  Over the last years, robotic cloth manipulation has gained relevance within
the research community. While significant advances have been made in robotic
manipulation of rigid objects, the manipulation of non-rigid objects such as
cloth garments is still a challenging problem. The uncertainty on how cloth
behaves often requires the use of model-based approaches. However, cloth models
have a very high dimensionality. Therefore, it is difficult to find a middle
point between providing a manipulator with a dynamics model of cloth and
working with a state space of tractable dimensionality. For this reason, most
cloth manipulation approaches in literature perform static or quasi-static
manipulation. In this paper, we propose a variation of Gaussian Process
Dynamical Models (GPDMs) to model cloth dynamics in a low-dimensional manifold.
GPDMs project a high-dimensional state space into a smaller dimension latent
space which is capable of keeping the dynamic properties. Using such approach,
we add control variables to the original formulation. In this way, it is
possible to take into account the robot commands exerted on the cloth dynamics.
We call this new version Controlled Gaussian Process Dynamical Model (C-GPDM).
Moreover, we propose an alternative kernel representation for the model,
characterized by a richer parameterization than the one employed in the
majority of previous GPDM realizations. The modeling capacity of our proposal
has been tested in a simulated scenario, where C-GPDM proved to be capable of
generalizing over a considerably wide range of movements and correctly
predicting the cloth oscillations generated by previously unseen sequences of
control actions.
