[mrnoble]

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).