Not an automatic roller winch, but we roll it up and place it on a cart that was designed for long folding tables. Our workspace isn’t big enough for even a quarter field so we have to move our stuff to the school commons area for drive practice. Field elements and all. (2018 was a p.i.t.a to move the scale between double doors every other day).
We have large diameter PVC pipes that the carpet sections wrap around and then you place them on the cart. Still super heavy but at least on the pipes you can roll it up easier and carry it without it sagging in the middle. If you wanted to motorize the system you could have a pipe with a split end to tuck the start of the carpet into like a C. As the weight of the carpet roll wraps tight it’ll clamp the inside end tightly. The outside ends of the pipe will have to have your sprocket for the input of the crank/winch. But then you have the shaft it gets rolled around handled.