Grasping Non-stretchable Cloth Polygons

In this paper, we examine non-stretchable two-dimensional polygonal cloth, and place bounds on the number of fingers needed to immobilize it. For any non-stretchable cloth polygon, it is always necessary to pin all of the convex vertices. We show that for some shapes, more fingers are necessary. No more than one-third of the concave vertices need to be pinned for simple polygons, and no more than one-third of the concave vertices plus two fingers per hole are necessary for polygons with holes.

[1]  Chandler Davis.  THEORY OF POSITIVE LINEAR DEPENDENCE. , 1954 .

[2]  Franco P. Preparata,et al.  The Medial Axis of a Simple Polygon , 1977, MFCS.

[3]  Steve Fisk,et al.  A short proof of Chvátal's Watchman Theorem , 1978, J. Comb. Theory, Ser. B.

[4]  Harold S. Stone,et al.  Proceedings of 1986 ACM Fall joint computer conference , 1986 .

[5]  Van-Due Nguyen,et al.  Constructing stable force-closure grasps , 1986 .

[6]  J. O'Rourke.  Art gallery theorems and algorithms , 1987 .

[7]  Bernard Chazelle.  Triangulating a simple polygon in linear time , 1991, Discret. Comput. Geom..

[8]  N. Aisaka,et al.  Robot hand for handling cloth , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[9]  David E. Breen,et al.  A Particle-Based Model for Simulating the Draping Behavior of Woven Cloth , 1993 .

[10]  Cristian S. Calude,et al.  Journal of Universal Computer Science , 1994, J. Univers. Comput. Sci..

[11]  Franz Aurenhammer,et al.  A Novel Type of Skeleton for Polygons , 1995, J. Univers. Comput. Sci..

[12]  Nobuyuki Kita,et al.  Strategy for unfolding a fabric piece by cooperative sensing of touch and vision , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[13]  Joel W. Burdick,et al.  New bounds on the number of frictionless fingers required to immobilize 2D objects , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[14]  Franz Aurenhammer,et al.  A Novel Type of Skeleton for Polygons , 1996 .

[15]  S. Crawford,et al.  Volume 1 , 2012, Journal of Diabetes Investigation.

[16]  Kyoko Hamajima,et al.  Planning strategy for task of unfolding clothes , 1997, Robotics Auton. Syst..

[17]  Vijay Kumar,et al.  Robotic grasping and contact: a review , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[18]  Taku Komura,et al.  Topology matching for fully automatic similarity estimation of 3D shapes , 2001, SIGGRAPH.

[19]  Robert Connelly,et al.  TENSEGRITY STRUCTURES: WHY ARE THEY STABLE? , 2002 .

[20]  Micha Sharir,et al.  On the existence and synthesis of multifinger positive grips , 2015, Algorithmica.

[21]  Kwang-Jin Choi,et al.  Stable but responsive cloth , 2002, SIGGRAPH Courses.

[22]  Nancy M. Amato,et al.  Planning motion in completely deformable environments , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[23]  Fred Rothganger,et al.  Capturing a Convex Object With Three Discs , 2007, IEEE Transactions on Robotics.

[24]  Mark H. Overmars,et al.  Immobilizing Hinged Polygons , 2007, Int. J. Comput. Geom. Appl..

[25]  Hiroaki Seki,et al.  Spreading of clothes by robot arms using tracing method , 2007 .

[26]  Subir Kumar Ghosh,et al.  Visibility Algorithms in the Plane , 2007 .

[27]  Pierre Alliez,et al.  Computational geometry algorithms library , 2008, SIGGRAPH '08.

[28]  K. Fernow.  New York , 1896, American Potato Journal.