Perhaps my favorite experience in robotics at Princeton was participating in the Brown University IEEE Robotics Olympiad in 2013 and 2014. Entering this competition for the first time as a freshman with some of my fellow classmates has forged strong friendships and served as inspiration for us to found the Princeton Robotics Club.
The premise of the contest was to construct a small robot that would autonomously navigate its way through a 16 x 16 cell maze as quickly as possible, all on a $500 budget. Detailed competition rules can be found here: Brown IEEE Robotics Olympiad. This provided great experience in fabrication, control, and heuristics.
Some technical specs of our 3rd place 2014 entry: