On the Reconfiguration of Chains (Extended Abstract)

A chain is a sequence of rigid rods or links consecutively connected at their endjoints, about which they may rotate freely. A planar chain is a chain whose rods lie in the plane, with rods allowed to pass over one another as they move. A convex obtuse polygon P is a convex polygon with each interior angle not less than π/2. We consider the following reconfiguration problem.

[1]  Vitit Kantabutra Reaching a Point with an Unanchored Robot Arm in a Square , 1997, Int. J. Comput. Geom. Appl..

[2]  Vitit Kantabutra,et al.  New Algorithms for Multilink Robot Arms , 1986, J. Comput. Syst. Sci..

[3]  Marc J. van Kreveld,et al.  Folding rulers inside triangles , 1993, CCCG.

[4]  Micha Sharir,et al.  Planning, geometry, and complexity of robot motion , 1986 .

[5]  Paul G. Spirakis,et al.  Strong NP-Hardness of Moving Many Discs , 1984, Inf. Process. Lett..

[6]  Sue Whitesides,et al.  Reconfiguring closed polygonal chains in Euclideand-space , 1995, Discret. Comput. Geom..

[7]  James U. Korein,et al.  A geometric investigation of reach , 1985 .

[8]  John E. Hopcroft,et al.  On the movement of robot arms in 2-dimensional bounded regions , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[9]  Sue Whitesides,et al.  Algorithmic Issues in the Geometry of Planar Linkage Movement , 1992, Aust. Comput. J..

[10]  John E. Hopcroft,et al.  Movement Problems for 2-Dimensional Linkages , 1984, SIAM J. Comput..

[11]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[12]  Deborah A. Joseph,et al.  On the complexity of reachability and motion planning questions (extended abstract) , 1985, SCG '85.

[13]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[14]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[15]  Vitit Kantabutra Motions of a short-linked robot arm in a square , 1992, Discret. Comput. Geom..