Algorithmica

, Volume 2, Issue 1–4, pp 403–430

Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape

  • Vladimir J. Lumelsky
  • Alexander A. Stepanov
Article

Abstract

The problem of path planning for an automaton moving in a two-dimensional scene filled with unknown obstacles is considered. The automaton is presented as a point; obstacles can be of an arbitrary shape, with continuous boundaries and of finite size; no restriction on the size of the scene is imposed. The information available to the automaton is limited to its own current coordinates and those of the target position. Also, when the automaton hits an obstacle, this fact is detected by the automaton's “tactile sensor.” This information is shown to be sufficient for reaching the target or concluding in finite time that the target cannot be reached. A worst-case lower bound on the length of paths generated by any algorithm operating within the framework of the accepted model is developed; the bound is expressed in terms of the perimeters of the obstacles met by the automaton in the scene. Algorithms that guarantee reaching the target (if the target is reachable), and tests for target reachability are presented. The efficiency of the algorithms is studied, and worst-case upper bounds on the length of generated paths are produced.

Key words

Robotics Robot motion planning Collision avoidance algorithms Planning with uncertainty Provable algorithms 

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References

  1. [1]
    J. T. Schwartz and M. Sharir, On the “piano movers” problem: I. The case of a two-dimensional rigid polygonal body moving amidst polygonal barriers,Comm. Pure Appl. Math.,36 (1983), 345–398.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    T. Lozano-Perez and M. Wesley, An algorithm for planning collision-free paths among polyhedral obstacles,Comm. ACM,22 (1979), 560–570.CrossRefGoogle Scholar
  3. [3]
    H. Moravec, The Stanford cart and the CMU rover,Proc. IEEE,71 (1983), 872–874.CrossRefGoogle Scholar
  4. [4]
    R. A. Brooks, Solving the find-path problem by good representation of free space,IEEE Trans. Systems Man Cybernet.,13 (1983).Google Scholar
  5. [5]
    T. O. Binford, Visual perception by computer,Proceeding of the IEEE Systems Science and Cybernetics Conference, Miami, FL, 1971.Google Scholar
  6. [6]
    J. Reif, Complexity of the mover's problem and generalizations,Proceedings of the 20th Symposium on the Foundations of Computer Science, 1979.Google Scholar
  7. [7]
    D. L. Pieper, The kinematics of manipulators under computer control, Ph.D. Thesis, Stanford University, 1968.Google Scholar
  8. [8]
    R. Paul, Modeling trajectory calculation and servoing of a computer controlled arm, Ph.D. Thesis, Stanford University, 1972.Google Scholar
  9. [9]
    J. T. Schwartz and M. Sharir, On the “piano movers” problem: II. General techniques for computing topological properties of real algebraic manifolds,Adv. in Appl. Math.,4 (1983), 298–351.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    J. Hopcroft, D. Joseph, and S. Whitesides, On the movement of robot arms in 2-dimensional bounded regions,Proceedings of the IEEE Foundations of Computer Science Conference, Chicago, IL, 1982.Google Scholar
  11. [11]
    B. Bullock, D. Keirsey, J. Mitchell, T. Nussmeier, and D. Tseng, Autonomous vehicle control: an overview of the hughes project,Proceedings of the IEEE Computer Society Conference “Trends and Applications, 1983: Automating Intelligent Behavior”, Gaithersburg, MD, 1983.Google Scholar
  12. [12]
    A. M. Thompson, The navigation system of the JPL robot,Proceedings of the Fifth Joint International Conference on Artificial Intelligence, Cambridge, MA, 1977.Google Scholar
  13. [13]
    D. M. Kersey, E. Koch, J. McKisson, A. M. Meystel, and J. S. B. Mitchell, Algorithm of navigation for a mobile robot,Proceedings of the International Conference on Robotics, Atlanta, GA, 1984.Google Scholar
  14. [14]
    M. Blum and D. Kozen, On the power of the compass (or, why mazes are easier to search than graphs),Proceedings of the 19th Annual Symposium on Foundation of Computer Science, Ann Arbor, MI, 1978.Google Scholar
  15. [15]
    W. Lipski and F. Preparata, Segments, rectangles, contours,J. Algorithms,2 (1981), 63–76.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    H. Abelson and A. diSessa,Turtle Geometry, MIT Press, Cambridge, MA, 1980, pp. 176–199.Google Scholar
  17. [17]
    C. Yap, Algorithmic motion planning, inAdvances in Robotics, Vol. 1 (J. Schwartz and C. K. Yap, eds.), Lawrence Erlbaum, NJ, 1986.Google Scholar
  18. [18]
    L. Meijdam and A. de Zeeuw, On expectations, information, and dynamic game equilibria, inDynamic Games and Applications in Economics (T. Basar, ed.), Springer-Verlag, New York, 1986.Google Scholar
  19. [19]
    E. Moore, The firing squad synchronization problem, inSequential Machines (E. Moore, ed.), Reading, MA, 1964.Google Scholar
  20. [20]
    J. Traub, G. Wasilkowski, and H. Wozniakowski,Information, Uncertainty, Complexity, Addison-Wesley, Reading, MA, 1983.MATHGoogle Scholar
  21. [21]
    J. Reif, A survey on advances in the theory of computational robotics, inAdaptive and Learning Systems (K. Narendra, ed.), Plenum, New York, 1986.Google Scholar
  22. [22]
    W. S. Massey,Algebraic Topology, Harcourt, Brace, & World, New York, 1967.MATHGoogle Scholar
  23. [23]
    V. Lumelsky, Effect of robot kinematics on motion planning in unknown environment,Proceedings of the 24th IEEE Conference on Decision and Control, Fort Lauderdale, FL, 1985.Google Scholar
  24. [24]
    V. Lumelsky, Continuous motion planning in unknown environment for a 3D cartesian robot arm,Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, 1986.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Vladimir J. Lumelsky
    • 1
  • Alexander A. Stepanov
    • 2
  1. 1.Yale UniversityNew HavenUSA
  2. 2.Polytechnic UniversityBrooklynUSA

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