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This paper presents a technique for adaptively tracking bathymetric contours using an autonomous underwater vehicle (AUV) equipped with a single altimeter sonar. An adaptive feature mapping behavior is developed to address the problem of how to locate and track features of unknown extent in an environment where a priori information is unavailable. This behavior is implemented as part of the layered control architecture used by the AUV Odyssey II. The new adaptive feature mapping behavior builds on previous work in layered control by incorporating planning and mapping capabilities that allow the vehicle to alter its trajectory online in response to sensor data in order to track contour features. New waypoints are selected by evaluating the expected utility of visiting a given location balanced against the expected cost of traveling to a particular cell. The technique is developed assuming sensor input in the form of a single, narrow-beam altimeter sensor attached to a non-holonomic, dynamically controlled survey-class AUV such as the Odyssey II. Simulations of the Charles River basin which have been constructed from real bathymetry data are used as test missions. The 7-m contour line of a prominent trench in the river serves as the target feature. The adaptive contour following behavior tracks the contour despite navigation error and environmental disturbances, supplying the capability of autonomously detecting and following distinctive bathymetric features using a point sensor. This behavior provides a foundation for future research in tracking of dynamic features in the water-column and for concurrent mapping and localization over natural terrain using a point sensor.