A self-cleaning coop is simply one that does not collect guano. (If it doesn't pile up, you don't have to shovel it!)
Think of it as a floorless box. The guano goes straight to the ground, and has no other place to collect.
In my case, I have six hens, so my chicken-tractor coop is a barn-shaped box 36" X 36" X 19" at the peak.
That allows exactly 1 square foot of roost space for each hen. I have two roosts that run across the box just above the bottom edge, so everyone has a place to perch.
There is a chicken ladder that rises between the roosts so the hens can get in and out easily.
The roosts also lead directly into the two nest boxes, so the hens can go in & out easily there, too.
I think it's been 2 1/2 years since I built my Hen Haven Chicken Tractor. In that time I have not had to clean it at all. Ditto for the nests, which are also designed for low maintenance.
With the nests, I occasionally have to add a little grass, and sometimes have to remove a broken egg (three, to date), but they never get pooped in, and the eggs never get pecked. That's really just a matter of making them the right size & shape.
I'm a pretty good designer. (Brag-brag!)
The coop is floorless, but it can be closed at night if necessary by sliding floor panels. They accumulate some droppings overnight, but they are self-cleaning when opened, so they don't make any extra work. I'm in Florida, so I almost never have to close the coop.
The coop, BTW, sits on a 6' X 6' X 24" high run, giving the six hens more than the usual amount of roaming space, and the whole thing just trundles around like a wheelbarrow when I move it. The weight distribution worked out just right. The ground does all the heavy lifting.
My coop design can be adapted to other chicken tractors, of course.