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We present an approach for distributed real-time recognition tasks using a swarm of mobile robots. We focus on the visual recognition of hand gestures, but the solutions that we provide have general applicability and address a number of challenges common to many distributed sensing and classification problems. In our approach, robots acquire and process hand images from multiple points of view, most of which do not allow for a satisfactory classification. Each robot is equipped with a statistical classifier, which is used to generate an opinion for the sensed gesture. Using a low-bandwidth wireless channel, the robots locally exchange their opinions. They also exploit mobility to adapt their positions to maximize the mutual information collectively gathered by the swarm. A distributed consensus protocol is implemented, to allow to rapidly settle on a decision once enough evidence is available. The system is implemented and demonstrated on real robots. In addition, extensive quantitative results of emulation experiments, based on a real image dataset, are reported. We consider different scenarios and study the scalability and the robustness of the swarm performance for distributed recognition.