Modules over the Drinfeld double vs Yetter-Drinfeld modules

Question

Let $H$ be a finite Hopf algebra. How can I prove that Yetter-Drinfeld modules over $H$ (see https://en.wikipedia.org/wiki/Yetter%E2%80%93Drinfeld_category) coincide with modules over the Drinfeld double of $H$ (see Equality of two definitions of the Drinfeld Double)? (To be precise, I would be interested in a "computational" proof, as opposed to the obvious categorical argument.)