It is important to note that a ROBOT is ONLY acting by the control of a specific person, and whomever that specific person allows to utilize that control.
If a robot SEEMS to act on his own, it is merely that he was programmed to do that by the person in control. I would likely put the analogy a different way, but really will not argue with the point that we, as unregenerate sinners, are controlled by another. That would TYPICALLY be Satan, the god of this world, and the father of the unrighteous.
We, as unregenerate sinners, are PROGRAMMED via the fallen nature to do the will of that "father," and the will of our own ego that is so easily manipulated by that "father."
John 8
44 Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.
II Timothy 2
26 And that they may recover themselves out of the snare of the devil, who are taken captive by him at his will.
This is why I would not argue against the point of the unregenerate being robots of Satan. Too much has been stated by the Apostles that make it a valid analogy. Taking the whole idea apart, we would find certain flaws in this, as with any human thinking on spiritual matters. It is a good way to see this, and anyone wishing to have true freedom and liberty must first gain freedom from that slavery.
Romans 6
16 Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness?
Romans 6
20 For when ye were the servants of sin, ye were free from righteousness.
21 What fruit had ye then in those things whereof ye are now ashamed? for the end of those things is death.
A slave is a better comparison, but the robot has a specific meaning that could be applicable to the discussion.