The tricky part is going to get the "twist" out of the rope as it comes in. Winding on a spool will lead to rotations about the long axis of the rope, one for each loop. That leads to the rope being figure-eighted if held loose and it leads to a kinked rope that eventually cannot be straighted out. Our water ski show has some long, long term waterskiers that have been doing skiing for over 60+ years and when I first started with them I was blown away by what ski rope winding zealots they were. Seriously, they would spend a long, long time teaching adults and the kids how to wind ropes. Every time one was found with the slightest loop or kink they would the kid or adult straighten it out by rewinding the rope. I have to say that after doing this now for several years I can roll a rope properly with the flick of a wrist twist, and I can see just how perfect the rope lays afterwords. The ropes should end up would without one single rotation in the rope. I just put all our ropes away in storage. If they were still out I would take a photo to show what a good coiled rope should be.
A good example to practice on is a flat extension cord. If that can be rolled so that one side always faces in (or out) when coiled then you have it right. A perfect rolled rope should have no figure eights and every loop should be consistent and have no lumps at the bottom or side.
Good luck with the project. I've worked with college engineers on projects many times and it is always interesting to see the things they think of to solve problems.