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Efficient mapping of unknown environments is a fundamental function for mobile robot intelligence. To do so requires good exploration strategies and solving the simultaneous localization and mapping problem. The approach presented in this paper is an integration of our solutions into the problems of exploration and map building with a single robot. The exploration algorithm is based on the Voronoi fast marching (VFM) method to determine a motion plan toward the most unexplored and free zones of the environment. One consistent global map of the workspace is created using the simultaneous localization and modeling (SLAM) algorithm based on a nonlinear evolutive filter called the evolutive localization filter. The combination of the extended Voronoi transform and the fast marching method in the VFM method provides potential maps for robot navigation in previously unexplored dynamic environments. The logarithm of the extended Voronoi transform imitates the repulsive electric potential from walls and obstacles. The method uses a fast marching technique to determine a motion plan. A new strategy such that the robot determines the zones that it must explore in an autonomous way is described. As the robot carries out the exploration, it constructs a consistent map of the environment using the SLAM algorithm.