OK, I think I've got the ParkerCam figured out. Here's the current arrangement:
And here's what the ParkerCam sees:
It's impossible to keep up with him sometimes, so very often you'll just see an empty rug. Or, after Parker has done some redecorating, a scrunched-up rug:
Now we're going for a walk, so I can get lunch before Whole Foods turns into a zoo.