[s_forbes]

You're right that a robot, by itself, would accelerate the same regardless of it's mass. Using Newton's second law and the formula for frictional force we have two equations:

Ff = m * a
Ff = mu * N = mu * m * g

Setting them equal, we get:

m * a = mu * m * g ---> a = mu * g

The masses cancel, showing that the maximum acceleration of the robot depends just on mu and g (which are both the same for everyone)

The difference between driving with wheels and driving via fans is that the fans provide a pushing force that doesn't decrease with mass. So we just have Newtons second law:

F(fan) = m * a ---> a = F(fan) / m

In this case, acceleration does depend on mass. The lighter you make the robot, the faster it can accelerate.

(It's a little more complicated than this because of the added mass of the trailer, but using a fan still allows you to decrease your overall mass but keep the same pushing force)