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We propose an approach for vision-based navigation of underwater robots that relies on the use of video mosaics of the sea bottom as environmental representations for navigation. We present a methodology for building high-quality video mosaics of the sea bottom in a fully automatic manner, which ensures global spatial coherency. During navigation, a set of efficient visual routines are used for the fast and accurate localization of the underwater vehicle with respect to the mosaic. These visual routines were developed taking into account the operating requirements of real-time position sensing, error bounding, and computational load. A visual servoing controller, based on the vehicle's kinematics, is used to drive the vehicle along a computed trajectory, specified in the mosaic, while maintaining constant altitude. The trajectory toward a goal point is generated online to avoid undefined areas in the mosaic. We have conducted a large set of sea trials, under realistic operating conditions. This paper demonstrates that without resorting to additional sensors, visual information can be used to create environment representations of the sea bottom (mosaics) and support long runs of navigation in a robust manner.