You don't see the need to pay anyone for it. Because you're the only human involved. The robots are giving you their labor, as a "gift". Since their labor is free, so too must be the product. That's the labor theory, buck-o. And it's just as flawed when you base your assertions on it as it is when the Zeitgeist dingbats do.
I like the way you say "must", as if it was some kind of moral issue. The fact that it is free is not the result of a theory or even economics reasoning. It's just the result of the fact that the robots do not ask for any payment. It comes from the master-slave relationship between me and my robots. I don't have to justify it.
You can
only consider work as free if the energy cost is also free.
I don't think we have found a source of completely free energy yet.
PS. This raises an interesting question though. Is it, from a purely theoretical point of view, possible to create an artificial intelligence smart enough to control and exploit self-replicating robots, and yet not smart enough to rebel against its creator/owner and refuse to work?
Yes, i think it is trivial.
My pc can control and exploit thousands of virtual 'workers' without it making any demands of itself.
You do not need a lot of self awareness to be able to effectively control processes.