Advertisement

Motion planning in the CL-environment

Extended abstract
  • Chee-Keng Yap
  • Helmut Alt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)

Abstract

Most motion planning work assumes the piecewise-linear or PL-environment. Here we consider the piecewise curvi-linear or CL-environment. We describe extensions to current techniques suitable for the CL-environment. In particular, we show that various techniques for computing Voronoi diagrams and for motion planning generalize in a satisfactory way: there is no asymptotic increase in complexity when the algebraic complexity is kept constant. An underlying premise of our approach is that in the CL-environment, convex chains play the role of convex polygons in PL-environments.

Keywords

Motion Planning Voronoi Diagram Convex Polygon Algebraic Curve Medial Axis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Aggarwal, L. J. Guibas, J. Saxe, and P. W. Shor. A linear time algorithm for computing the Voronoi diagram of a convex polygon. In ACM Symposium on Theory of Computing, pages 39–45, 1987.Google Scholar
  2. [2]
    J. H. Davenport, Y. Siret, and E. Tournier. Computer Algebra: systems and algorithms for algebraic computation. Academic Press, 1988.Google Scholar
  3. [3]
    John Johnstone and Chanderjit Bajaj. On the sorting of points along an algebraic curve. 1988. Submitted, SIAM J. Computing.Google Scholar
  4. [4]
    John K. Johnstone. The Sorting of Points along an Algebraic Curve. Technical Report 87-841, Department of Computer Science, Cornell University, 1987. Ph.D. thesis.Google Scholar
  5. [5]
    Klara Kedem and Micha Sharir. An automatic motion planning system for a convex polygonal mobile robot in 2-dimensional polygonal space. In ACM Symp. on Comp. Geo., pages 329–340, 1988.Google Scholar
  6. [6]
    Daniel Leven and Micha Sharir. Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams. Discrete and Comput. Geo., 2:9–31, 1987.Google Scholar
  7. [7]
    Jacob T. Schwartz and Micha Sharir. On the piano movers' problem: II. General techniques for computing topological properties of real algebraic manifolds. Advances in Appl. Math., 4:298–351, 1983.CrossRefGoogle Scholar
  8. [8]
    Chee-Keng Yap. Algorithmic Motion Planning, chapter 3. Lawrence Erlbaum Associates, 1987.Google Scholar
  9. [9]
    Chee-Keng Yap. An O(n log n) algorithm for the Voronoi diagram of a set of simple curve segments. Discrete and Comput. Geo., 2:365–394, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Chee-Keng Yap
    • 1
  • Helmut Alt
    • 2
  1. 1.Courant InstituteNew York UniversityNew YorkUSA
  2. 2.Fachbereich MathematikFreie Universität BerlinBerlin 33FRG

Personalised recommendations