  Modelling the physical properties of everyday objects is a fundamental
prerequisite for autonomous robots. We present a novel generative adversarial
network (Defo-Net), able to predict body deformations under external forces
from a single RGB-D image. The network is based on an invertible conditional
Generative Adversarial Network (IcGAN) and is trained on a collection of
different objects of interest generated by a physical finite element model
simulator. Defo-Net inherits the generalisation properties of GANs. This means
that the network is able to reconstruct the whole 3-D appearance of the object
given a single depth view of the object and to generalise to unseen object
configurations. Contrary to traditional finite element methods, our approach is
fast enough to be used in real-time applications. We apply the network to the
problem of safe and fast navigation of mobile robots carrying payloads over
different obstacles and floor materials. Experimental results in real scenarios
show how a robot equipped with an RGB-D camera can use the network to predict
terrain deformations under different payload configurations and use this to
avoid unsafe areas.
