Isaac Asimov has pretty well covered the artistic possibilities of human relations to robots, although mostly in short stories. His robot stories are predicated upon the "three laws of robotics," which were limits imposed before anthropomorphic robots could enter society.
1. A robot may not injure a human being or, through inaction, allow a human being to come to harm.
2. A robot must obey the orders given to it by human beings, except where such orders would conflict with the First Law.
3. A robot must protect its own existence as long as such protection does not conflict with the First or Second Laws.
According to this Wikipedia article on the three laws
, they were first articulated in a 1942 short story. I recommend I, Robot
(a collection of short stories) as a starting point for Asimov's highly intelligent, well-thought-out fiction about robots.