I'm not sure if it's still worth to answer your question, since you may have finished the essay, but in any case, for the discussion itself, well, AI probably will have rights.

I think there are 3 points of comparison that makes the topic clearer.

1st: the rights of animals.

There are a bunch of rules that are basically about preservation of life. Some places may go further, some may not, but still this is the point in consideration. In my country if someone poisons or runs over an animal, if it is discovered, you have to at least pay something (and in running over, you get bad points in your driving license).

2nd: the rights of the owner, also just like pets.

One thing is to own something in nature; another one is on society. Owning on society means you need to have rights to guarantee that if it is taken from your, or if there's such a risk, you have the possibility to get back or avoid the problem. So rights to avoid breaking, stealing and so on.

3rd: patents and copywrights.

Specially if you're considering only the software, not the robot itself, this is pretty much the thing. As a software, it's like any other. So there will have the rights of protecting from being hacked, copied, modified without your permission and so on. We don't have a right about modifying the DNA of your pet, because it makes no sense more than "you have to steal the cat first", and that's illegal. But you can modify the "DNA of the software" without touching it directly. So there certainly will have eventually laws for this type of protection.

I hope it helps.