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We address two key goals pertaining to autonomous mobile robots: one, to develop fast accurate sensory capabilities - at present, the localization of sound sources - and second, the integration of such sensory modules with other robot functions, especially its motor control and navigation. A primary motivation for this work was to devise effective means to guide robotic navigation in environments with acoustic sources. We designed and built a biomimetic sound-source localization apparatus. In contrast to the popular use of time-of-arrival differences in free field microphone arrays, our system is based on the principles observed in nature, where directional acoustic sensing evolved to rely on diffraction about the head with only two ears. In this paper we present an integrated robot phonotaxis system which utilizes the robot's movement to resolve frontback localization ambiguity. Our system achieves high angular localization acuity (± 2°) and it was successfully tested in localizing a single broadband source and moving towards it within a cluttered laboratory environment.