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Reaching a goal with directional uncertainty

  • Mark de Berg
  • Leonidas Guibas
  • Dan Halperin
  • Mark Overmars
  • Otfried Schwarzkopf
  • Micha Sharir
  • Monique Teillaud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 762)

Abstract

We study two problems related to planar motion planning for robots with imperfect control, where, if the robot starts a linear movement in a certain commanded direction, we only know that its actual movement will be confined in a cone of angle α centered around the specified direction.

Keywords

Convex Hull Simple Polygon Total Complexity Goal Region Global Illumination 
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.

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References

  1. 1.
    B. Bhattacharya, D. G. Kirkpatrick, and G. T. Toussaint. Determining sector visibility of a polygon. In Proc. 5th Annu. ACM Sympos. Comput. Geom., pages 247–254, 1989.Google Scholar
  2. 2.
    A. J. Briggs. An efficient algorithm for one-step planar compliant motion planning with uncertainty. In Proc. 5th Annu. ACM Sympos. Comput. Geom., pages 187–196, 1989.Google Scholar
  3. 3.
    B. R. Donald. The complexity of planar compliant motion planning under uncertainty. Algorithmica, 5:353–382, 1990.CrossRefGoogle Scholar
  4. 4.
    H. Edelsbrunner, L. J. Guibas, and M. Sharir. The complexity and construction of many faces in arrangements of lines and of segments. Discrete Comput. Geom., 5:161–196, 1990.Google Scholar
  5. 5.
    M. Erdmann. On motion planning with uncertainty. Technical Report 810, AI Laboratory, MIT, 1984.Google Scholar
  6. 6.
    J. Friedman, J. Hershberger, and J. Snoeyink. Compliant motion in a simple polygon. In Proc. 5th Annu. ACM Sympos. Comput. Geom., pages 175–186, 1989.Google Scholar
  7. 7.
    J. Friedman, J. Hershberger, and J. Snoeyink. Input-sensitive compliant motion in the plane. In Proc. 2nd Scand. Workshop Algorithm Theory, volume 447 of Lecture Notes in Computer Science, pages 225–237. Springer-Verlag, 1990.Google Scholar
  8. 8.
    P. Heckbert and J. Winget. Finite-element methods for global illumination. To appear.Google Scholar
  9. 9.
    K. Kedem, R. Livne, J. Pach, and M. Sharir. On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles. Discrete Comput. Geom., 1:59–71, 1986.Google Scholar
  10. 10.
    J.-C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Boston, 1991.Google Scholar
  11. 11.
    A. Lazanas and J.-C. Latombe. Landmark-based robot navigation. Submitted to Algorithmica.Google Scholar
  12. 12.
    T. Lozano-Pérez, M. T. Mason, and R. H. Taylor. Automatic synthesis of finemotion strategies for robots. Internat. J. Robotics Research, 3:3–24, 1984.Google Scholar
  13. 13.
    J. Matousek, N. Miller, J. Pach, M. Sharir, S. Sifrony, and E. Welzl. Fat triangles determine linearly many holes. In Proc. 32nd Annu. IEEE Sympos. Found. Comput. Sci., pages 49–58, 1991.Google Scholar
  14. 14.
    M. van Kreveld. On fat partitioning, fat covering, and the union size of polygons. In Proc. 3rd Workshop Algorithms Data Struct., Lecture Notes in Computer Science, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Mark de Berg
    • 1
  • Leonidas Guibas
    • 2
    • 3
  • Dan Halperin
    • 4
  • Mark Overmars
    • 1
  • Otfried Schwarzkopf
    • 1
  • Micha Sharir
    • 5
    • 6
  • Monique Teillaud
    • 7
  1. 1.Vakgroep InformaticaUniversiteit UtrechtTB Utrechtthe Netherlands
  2. 2.Dept. of Computer ScienceStanford UniversityUSA
  3. 3.DEC Systems Research CenterPalo Alto
  4. 4.Robotics Laboratory, Dept. of Computer ScienceStanford UniversityStanford
  5. 5.School of Mathematical SciencesTel Aviv UniversityIsrael
  6. 6.Courant Institute of Mathematical SciencesNew York UniversityUSA
  7. 7.INRIASophia-Antipolis CedexFrance

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