In So You Think You Can Dance there is usually a camera movement I can't decipher how is made.
In this case the camera move right to left, and enter forward to the scenery. Time 0:42
My only guess is camera is floating with some kind of cable over a rail on ceiling.
At 8:41 the camera enters stage and circles around.
Here's my guess - a guy is holding the camera but the angle looks like is very high and moves very fast and smooth.
That effect usually also happen at the end of the show when all dancers are on stage. And either they edit the video, or the guy with the camera is very sneaky because I haven't see it yet.