Exact geometry and robot motion planning: Speculations on a few numerical experiments

  • Claudio Mirolo
  • Enrico Pagello
1 Synthesis Tasks Motion Planning for Robots
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1416)


Rather than presenting a specific technique to plan free motions, the main purpose of this paper is discussing the potential of possible approaches from different viewpoints. The focus is on planning simple motions on the basis of a fine grain description of the workspace. We consider the problem of planning translations of a convex polygon in a cluttered polygonal environment, i.e., in the presence of several convex bodies with several sides, as a toy example to address a number of questions: limits of some popular approaches, development of more refined—but practical—techniques, comparison between algorithmic and intuitive motion planning, use of dynamic techniques, potential of parallelization. Most of the ongoing considerations will take the results of a few numerical experiments as their starting point.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. J. Atallah, R. Cole, and M. T. Goodrich. Cascading divide-and-conquer: A technique for designing parallel algorithms. SIAM J. Comput., 18:499–532, 1989.Google Scholar
  2. 2.
    J. L. Bentley and T. A. Ottmann. Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput., C-28:643–647, 1979.Google Scholar
  3. 3.
    S. Cameron. Collision detection by four dimensional intersection testing. IEEE Trans. on Robotics and Automation, RA-6(3):291–302, 1990.Google Scholar
  4. 4.
    J. Canny. The Complexity of Robot Motion Planning. MIT Press, Cambridge, 1988.Google Scholar
  5. 5.
    J. Canny and M.C. Lin. An opportunistic global path planner. IEEE Trans. Pattern Analysis and Machine Intelligence, 10:102–120, 1993.Google Scholar
  6. 6.
    J. D. Cohen, M. C. Lin, D. Manocha, and M. K. Ponamgi. I-collide: An interactive and exact collision detection system for large-scale environments. In Proc. ACM Interactive 3D Graphics Conf., pages 189–196, 1995.Google Scholar
  7. 7.
    A. P. del Pobil, M. Pérez, and B. Martinez. A practical approach to collision detection between general objects. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 779–784, 1996.Google Scholar
  8. 8.
    D. P. Dobkin and D. G. Kirkpatrick. Fast detection of polyhedral intersection. Theoret. Comput. Sci., 27(3):241–253, 1983.Google Scholar
  9. 9.
    D. P. Dobkin and D. G. Kirkpatrick. Determining the separation of preprocessed polyhedra — A unified approach. In Proc. 17th ICALP Internat. Colloq. Au-tomata Lang. Program., volume 443 of Lecture Notes Comput. Sci., pages 400–413. Springer-Verlag, 1990.Google Scholar
  10. 10.
    E. G. Gilbert and C. J. Ong. New distances for the separation and penetration of objects. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 579–585, 1994.Google Scholar
  11. 11.
    O. Günther and E. Wong. A dual approach to detect polyhedral intersections in arbitrary dimensions. Bit, 31(1):2–14, 1991.Google Scholar
  12. 12.
    P. Jiménez and C. Torras. Speeding up interference detection between polyhedra. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 1485–1492, 1996.Google Scholar
  13. 13.
    J.-C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Boston, 1991.Google Scholar
  14. 14.
    M. C. Lin, D. Manocha, and M. Ponamgi. Fast algorithms for penetration and contact determination between non-convex polyhedral models. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 2707–2712, 1995.Google Scholar
  15. 15.
    V. J. Lumelsky. Effect of kinematics on motion planning for planar robot arms moving amidst unknown obstacles. IEEE J. of Robotics and Automation, RA-3(3):207–223, 1987.Google Scholar
  16. 16.
    C. Mirolo. Convex minimization on a grid and applications. In Proc. 6th Canad. Conf. Comput. Geom., pages 314–319, 1994.Google Scholar
  17. 17.
    C. Mirolo. Collision detection: Experimental results. Techn. Rep. UDMI/03/97/RR, Dip. di Matematica e Informatica dell'Univ. di Udine, Udine, Italy, February 1997.Google Scholar
  18. 18.
    C. Mirolo and E. Pagello. A solid modeling system for robot action planning. IEEE Computer Graphics and Applications, 9(1):55–69, 1989.Google Scholar
  19. 19.
    C. Mirolo and E. Pagello. A cell decomposition approach to motion planning based on collision detection. In Proc. of ICAR'95, pages 481–488, 1995.Google Scholar
  20. 20.
    C. Mirolo and E. Pagello. A practical motion planning strategy based on a plane-sweep approach. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 2705–2712, 1997.Google Scholar
  21. 21.
    C. Mirolo, E. Pagello, and W. H. Qian. Simplified motion planning strategies in flexible manufacturing. In Proc. of IEEE ISATP'95, pages 394–399, 1995.Google Scholar
  22. 22.
    K. Mulmuley. Computational Geometry: An Introduction Through Randomized Algorithms. Prentice Hall, Englewood Cliffs, NJ, 1993.Google Scholar
  23. 23.
    N. J. Nilsson. Principles of Artificial Intelligence. Tioga Publ. Company, Palo Alto, CA, 1980.Google Scholar
  24. 24.
    J. H. Reif. Complexity of the mover's problem and generalizations. In Proc. 20th Annu. IEEE Sympos. Found. Comput. Sci., pages 421–427, 1979.Google Scholar
  25. 25.
    R. Seidel. A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons. Comput. Geom. Theory Appl., 1:51–64, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Claudio Mirolo
    • 1
  • Enrico Pagello
    • 2
  1. 1.Università di UdineDipartimento di Matematica e InformaticaUdineItaly
  2. 2.Ist. CNR-Ladseb, Corso Stati Uniti 4Universitá di Padova, Dip. di Elettronica e InformaticaPadovaItaly

Personalised recommendations