Similar to the Royal Rainbow is the Hyper Rainbow, which is also vomited from the King's mouth. Unlike the Royal Rainbow, however, the Hyper Rainbow spreads out surrounds the Katamari rather than simply picking it up. It does not appear to be any more powerful or any faster than the regular Royal Rainbow, so the naming seems to simply be another one of the King's quirks. It has thus far only been used in Me & My Katamari.
The RoboKing does not use the "Royal" rainbow. He calls it the Robo Rainbow.
The Royal Rainbow can be rolled up as an object in We ♥ Katamari. It is sticking out of the King's mouth while he flies around. It can be rolled up at around 3000 meters.