With the help of the spirit Ariel, Prospero summons a tempest to shipwreck King Alonso's ship and exact revenge on those members of royalty who usurped his position as Duke of Milan: Alonso (the King of Naples) and Antonio (Prospero's brother and current Duke of Milan).
Prospero tells Miranda,
This King of Naples, being an enemy...
Should presently extirpate me and mine
Out of the dukedom and confer fair Milan
With all the honours on my brother: where on
A treacherous army levied, one midnight...
Bore us some leagues to the sea...
Here in this island we arrived
The other members of royalty who now find themselves stranded are Ferdinand (the king's son) and Sebastian (the king's brother).
Other than shipwrecking them, it is unclear how Prospero plans to get his revenge. He doesn't seem to want them dead, because in act 1, scene 2, he asks,
But are they, Ariel, safe?
Ariel has dispersed them throughout the island. Ferdinand, who Ariel says was the first to jump ship, finds himself alone in what Ariel calls
an odd angle of the island.
Alonso, Antonio, and Sebastian are together but seemingly farther away from Prospero. Ferdinand arrives at Prospero's camp as early as act 1, scene 2. The others don't arrive until the end of the play.