Forty years ago the notion of configuration space (C-space) revolutionised robot motion planning for rigid and articulated objects. Despite great progress, handling deformable materials has remained elusive because of their infinite-dimensional shape-state space. Finding low-complexity representations has become a pressing research goal. This work tries to make a tiny step in this direction by proposing a state representation for textiles relying on the C-space of some distinctive points. A stratification of the configuration space for n points in the cloth is derived from that of the flag manifold, and topological techniques to determine adjacencies in manipulation-centred state graphs are developed. Their algorithmic implementation permits obtaining cloth state–space representations of different granularities and tailored to particular purposes. An example of their usage to distinguish between cloth states having different manipulation affordances is provided. Suggestions on how the proposed state graphs can serve as a common ground to link the perception, planning and manipulation of textiles are also made.

四十年前，配置空间 (C-space) 的概念彻底改变了刚性和铰接物体的机器人运动规划。尽管取得了很大进展，但由于其无限维的形状状态空间，处理可变形材料仍然难以捉摸。寻找低复杂度的表示已经成为一个紧迫的研究目标。这项工作试图通过提出一种依赖于某些独特点的 C 空间的纺织品状态表示，朝着这个方向迈出一小步。n的配置空间的分层布料中的点来自标志流形的点，并且开发了用于确定以操作为中心的状态图中的邻接的拓扑技术。他们的算法实现允许获得不同粒度的布料状态空间表示，并针对特定目的进行定制。提供了它们用于区分具有不同操作可供性的布料状态的示例。还就拟议的状态图如何作为连接纺织品的感知、规划和操作的共同点提出了建议。