There is now a robot that flies like a jellyfish swims. From io9

Unlike a jellyfish (or umbrella), the robot doesn’t have a continuous membrane. Rather, it has four 8-centimeter-long Mylar wings. A small motor, which is connected to an external power source via a wire, pulls in and pushes out the wings as it rotates. And, well, that’s about it.

io9 also has videos of the thing and it is well worth the time to read the whole thing.