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We present an on-board robotic module which can determine relative positions among miniature robots. The module uses high-frequency modulated infrared emissions to enable nearby robots to determine the range, bearing, and message of the sender with a rapid update rate. A CSMA protocol is employed for scalable operation. We describe a technique for calculating the range and bearing between robots, which can be generalized for use with more sophisticated relative positioning systems. Using this method, we characterize the accuracy of positioning between robots and identify different sources of imprecision. Finally, the utility of this module is clearly demonstrated with several robotic formation experiments, where precise multi-robot formations are maintained throughout difficult maneuvers.