Odyssey - Michael P Kube-McDowell

A man without memory is stranded in a world-enveloping city filled with robots gone wild. At his side is a mysterious young woman who claims to know who he is but refuses to tell him. According to The
Three Laws of Robotics, 'a robot may not injure a human being' which narrows the suspects dramatically when the robots find a dead human body.
The man calls himself Derec; the woman is known as Katherine. Their real identities, along with that of the murder victim and the murderer, are just a few of the life-and-death mysteries the unlikely pair are forced to solve to survive on the fantastic streets of Isaac Asimov's Robot City.