13732 Woodall was discovered in 1998 by LINEAR, a collaboration project of the United States Air Force, NASA, and the MIT's Lincoln Laboratory for the systematic detection and tracking of near-Earth objects.
It was discovered on 14 September 1998, by the Lincoln Near-Earth Asteroid Research (LINEAR) team at Lincoln Laboratory's Experimental Test Site in Socorro, New Mexico. The Lincoln Near-Earth Asteroid Research (LINEAR) project is a collaboration of the United States Air Force, NASA, and the MIT's Lincoln Laboratory for the systematic detection and tracking of near-Earth objects. 
