Two-Finger Caging of Nonconvex Polytopes

In general, any object can be restricted or caged within a bounded region if we evenly place a sufficient number of fingers around the object. This naive approach often leads to inefficient utilization of fingers because only two fingers are sufficient to cage most nonconvex objects. In this paper, we propose an algorithm that identifies all the caging sets, i.e., set of two-finger placements that cage a given polytope representing the object. Whether a finger placement could cage the object can be queried efficiently from a structure generated by the algorithm. We implemented and tested the algorithm in the case of 2-D and 3-D objects.

[1]  A. Frank van der Stappen,et al.  Caging Polygons with Two and Three Fingers , 2008, Int. J. Robotics Res..

[2]  Andrew Blake,et al.  Caging planar objects with a three-finger one-parameter gripper , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[3]  Andrew Blake,et al.  Caging 2D bodies by 1-parameter two-fingered gripping systems , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[4]  Gino van den Bergen.  A Fast and Robust GJK Implementation for Collision Detection of Convex Objects , 1999, J. Graphics, GPU, & Game Tools.

[5]  Jean Ponce,et al.  Manipulating Parts with an Array of Pins: A Method and a Machine , 2001, Int. J. Robotics Res..

[6]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[7]  Joel W. Burdick,et al.  A General Stance Stability Test Based on Stratified Morse Theory With Application to Quasi-Static Locomotion Planning , 2008, IEEE Transactions on Robotics.

[8]  Andrew Blake,et al.  Error-tolerant visual planning of planar grasp , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[9]  David J. Kriegman,et al.  On manipulating polygonal objects with three 2-DOF robots in the plane , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[10]  Alberto Rodriguez,et al.  Two Finger Caging: Squeezing and Stretching , 2008, WAFR.

[11]  Fred Rothganger,et al.  Motion planning for disc-shaped robots pushing a polygonal object in the plane , 2002, IEEE Trans. Robotics Autom..

[12]  Gert Vegter,et al.  In handbook of discrete and computational geometry , 1997 .

[13]  Joseph O'Rourke,et al.  Handbook of Discrete and Computational Geometry, Second Edition , 1997 .

[14]  Kenneth Y. Goldberg,et al.  Gripping parts at concave vertices , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[15]  Attawith Sudsang,et al.  Coverage Diameters of Polygons , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[16]  Barry Joe,et al.  Three-Dimensional Boundary-Constrained Triangulations , 1992 .

[17]  Attawith Sudsang,et al.  Two-finger caging of concave polygon , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[18]  Attawith Sudsang.  A sufficient condition for capturing an object in the plane with disc-shaped robots , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[19]  David J. Kriegman,et al.  Let Them Fall Where They May: Capture Regions of Curved Objects and Polyhedra , 1997, Int. J. Robotics Res..

[20]  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).

[21]  Narayan Srinivasa,et al.  Grasping and in-hand manipulation: experiments with a reconfigurable gripper , 1997, Adv. Robotics.

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