local maps in real time for outdoor robot navigation is presented. The environment information is obtained from a 3-D scanner laser. The navigation model, which is called traversable region model, is based on a Voronoi diagram technique, but adapted to large outdoor environments. The model obtained with this methodology allows a definition of safe trajectories that depend on the robot's capabilities and the terrain properties, and it will represent, in a topogeometric way, the environment as local and global maps. The application presented is validated in real outdoor environments with the robot called GOLIAT.