3 very spoilt cats here and no problem with them trying to sleep on either baby. Whilst I found they like to sleep in cots, basinettes, prams etc it is only when they are empty. If they try to jump in with a baby there they jump straight out of their own accord. The only time they walk over the baby is when they are trying to get to me and I am there to stop them. They don't seem to fond of small crying humans