  Manipulation of deformable objects is a desired skill in making robots
ubiquitous in manufacturing, service, healthcare, and security. Deformable
objects are common in our daily lives, e.g., wires, clothes, bed sheets, etc.,
and are significantly more difficult to model than rigid objects. In this
study, we investigate vision-based manipulation of linear flexible objects such
as cables. We propose a geometric modeling method that is based on visual
feedback to develop a general representation of the linear flexible object that
is subject to gravity. The model characterizes the shape of the object by
combining the curvatures on two projection planes. In this approach, we achieve
tracking of the position and orientation (pose) of a cable-like object, the
pose of its tip, and the pose of the selected grasp point on the object, which
enables closed-loop manipulation of the object. We demonstrate the feasibility
of our approach by completing the Plug Task used in the 2015 DARPA Robotics
Challenge Finals, which involves unplugging a power cable from one socket and
plugging it into another. Experiments show that we can successfully complete
the task autonomously within 30 seconds.
