We had the following two ideas:
For those who are interested in the Mechanical Aspects of the project, we have several Lego Mindstorm Kits, and we also have several Laptops to program them with. Several small groups can create robots for specific tasks and compete.
However, Lego Mindstorms does not allow us to learn about electronics and more advanced programming.
For those who are interested in Electronics and Programming, we can do projects based on Arduino Microcontroller boards. A board like the one shown on the right is only $30.
The first thing that we can make is the interesting device described on this page.