Shake Your Camera to Take Sharper Photos

Computational photography is changing the way how photos are taken. More and more cell phones are using computation to offset the small lenses allowed on the phones and the progress has been amazing. What I am still waiting on is a way to allow shaky cameras to take sharper photos. Arguably, a shaky camera can provide more information of a scene than a steady camera. It seems like our brain-eye (and inertial?) system can process it, which gives us a stable (and sharp!) perception of the world while moving. Since most phone users are not so good at holding their cameras steady, why not taking advantage of the shaking? Even better would be allowing a shaky telescope to provide a sharper view of the planets! Has this been done before? Can someone point me to a product or a paper using this approach?