In the beginning, Prospero asks Ariel:
"Hast thou, spirit, perform'd to point the tempest that I bade thee?"
Then, Ariel responds "To every article." and describes in detail the fierce storm.
This seems to have Prospero's plans written all over it. However, did he plan out any of the rest?
After assuring Ariel's servitude to him, Prospero tells her simply:
"Go make thyself like a nymph o' the sea: be subject to no sight but thine and mine, invisible to every eyeball else. Go take this shape and hither come in't: go, hence with diligence!"
That's it. No special instructions except to make herself like a nymph and invisible. What she does, however, is quite a bit more, such as leading an enchanted Ferdinand into a soon-to-be-enchanted Miranda. For this, Prospero says:
"At the first sight, they have changed eyes. Delicate Ariel, I'll set thee free for this."
and then questions if this is really the best plan:
"They are both in either's powers; but this swift business I must uneasy make, lest too light winning make the prize light."
Then later Prospero seems to be watching over all when before Ariel saves Gonzalo and Alonso she says:
"My master through his art forsees the danger that you, his friend, are in; and sends me forth- for else his project dies- to keep them living."
Yet, after she wakes them and is confident that they are safe, she says:
"Prospero my lord shall know what I have done: so king, go safely on to seek thy son."
These points lead to me questioning if Prospero really knows what is going on. If he could really see the danger of Gonzalo and Alonso, then wouldn't he have seen what Ariel did? Why then was she going off to report? Does Prospero really tell Ariel backstage exactly what he wants her to do, or does he just tell her general acts? Maybe Ariel just goes the extra mile in everything in order to get freed for her service. Either way, I don't think Prospero knows exactly what he's doing, but is sometimes sitting, waiting for Ariel to act and will then respond to however her actions pan out.
It seems like Prospero knows what is going on...or at least is willing to roll with the punches. Maybe Shakespeare is telling us that absolute power doesn't always mean absolute control, or maybe he's talking to us about free will, or how all of our actions tie back into God's plan. Also, I miss that show. Nice reference.