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.

翻译：近年来，机器人操作领域取得了显著进展，但非刚性物体（如布料衣物）的操控仍是一个开放性问题。与非刚性物体的物理交互具有不确定性和建模复杂性，因此从样本数据中提取有用信息可显著提升建模性能。然而，由于状态表示的高维性，此类模型的训练是一项具有挑战性的任务。本文提出控制高斯过程动力学模型（CGPDM），通过将高维非线性动力学嵌入低维流形中进行学习。CGPDM由低维潜空间构成，该空间包含可施加外部控制变量的关联动力学，以及到观测空间的映射。通过引入高斯过程（GP）先验，两个映射的参数均被边缘化。因此，CGPDM将高维状态空间投影到更低维度的潜空间中，从而能够从训练数据中学习系统动力学。CGPDM的建模能力已在仿真和真实场景中得到验证，结果表明其能够泛化多种运动模式，并准确预测由未见过的控制动作序列所产生的布料运动。