Virtual rope theory for fabric manipulation

This paper describes a representational method of fabric manipulation, referred to as the virtual rope theory. According to this theory, manipulation of a fabric by robotic grippers is considered equivalent to manipulation of a deformable rope. Based on the theory, we define various fabric manipulations; we can judge the success or failure of these manipulations quantitatively. We first represent the topology of rope manipulations using fingers, grippers, and a floor. These representations determine the boundary conditions of a task defined by differential geometric coordinates. Finally, we confirm the applicability of virtual rope theory by experimental unfolding of a fabric.