  Over the last years, significant advances have been made in robotic
manipulation, but still, the handling of non-rigid objects, such as cloth
garments, is an open problem. Physical interaction with non-rigid objects is
uncertain and complex to model. Thus, extracting useful information from sample
data can considerably improve modeling performance. However, the training of
such models is a challenging task due to the high-dimensionality of the state
representation. In this paper, we propose Controlled Gaussian Process Dynamical
Model (CGPDM) for learning high-dimensional, nonlinear dynamics by embedding it
in a low-dimensional manifold. A CGPDM is constituted by a low-dimensional
latent space, with an associated dynamics where external control variables can
act and a mapping to the observation space. The parameters of both maps are
marginalized out by considering Gaussian Process (GP) priors. Hence, a CGPDM
projects a high-dimensional state space into a smaller dimension latent space,
in which it is feasible to learn the system dynamics from training data. The
modeling capacity of CGPDM has been tested in both a simulated and a real
scenario, where it proved to be capable of generalizing over a wide range of
movements and confidently predicting the cloth motions obtained by previously
unseen sequences of control actions.
