The problem here is that "self solving" would necessitate that the cube be able to determine what is "wrong" with itself and ultimately figure out not only the "right" self-configuration, but how to get there. That may be a bit much to ask of a cube considering how hard it is for a human to do that.

Stranger still, it might turn out that the cube decides that it's fine the way it already is and it doesn't need to conform to a "right" configuration based on our expectations. In which case; perhaps we're already invented what you're looking for?