Coverage Diameters of Polygons

This paper formalizes and proposes an algorithm to compute coverage diameters of polygons in 2D. Roughly speaking, the coverage diameter of a polygon is the longest possible distance between two points through which the polygon cannot pass in between. The primary use of coverage diameter is to form a cage for transporting an object, not necessarily convex, with multiple disc-shaped robots. The main idea of the computation of coverage diameter is to convert the problem into a graph structure, then perform the search for a solution path in that graph. The proposed algorithm runs in O(n2 log n) time for the input polygon with n vertices

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

[2]  Kenneth Y. Goldberg,et al.  Orienting polygonal parts without sensors , 1993, Algorithmica.

[3]  Attawith Sudsang,et al.  Capturing a concave polygon with two disc-shaped fingers , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[4]  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).

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

[6]  Jean Ponce,et al.  A new approach to motion planning for disc-shaped robots manipulating a polygonal object in the plane , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[7]  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).

[8]  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).

[9]  Vijay Kumar,et al.  Object closure and manipulation by multiple cooperating mobile robots , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

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

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