You can use a universal system for distance. They can be based on any arbitrary standard your king wants. One royalength is equal to the king's height as measured on one specific day when he is feeling particularly tall. One royalwee is equal to the volume the king excreted that morning. These constants can apply on any planet capable of supporting human life.
You can establish a royalbeat as a time standard based on the king's heartbeat at rest. While this standard can apply on other planets, it's difficult to build larger units from it that apply off Royalworld. Say 100 royalbeats is a royalminute, 100 royalminutes is a royalhour, and 100 royalhours is a royalday. While that royalday may last from sunrise to sunrise on Royalworld, it may run too long or too short on another world because of different rotation speeds. And while 100 royaldays makes a royalyear at home, it probably won't match the period of solar orbit on any other planet.
Weight is a relationship between two masses. The royalbulk (the king's weight one morning when he felt particularly svelte) will be almost useless on any other planet. Since the other planets will each have different masses and attract a weight differently, an object that weighs one royalbulk on Royalworld will not weigh the same on another planet.
How's that for starters?
