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This paper addresses the problem of real-time moving-object detection, classification and tracking in populated and dynamic environments. In this scenario, a mobile robot uses 2D laser range data to recognize, track and avoid moving targets. Most previous approaches either rely on pre-defined data features or off-line training of a classifier for specific data sets, thus eliminating the possibility to detect and track different-shaped moving objects. We propose a novel and adaptive technique where potential moving objects are classified and learned in real-time using a Fuzzy ART neural network algorithm. Experimental results indicate that our method can effectively distinguish and track moving targets in cluttered indoor environments, while at the same time learning their shape.