If one holds the using electricity is NOT a form of burning (which some people do, even though using electricity heats things and the material used is eventally consumed), it might be considered possible to make a computerized electric car that wold be usable on Shabbos but for the issue of “Shavus”.
Of course, one can always convert to being “Reform”, which solves the problem.
Note that if you allow an autonomous car are Shabbos, you are probably allowing any use of computers or smartphones and even electric lights.
A mechanically powered car violated laws of physics, since you need to have energy from some source, so presumably the question is on a mechanical car powered by some form of energy.