  Manipulation of elastoplastic objects like dough often involves topological
changes such as splitting and merging. The ability to accurately predict these
topological changes that a specific action might incur is critical for planning
interactions with elastoplastic objects. We present DoughNet, a
Transformer-based architecture for handling these challenges, consisting of two
components. First, a denoising autoencoder represents deformable objects of
varying topology as sets of latent codes. Second, a visual predictive model
performs autoregressive set prediction to determine long-horizon geometrical
deformation and topological changes purely in latent space. Given a partial
initial state and desired manipulation trajectories, it infers all resulting
object geometries and topologies at each step. DoughNet thereby allows to plan
robotic manipulation; selecting a suited tool, its pose and opening width to
recreate robot- or human-made goals. Our experiments in simulated and real
environments show that DoughNet is able to significantly outperform related
approaches that consider deformation only as geometrical change.
