Dr. Judith Klinger, a German scholar at the University of Potsdam, has very recently published an extensive study on Robin Hood[1] -- it's only available in German as far as I know, though. Her study is based mainly on poems and ballads written around the middle of the 15th century, in which Robin Hood is mentioned. She assumes that Robin Hood, if he actually lived (a question that is very much discussed and isn't answered in the book) must have lived 200 years earlier, due to two reasons: a) Him using a bow makes it very likely, that he lived before the invention of gunpowder and b) the mentioning of a king Edward in many of her sources (and three kings of that name were born between 1239 and 1312). During that time the nicknames "Robbehood" and "Robynhood" can also be found in many official documents. Klinger is able to identify many localities mentioned in her sources, interestingly enough Hood's pillages were situated in Barnsdale, north of Sherwood forest in earlier sources. Klinger also presents quite a few candidates as possible origins of the myth (like the knight Roger Godberd or a certain Lionel, who lived with a bunch of bandits in the forest), but says there's no compelling evidence that one of them actually was the model for Robin Hood.

Oh just a quick edit: The motif of the robber who steals from the rich and gives to the poor cannot be found in the early sources Klinger analyzes -- Robin Hood is simply presented as a rascal robber. The "hero redistributing the riches" wasn't introduced until much later.

[1]Robin Hood: Auf der Suche nach einer Legende. Darmstadt: Lambert Schneider Verlag 2015.