Current models of antineutrino production in nuclear reactors predict detection rates and spectra at odds with the existing body of direct reactor antineutrino measurements. High-resolution antineutrino detectors operated close to compact research reactor cores can produce new precision measurements useful in testing explanations for these observed discrepancies involving underlying nuclear or new physics. Absolute measurement of the 235U-produced antineutrino spectrum can provide additional constraints for evaluating the accuracy of current and future reactor models, while relative measurements of spectral distortion between differing baselines can be used to search for oscillations arising from the existence of eV-scale sterile neutrinos. Such a measurement can be performed in the United States at several highly-enriched uranium fueled research reactors using near-surface segmented liquid scintillator detectors. We describe here the conceptual design and physics potential of the PROSPECT experiment, a U.S.-based, multi-phase experiment with reactor-detector baselines of 7-20 meters capable of addressing these and other physics and detector development goals. Current R&D status and future plans for PROSPECT detector deployment and data-taking at the High Flux Isotope Reactor at Oak Ridge National Laboratory will be discussed.