Our cat box is in the laundry room. Luckily the door to the room was hung poorly and the door tends to swing open. So we put a security chain, like the ones on hotel room doors, on the laundry room door. It holds the door open about 6 inches, which lets the cats in, but not the dogs.

Sorry, I'm not help about the automatic cat box. With 2 cats it didn't seem feasible for us.