This would be a rather ordinary standard umbrella with a rather simple twist - it comes with a keychain remote finder system included. Employing RFID technology, your umbrella will respond by making a distinct sound when you press the button on its specific supplied finder unit. Simply follow the sound and Viola! you have recovered your treasured brolly. My personal choice for the type of sound clip my own umbrella would play is "Signed, Sealed, and Delivered" by Stevie Wonder.
I realize this isn't exactly as advertised. The umbrella does not actaully "come home" of its own accord, but the end result is still the same - you get your umbrella back in your hands.
Useful, too if your spouse has taken your umbrella to work and forgotten where she left it. Simply give her the remote before she toddles off to the salt mines, phone her near quitting time and have her press the button. Stay on the line with her until she has your umbrella in her grasp and she has assured you she will bring it home even if it kills her. I suggest you have some token of reward waiting at home for her, such as a bouquet of a suitable floral assortment, or a copy of her favourite sensationalist tabloid.
*Inspired by GutPunchLullabies' Unstealable Umbrella.-- Canuck, Nov 16 2007 What you need is an implantable umbrella. The space between the radius and the ulna is under-used: it ought to be possible to create a tubular pocket in this space, and fill it with a spring-loaded umberella.-- MaxwellBuchanan, Nov 16 2007 There's a tough, inelastic membrane between the radius and ulna, actually. It helps your forearm twist up properly without coming all floppy in the middle.-- GutPunchLullabies, Nov 16 2007 I don't think I'd mind my forearm being all floppy in the middle, if I had an integral umbrella. There must be a technical term for the space between the radius and the ulna.-- MaxwellBuchanan, Nov 16 2007 More umbrella ideas, people. Let's go.-- globaltourniquet, Nov 16 2007 There are plenty of umbrellas up for "borrowing" at most fine eateries. Just explain that you left your black umbrella last time you visited and they will bring out a box of about 60 for you to pick from. Umbrellas like ball point pens are never owned just used for a time and then both parties move on. (See homing pen) It's a mystery.-- Monty6, Nov 17 2007 random, halfbakery