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Sensor-based localization is one of the fundamental problems in mobile robots. We present a technique for online robot localization in an a priori known indoor environment. Our approach uses the local Voronoi diagram, generated from a laser range scan, to match it against the global Voronoi diagram of the robot's workspace. The result from this process is used to estimate the robot's position in the map or to correct the robot's odometry. Experiments with real data are presented to validate this algorithm.