"let's make a robot ___ creates a copy of itself"
What would be the right word to use here? That or which?
I think both are correct depending upon the context you are using them. If you have many robots and now, want to make one that creates a copy of itself, you use that because you are using a defining clause to distinguish this robot from the others.
You use which, when your clause is non-defining as in when you just intend to give a description of the robot.
A defining clause is one that adds something essential to your sentence and your clause definitely does that.
An alternate example: My bike that has a broken seat is in the garage and My bike, which has a broken seat, is in the garage are both correct but the first implies that you have many bikes in your garage.
As a standalone sentence, I think that is better because you are not producing robots in bulk.