Mass Spring Model
My first approach to solve the problem of teaching robots about deformable objects is to use a physical model [Morris, Teshner]. The robot will receive information about a new object through two ways: a colour camera and force sensors. It will try to overlay a 2D-mesh to the image. It will treat every vertex in the mesh as a punctual mass and every edge as a spring. Then it will try to learn the correct parameters so that the mass-spring mesh can deform in a similar way to the real object. Thus, being able to predict the behaviour of the object when forces are applied to it.
This video shows a mesh that behaves a little bit like a sponge that is pressed at both sides. It was produced using the physical model in 2D (it may latter be required to do it in 3D).
More videos in: Videos
This other video shows preservation of lenghts, angles (our extension) and areas collaborating to take the figure back to its original shape. Note the force is being applied from the left and the object is pinned at the right side.