Cats remind of myself. Soft and cuddly when they are in the mood, and not as needy and sloppy and slurpy as dogs.
They are fastidiously clean and very self-sufficient, which is convenient.
I love all animals, but cats are purrr-fect (couldn't help that predictable little pun.)
Birds, like the sweet smart cockatiel variety that can whistle Yankee-Doodle with you, is nice too.
Perhaps there is no "perfect pet" for anyone, including Aspies, cause no two are alike.