||Asteroid astrometry has had a rich history, is enjoying a vibrant present, and promises an outstanding future. I'll give some examples of applications of asteroid astrometry drawn from a variety of astronomical endeavors.
Asteroid astrometry underlies orbit and ephemeris computation. Studies of orbits and their distribution have in the past been used to determine the astronomical unit, the equator and equinox, planetary masses, delineate asteroid families, and enable long-term dynamical studies of the solar system. At present, a number of near-Earth asteroid (NEA) search programs are providing large numbers of asteroid positions, mostly of relatively poor astrometric accuracy, though sufficient that close to 100,000 asteroids have been numbered. Work is flourishing on asteroid shapes from occultation studies, and asteroid mass determination from asteroid-asteroid encounter perturbations. Over the last decade and more, Doppler/delay radar observations, mostly of NEAs, have complemented optical astrometry, and have recently enabled an elegant investigation of the Yarkovsky effect.
Large all-sky survey telescopes, such as Pan-STARRS, DCT, and, eventually, LSST, will accelerate the rate of asteroid observation by two orders of magnitude. Within the next decade, good orbits should be secured for 10,000 Kuiper Belt Objects (KBOs), several million main-belt asteroids, and tens of thousands of NEAs. Most of the groundbased telescopic observations will be accurate to about 30 mas. That accuracy will be surpassed by three orders of magnitude when the astrometric satellite GAIA is realized. GAIA's astrometric and photometric data will enable new fields of asteroid study: multi-parameter modeling of asteroids' shapes, light-scattering properties, and rotation; detection and orbital characterization of binary asteroids; greatly improved determinations of asteroid masses, sizes, and densities; and a means of testing general relativity. I speculate that classical methods of orbit computation will become obsolete and will be replaced by the equivalence between astrometric observations and orbital-element probability density.