Environmental structures of interest like mountains, tunnels, and deposits of minerals, oil or gas produce distortions in the local gravitational field. Sensing gravity anomalies and comparing them to a gravity map can provide positioning immune to the drift of purely inertial navigation systems. Existing gradiometers with sufficient sensitivity are large and heavy, requiring manned aircraft and helicopters for their operation. This makes comprehensive high-resolution gravity mapping slow, risky in terrain-hugging (low and slow) flight, and expensive. We propose to develop an unmanned aerial vehicle with an integrated atom-optic gravity gradiometer. Such a system combines the unparalleled sensitivity of quantum sensors with the utility of an unmanned aerial platform. This sensor would eliminate risk to a flight crew, make surveying less conspicuous, and allow automated terrain-hugging flight. This, in turn, would enable measuring gravity with high spatial resolution, with high sensitivity, and at low cost.