Topological representation of cloth state for robot manipulation: Deriving the configuration space of a rectangular cloth

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.
This work is supported by the European Research Council (ERC) within the European Union Horizon 2020 Programme under grant agreement ERC-2016-ADG-741930 (CLOTHILDE: CLOTH manIpulation Learning from DEmonstrations) and by the Spanish State Research Agency through the María de Maeztu Seal of Excellence to IRI (MDM-2016-0656). We thank Dr Jordi Sanchez Riera for providing us with cloth simulations.