I’m going to assume that your team chose the circular base for valid reasons, ones which overcome the multiple other reasons why a square or rectangular base would be significantly easier to construct; bumpers being one of many I can think of. Would you mind articulating some of your reasons?
If you’re absolutely set on the round base, I think it is more likely that your frame will be constructed as a decagon or other polyhedron. You will just need to cut plywood pieces to fit each side, with a matching angle, and put the pieces together with brackets (which you will probably need to manufacture or modify).
While I can’t comment on the merits of this specific team, a circular robot frame allows the maximum area inside the perimeter limits, which also allows the maximum area for a catcher.
Soaking the plywood in water overnight and then clamping it to a form and allowing it to dry would be a way to construct the curved plywood. Pool noodles and fabric are flexible, though attaching would still require some work (think attaching fabric on a round seat cushion)
Make your own plywood in the shape you need. Take enough strips of thin pliable plywood to build up sufficient thickness, spread glue around the interior sides and clamp them altogether around an appropriate form.
We tried a circular robot last season. It was a bit of a nightmare. We tried to bend circular aluminum tubing into a giant circle and welding it. Unfortunately after 4 circles, none of them matched! We left the design week 3 and switched to a hexagonal robot. Most of the volume and WAAAAY easier to build. We were considering the soaking plywood in water trick and then tried making a bunch of 2-3 inch wide slices on a table saw with a slight bevel to the edges so when put together it would have the correct arc to match the robot’s diameter. When glued together they were quite strong. They supported the weight of a person standing on them. That being said, I don’t know the effectiveness on the robot because we went away from that design. Good luck to you!
IMO with the 20" extension rule this year I don’t think there is much gained by building a round robot just to maximize the catcher. Just doing some quick math I got that a round robot could have up to 4492.6 inches sq to catch in, and a square robot would have 4280 inches sq. That 5% may make the difference but I doubt it. You’re losing 2 inches of reach in the corners and gaining 3.8 inches of reach on the edges if building round over square. Hopefully your 6 foot wide catcher will do just fine without those few inches.
The team that had a round robot in our area last season laminated their own bent plywood. I think they used 1/8" so it was easier to bend, more likely to hold its shape and was most like commercially available 3/4" plywood with is usually 5-7 ply. If you really want it replicate commercially available plywood and its strength don’t forget to alternate the direction of the grain.
I believe they did their bumpers as two semi circles to make it easier to build and handle.
You can bend 3/4" plywood by kerfing with a table saw. https://www.youtube.com/watch?v=9NAISW-icgc
Shim the robot frame with a few layers of duct tape for tolerance and cover the edge in waxed paper. Fill the kerfing with adhesive with structural strength, and clamp the kerfed bumper material to the frame to dry. Be sure to use furniture grade birch plywood.