You say you can construct such robot, but in fact, you can't. That's because if you could, then it would cause a paradox with a predictor. So you can't (though it may be fun watching you try).
My point exactly - the existence of the Predictor proves more than lack of free will. It's lack of free will, so we are automatons that respond to stimuli in a deterministic way, sure.
But there are also some strong restrictions on the set of reactions that are allowed, for example none of them can lead to a functioning counter-predictor robot.
Don't mess with time travel.