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To navigate in unknown environments, mobile robots require the ability to build their own maps. A major problem for robot map building is that odometry-based dead reckoning cannot be used to assign accurate global position information to a map because of cumulative drift errors. This paper introduces a fast, on-line algorithm for learning geometrically consistent maps using only local metric information. The algorithm works by using a relaxation technique to minimize an energy function over many small steps. The approach differs from previous work in that it is computationally cheap, easy to implement and is proven to converge to a globally optimal solution. Experiments are presented in which large, complex environments were successfully mapped by a real robot.