Hi Nat,
Historically there are no royalties paid on these types of projects.
Mary Grandpre and Scott Hull were successful in leveraging a 1% royalty on the Harry Potter books after book 1. They didn't even ask on the first book even though there were quite a few spot illustrations in side. After the success of the 1st book they held out for a 1% royalty. It took many weeks of the publisher threatening to hire another illustrator but they held firm. You'll never get paid what you're worth or what you want until you're willing to walk away from a deal.
On a first book I wouldn't think anyone would have this kind of leverage because most publishers know that most books don't "earn out"...
The Harry Potter deal lead to other illustrators following the example but I would assume that most have been unsuccessful. Brett Helquist held out for a royalty on "The series of Unfortunate Events" books but was only successful in gaining a royalty after book 3. He also got a 1% royalty.