Our head mentor is also in charge of the school Robobots battle bot program. Him and I we playing around, and actually picked the ball up and drove around the room with it.
I guess you could just fit that with the FRC control system, put bumpers on it and submit it as your final robot. Make it powerful enough to get under another robot, pick it up, and use the other robot as a ram for the ball 
Even better would be to make a ball-balancing robot to drive the ball into the goal. THe only problem is that the robot will go with the ball
