YA sci-fi about people being 'equalised' and turned into robots, young boy and friend try to escape

[Laura]

I read this book about 15 years ago, it may be a semi-famous sci-fi author. It's YA fiction, and I really can't remember much more than is in the subject line. A young boy, and possibly a friend and a friendly robot (maybe robots are trying to take over? - think like cybermen on Dr Who) are trying to get away. The boy may be hiding in a big cave underground?
The society's obsessed with equality, so people are reduced/handicapped more and more until they can all become equal - so if someone's "too strong", they'll have their arm chopped off etc. I think people ended up largely made of robots. Thanks so much for any help you can give.

[Kate]

Harrison Bergeron by Kurt Vonnegut has the part about equality and handicapping people. I don't recall the escape part of this description, but it has been a long time since I read it. It is a short story.

[Laura]

Thanks a lot :) I've had a quick skim, and it's definitely the right idea (and I do love Vonnegut, so it's likely I would have read it). I thought it was an actual full-length book I was after, but I'll re-read this and see. Thanks so much for your help!