Caption: Plot of the Earth's axial tilt (AKA obliquity) versus time for 8,000 BCE--12,000 CE (based on J. Laskar, 1986, A&A, 157, 59 "Secular Terms of Classical Planetary Theories Using the Results of General Relativity").
The displayed time variation is the long-term axial tilt oscillation .
Features:
Quarternary glaciation as alternating relatively long glacial periods and relatively short interglacials of ∼ 10,000---20,000 years typically that occur in recent time at about 100,000 year intervals.????
The causes of the Quarternary glaciation have NOT been fully explained (see Wikipedia: Quarternary glaciation: Causes). However, the Milankovich cycles are probably NOT a main cause in themselves. They are the main drivers of the alternation of glacial periods and interglacials.
The main cause may be the gradual decline in the atmospheric carbon dioxide (CO_2) abundance over the geological time scale---the volcanic outgassing of CO_2 has been slowly losing to the locking up of CO_2 in calcium carbonate (CaCO_3) rock. The long-term decrease in CO_2 decreases the greenhouse effect in atmosphere.
The anthropogenic greenhouse gas emission is a relatively short-term modern process that causes global warming on a relatively short time scale.
We do NOT know when the next glacial period will start. Global warming and other anthropogenic effects may well affect the next start date.
One hypothesis suggests 50,000 years from now, but much smaller and larger times have been hypothesized (see Wikipedia: Quarternary glaciation: Next glacial period).