As in OTL but his two eldest sons die and the next sons are born as girls instead.
If he dies as OTL and still has his first two sons, and they have their children as OTL, then Richard II accedes to the throne as in OTL. Through his mother, Joan, he's also part of the next closest branch of Plantagenets (the Kents). Assuming that girl-John of Gaunt doesn't have an alt-Henry IV (with a weaker claim to the throne), Richard II isn't usurped. That said, it's possible he doesn't have any children - he didn't have any OTL, so maybe he was infertile, so that would have caused problems on his death.