Build a maze runner, to get outside it has to find blue doors and test those routes, avoiding the red doors. So the thing has to move, turn, sense colour, and build a picture of the tested routes. Starts in the centre, exits at the outside, green walls. This would involve other departments as well, so team work essential (physics - sense colours/differentiate, engineering/physics for the machine, comp guys for programming test and store routine).
The comp guys could build a and test in a virtual maze, which would simulate the inputs and commands for the physical machine/maze. It'd be fun and actually is as much robotics. Just an idea