I suspect they won't be protected. The phrasing is "the right to keep and bear arms", and there's a salient argument that because the robot is autonomous, it is the one bearing arms, not the human. Robots have no right to bear arms. A similar argument to the copyright office saying that AI generated stuff can't be copyrighted because the AI can't hold copyright.
Another interesting corollary is whether EMP/jamming devices will be considered arms under the 2nd amendment if autonomous robots become common on the battlefield.
When you say that robots have no rights, you imply that robots aren't people. And that's common sense today. But even today there's a non-trivial number of scientists who believe that we are just complex mechanism, and our consciousness is no more mysterious than dynamics of a sufficuently complex machine. If this idea of mechanical consciousness takes hold and spreads, in a few decades the supreme court will be considering a case, backed by solid scientific foundation, that "natural persons are fundamentally machines, and so machines created on american soil must be granted the same rights as natural persons."
Most people in US politics don’t hold that view though. As demonstrated by the frequent opposition to abortion.
So long as religion plays a fundamental part of political rallying, I can’t see enough people following the logic that AI deserves rights too.
To be honest, as someone who isn’t religious myself and who does believe our consciousness is mechanical, I’m also yet to be persuaded that AI is even remotely sophisticated enough for right. And I don’t think we will see AGI in my lifetime either.
I suspect with a disinterested Congress and an apolitical Supreme Court, wringing hands over interpretation of the intended meaning of words might be predictive of legal outcomes.
Another interesting corollary is whether EMP/jamming devices will be considered arms under the 2nd amendment if autonomous robots become common on the battlefield.