Libraries, manufacturing lines, and offices of the future all stand to benefit from knowing the exact spatial order of RFID-tagged books, components, and folders, respectively. To this end, radio-based localization has demonstrated the potential for high accuracy. Key enabling ideas include motion-based synthetic aperture radar, multipath detection, and the use of different frequencies (channels). But indoors in real-world situations, current systems often fall short of the mark, mainly because of the prevalence and strength of multipath reflections of the radio signal off nearby objects. In this paper we describe the design and implementation of MobiTagbot, an autonomous wheeled robot reader that conducts a roving survey of the above such areas to achieve an exact spatial order of RFID-tagged objects in very close (1--6 cm) spacings. Our approach leverages a serendipitous correlation between the changes in multipath reflections that occur with motion and the effect of changing the carrier frequency (channel) of the RFID query. By carefully observing the relationship between channel and phase, MobiTagbot detects if multipath is likely prevalent at a given robot reader location. If so, MobiTagbot excludes phase readings from that reader location, and generates a final location estimate using phase readings from other locations as the robot reader moves in space. Experimentally, we demonstrate that cutting-edge localization algorithms including Tagoram are not accurate enough to exactly order items in very close proximity, but MobiTagbot is, achieving nearly 100% ordering accuracy for items at low (3--6 cm) spacings and 86% accuracy for items at very low (1--3 cm) spacings.