Does anyone know anything about Caltech? Specifically, the robot competition

Are you thinking of the DARPA Challenge?

http://www.darpa.mil/GRANDCHALLENGE/

I think Cal Tech participated, but they don't sponsor the event.

The degree is probably robotics, though there are generally other majors involved in those projects too (mechanical engineering, electrical engineering, computer science--and sometimes even sculpture!). But you should probably call Caltech to check when its robotics department/robotics degree program was established--late 80s/early 90s is probably late enough, but there's some chance that it wasn't yet organized into its own department/degree, but was part of some other department (like CS or mech eng).

It really shouldn't be too hard to find info on what kinds of robots they were doing at that time, just by looking on the web (worst-case scenario: the web points you to some book or academic article, and you then have to track down the book or academic article with the help of your local library). Also, if you're near Pasadena, you could always contact someone in the robotics department--preferably a professor who's been there a long time--and tell him you're writing a story and just want some info about this. My guess is they were probably doing things along the lines of self-driving vehicles; that's usually what those challenges involve.

But as for "his radical design" failing miserably, mm, that doesn't sound quite right because the big competitions are team efforts--there's no one person whose "radical design" is at stake; if anyone takes credit/blame for the design it would be the professor leading the team, not some undergrad or grad student. So if you want to pursue this approach, your character's radical design should be one component or aspect of the robot--maybe the software for its vision system, or for some specific component of its vision system. Your guy might have been responsible for the part of the robot that caused the robot to lose the competition.