  Robotic manipulation of deformable, one-dimensional objects (DOOs) like ropes
or cables has important potential applications in manufacturing, agriculture,
and surgery. In such environments, the task may involve threading through or
avoiding becoming tangled with objects like racks or frames. Grasping with
multiple grippers can create closed loops between the robot and DOO, and If an
obstacle lies within this loop, it may be impossible to reach the goal.
However, prior work has only considered the topology of the DOO in isolation,
ignoring the arms that are manipulating it. Searching over possible grasps to
accomplish the task without considering such topological information is very
inefficient, as many grasps will not lead to progress on the task due to
topological constraints. Therefore, we propose a grasp loop signature which
categorizes the topology of these grasp loops and show how it can be used to
guide planning. We perform experiments in simulation on two DOO manipulation
tasks to show that using the signature is faster and succeeds more often than
methods that rely on local geometry or finite-horizon planning. Finally, we
demonstrate using the signature in the real world to manipulate a cable in a
scene with obstacles using a dual-arm robot.
