Topological representation of cloth state for robotmanipulation

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.

Automated summary

The notion of configuration space revolutionized robot motion planning, but handling deformable materials remains a challenge. This work proposes a state representation for textiles based on C-space, deriving a stratification for cloth points and developing topological techniques for manipulation-centred state graphs. The algorithmic implementation allows tailored cloth state-space representations for different purposes, with an example provided for distinguishing cloth states based on manipulation affordances.