RoboKing is a robot made in Katamari Forever by the Prince and all of the cousins as a replacement for the King, who had struck his head on a dark star, lost his memory and entered a deep slumber. Unfortunately, upon activation RoboKing goes on a rampage and destroys every star in the sky, setting in motion the events of Katamari Forever. Unlike the King of All Cosmos, RoboKing feels sorry for destroying the stars, even though he doesn't help The Prince with the task of rolling Katamaris. He is shown to be more sincere and less strict than the King, and seems to be prone to bouts of depression and anxiety, usually caused by the task of remaking all the stars in the sky. When ignoring RoboKing he is often saddened, unlike the King, who acts stuck up and aloof, and is often ignorant to others.
After the King woke up from his extended slumber, RoboKing became jealous of the King because all of the cousins were celebrating the his awakening. Unfortunately, when the King finds out that he has a replica, he orders the Prince to dismantle RoboKing's core. This is accomplished (of course), by rolling a Katamari around the restrained RoboKing until large enough to roll up the core that The Prince made earlier. However, when the game is finished and the Katamari Drive mode has been unlocked, RoboKing has returned, and is seemingly being threatened by the King to make more stars. RoboKing's kindness towards the Prince is most likely due to the fact that he was created by the Prince. It could also hint at how the Prince wants his father to be, or simply the Prince sees past the King's aggression and knows that his father does love him (and is only pushing him to do better).
RoboKing does not use the royal "we" like the King, and tends to be less aggressive. He wants to be nice to The Prince/Cousins which is hinted at by his telling the roller to "please" go roll a Katamari. He also wants the Prince or Cousin to be better than him when he says "...leave being OK to me."