[DonRotolo]

Basic 4 wheel drive is not the worst choice this year. If your team is comfortable with doing that, you will likely be more successful than trying an unknown design and having an epic fail.

Will a suspension help? I can't say, I have never tried it. Old Ford Model T cars - the first mass-produced cars - did not have much of a suspension, because it had to travel over very poor roads (modern cars could not possibly travel on early 20th century roads), and because suspensions cost money.

You should consider: what will the effects of a big jolt to the robot be? If there will be bad effects, then will they be solved with a suspension? Lastly, what kind of suspension exactly? Have a very specific, well-thought-out and buildable design in hand to show them, along with answers to those 3 questions, because if you don't, then don't expect anyone to consider your idea seriously.

Good luck.