The Boston University College of Engineering has an annual design competition.
This can be a fun and challenging project.
As in many robotics competitions, the size of the robot is limited in size. Usually the robot for this competition must be smaller than 12 inches in any of the three dimensions.
Materials are open for the project. some people use popsicle sticks, others use vex robotics kits, others use lego, others cut wood, metal or plastic. There are a lot of possiblitiies.
The electric circuit has some limits, but is pretty open to lots of solutions. Some robots in the past have been entirely mechanical.
This project is a great way to work with the design process. You come up with an idea that you think will work, build it, and bring it to the competition. Once at the competition, you will need to refine the design, fix repairs, and otherwise evolve your creation.
Follow the above link to emails about the competition
Information about the competition is here - http://www.bu.edu/eng/design/
Photos of past competitions are here - http://flickr.com/photos/connors934/sets/72157594155726509/
http://dhsrobotics.pbwiki.com/BuCompetition