The long-term (geological time scale) record of glacial and inter-glacial periods is driven by changes in the amount of solar radiation received at the top of the atmosphere (insolation), which in turn are related to the variations in the Earth's orbit around the sun. The orbit is elliptical rather than circular, and this difference is measured by the eccentricity of the orbit. Since it is possible to predict future eccentricity, it is also possible to estimate the onset of future ice ages.
A modifying influence to insolation as the driver of climate cycles is the level of atmospheric carbon dioxide. Berger and Loutre (2002) simulate future ice age onset with different levels of atmospheric CO2 (values from the last interglacial, a low but constant value of 210 ppm, and a human-induced concentration of 750 ppm returning to natural levels in 1000 years). The "Anthropocene" scenario leads to disappearance of the Greenland and West Antarctic ice sheets, which will take 50,000 years to return to natural glacial/inter-glacial cycles.
Reference
Berger, A. and M. F. Loutre, 2002: An exceptionally long interglacial ahead? Science, 297, 1287-1288.