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This paper describes an on-line algorithm for multi-robot simultaneous localization and mapping (SLAM). The starting point is the single-robot Rao-Blackwellized particle filter described by Hähnel et al., and three key generalizations are made. First, the particle filter is extended to handle multi-robot SLAM problems in which the initial pose of the robots is known (such as occurs when all robots start from the same location). Second, an approximation is introduced to solve the more general problem in which the initial pose of robots is not known a priori (such as occurs when the robots start from widely separated locations). In this latter case, it is assumed that pairs of robots will eventually encounter one another, thereby determining their relative pose. This relative attitude is used to initialize the filter, and subsequent observations from both robots are combined into a common map. Third and finally, a method is introduced to integrate observations collected prior to the first robot encounter, using the notion of a virtual robot travelling backwards in time. This novel approach allows one to integrate all data from all robots into a single common map.