We watched the Grand Parade today. Very impressive! I'll post some pictures when I get home.
Some of the cast swooped and whirled as if they were on a motorised platform, and I'm guessing that they were indeed. So I thought about how I'd design such a thing.
A circular base, with four six-inch wheels driven independently by electric motors, controlled with a microprocessor. But that leaves the question of how do the witches control the motion?
My first thought was, someone else remote controls them. But that's not going to work with sudden changes of direction; the witch will fall off if she isn't expecting it. I can see both her hands, so she can't be using hand controls. Then I thought foot controls, but that won't work when she's making sharp turns. So I don't know.
Then I thought, she's waving a magic wand. There could be a couple of buttons in the base that control the motion via wires that run inside her sleeve.