This answer is posted in the full knowledge that your chances of success are slim to none. Still; it might be a very valuable learning experience for you.
You are working with a group of people who currently have no motivation to work. They lack both intrinsic motivation and extrinsic motivation. Since I doubt you want to be paying 30 people out of your own pocket, giving them extrinsic motivation is pretty much out (unless you can threaten to fail the, which I don't think you can). Then again; extrinsic motivation in a build-and-design challenge isn't very good anyway.
The real question is why they don't have intrinsic motivation. I'm assuming this course is related to their study; so these are engineering or IT students of some sort. Or at least people with an interest in such.
You would have to have a meeting with all of them, separately, and talk to them about why they aren't motivated to put in real effort. Ask what is keeping them from putting in good effort, and see if there's any way you can deal with that problem.
You'll probably get a set of diverse answers, and likely there's not much you can do about a lot of them, but you might be able to figure out some issues that are fairly easy resolve and get some more people in on the project.
Maybe they need some coaching because they don't understand the subject matter. Maybe they prefer working on a different part of the assignment. Maybe they just don't care about the specific competition. Maybe they just have too much stuff to do. Maybe they have personal issues. Maybe they just don't care about school. Who knows. You'll have to find out.
Engage in honest, open dialogue and listen to them. A group of people only becomes a team when the individual members all care about and are motivated to accomplish the same goal. That means a lot of listening. (Not talking. Listening.)
If you're really interested in making the most of your role as a leader (here, and later) then take some time to read up on intrinsic motivation and how to encourage it in people and consider this project a good practice session.