I. Introduction
Manipulation of deformable objects, such as ropes and cloth, is an important but challenging problem in robotics. Open-loop strategies for deformable object manipulation are often ineffective, since the material can shift in unpredictable ways[1]. Perception of cloth and rope also poses a major challenge, since standard methods for estimating the pose of rigid objects cannot be readily applied to deformable objects for which it is difficult to concretely define the degrees of freedom or provide suitable training data[2]. Despite the numerous industrial and commercial applications that an effective system for deformable object manipulation would have, effective and reliable methods for such tasks remain exceptionally difficult to construct. Previous work on deformable object manipulation has sought to use sophisticated finite element models[1],[3], hand-engineered representations[4]–[7], and direct imitation of human-provided demonstrations[8],[9]. Direct model identification for ropes and cloth is challenging and brittle, while imitation of human demonstrations without an internal model of the object's dynamics is liable to fail in conditions that deviate from those in the demonstrations.