I can see large planetary motions being fairly predictable, mostly because the masses involved are large and there is a lot of data to anchor the models.
But it would be nearly impossible to predict the long-term motions of an object in the asteroid belt.
Small objects do not have much influence, but are themselves influenced by large objects. There are several highly developed and detailed models of the solar system. The smaller a body is, the more predictable its trajectory because uncertainty in its mass has little effect on massive bodies.