I've always been confused by this: "j'aurai du" translates as "I should have" and not as "I will have had to...." but these are not quite the same, I think. "I will have had to catch the 22 bus" suggests that I did catch that particular bus, to achieve whatever, whereas "I should have" suggests that I didn't catch that bus, and perhaps failed in my intention. Similarly for "j'aurai pu" - "I could have" not "I will have been able".
Any advice/explanation appreciated!