The grid pattern shelf liner works for me on a pretty plush carpet. Just a piece about 4" by 8". It may slowly creep but not bad at all. The grid shelf liner works so well for so many things. I use a 6" or so square of it to get a grip on jar lids; I put small pieces under microwave feet to keep it from inching backward every time I slam the door.
I have used it to make a gripper surface on the underside of a chair caddy (to hold magazines, remote and such) to name a few uses. You can buy it at the Dollar Store for very little.