This is PatH in disguise. I'm visiting JoanK while she recovers from minor surgery, and using her computer. I hadn't heard of Bernard Beckett either. He's a New Zealander. I wish I could remember who recommended the book.
I, Robot is a series of loosely connected short stories which sort of make an overall tale. I read it eons ago, and don't remember much, but Frybabe's story seems familiar. The movie is apparantly nothing like the book. Looking it up, I noticed that in addition to Will Smith it has Alan Tudyk, who played Wash in the Firefly/Serenity series.
Asimov wrote some detective stories involving collaboration between a robot and a human, which also explore this theme. In the first one, Caves of Steel, we watch the human, Elijah Baley, overcoming his horror or working with the robot, R. Daneel Olivaw, and the two becoming friends. I've read the nextwo, The Naked Sun and Robots of Dawn, but not a followup, Robots and Empire, which takes place long after Baley's death. They're good detective stories with the sci-fi important, but not dominant.