A Representation of Cloth States based on a Derivative of the Gauss Linking Integral

Robotic manipulation of cloth is a complex task because of the infinite-dimensional shape-state space of textiles, which makes their state estimation very difficult. In this paper we introduce the dGLI Cloth Coordinates, a finite low-dimensional representation of cloth states that allows us to efficiently distinguish a large variety of different folded states, opening the door to efficient learning methods for cloth manipulation planning and control. Our representation is based on a directional derivative of the Gauss Linking Integral and al-lows us to represent spatial as well as planar folded configurations in a consistent and unified way. The proposed dGLI Cloth Coordinates are shown to be more accurate in the representation of cloth states and significantly more sensitive to changes in grasping af-fordances than other classic shape distance methods. Finally, we apply our representation to real images of a cloth, showing that with it we can identify the different states using a distance-based classifier.& COPY; 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )