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Path Planning for Autonomous Mobile Robots Using the Boundary Integral Equation Method

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Abstract

Path planning is a fundamental problem in mobile robotics. The objective of path planning is to find a sequence of states that carries a robot from some start state to the goal while avoiding obstacles. This paper focuses on point-to-point path planning, ie., developing a path between given points in a known environment with obstacles. A novel environment representation method is introduced which utilizes the Boundary Integral Equation (BIE) method to map the environment into continuous Harmonic potential fields. Different mappings and mechanisms for utilizing these mappings for path planning are developed, and a collection of path planning algorithms are described which exploit the properties of Harmonic fields and the computational efficiency of the BIE method.

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References

  1. Barraquand, J., Langlois, J., Latombe, J.C.: Numerical potential field techniques for robot path planning. Technical report STAN-CS-89-1285, Stanford University (1989)

  2. Becker, A.A.: The Boundary Element Method in Engineering. McGraw-Hill International, New York (1992)

    Google Scholar 

  3. Borenstein, J., Koren, Y.: Real-time obstacle avoidance for fast mobile robots in cluttered environments. In: Proc. of IEEE Intl Conf. on Robotics and Automation, pp. 572–577 (1990)

  4. Cao, X., Sun, H., Jia, Q.: Establish the special virtual manipulator model for mobile robot obstacle avoidance and path planning. In: Proc. of the 2007 International Conference on Information Acquisition, Jeju City, Korea, 9–11 July 2007, pp. 511–516

  5. Connolly, C.I., Burns, J.B.: Path planning using Laplace’s equation. In: Proc. of the Int. Conf. on Robotics and Automation, Cincinnati, OH, pp. 2102–2106 (1990)

  6. Doyle, P., Snell, J.L.: Random Walks And Electric Networks. The Mathematical Association of America, New Jersey (1984)

    MATH  Google Scholar 

  7. Dudek, G., Jenkin, M.R.M.: Computational Principles of Mobile Robotics. Cambridge University Press, New York (1999)

    Google Scholar 

  8. Heath, M.: Scientific Computing: an Introductory Survey. Mc-Graw Hill, New York (1997)

    Google Scholar 

  9. Iñiguez, P., Rosell, J.: Efficient path planning on a non-regular grid, in topics in artificial intelligence. In: Escrig, M.T., Toledo, F., Golobardes, E. (eds.) 5th Catalonian Conference on AI, Castellon, Spain, pp. 345–354 (2002)

  10. Iñiguez, P., Rosell, J.: Probabilistic harmonic-function-based method for robot motion planning. In: Proc 16th IEEE/RSJ Int. Conf. on Intell. Robots and Systems (IROS’03), Las Vegas, pp. 382–387 (2003)

  11. Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Rob. Res. 5(1), 90–98 (1986)

    Article  MathSciNet  Google Scholar 

  12. Kim, J.-O., Khosla, P.K.: Real-time obstacle avoidance using harmonic potential functions. IEEE Trans. Robot. Autom. 8(3), 338–349 (1992)

    Article  Google Scholar 

  13. Koditschek, D.E.: Exact robot navigation by means of potential functions: some topological considerations. In: Proc. of the IEEE Int. Conf. on Rob. and Aut., Raleigh, NC, pp. 1–6 (1987)

  14. Kreyszig, E.: Advanced Engineering Mathematics. Wiley, New York (1979)

    MATH  Google Scholar 

  15. Krogh, B.H.: A generalized potential field approach to obstacle avoidance control. SME MS84, 484 (1984)

    Google Scholar 

  16. Kythe, P.K.: Boundary Element Methods. CRC, Boca Raton (1995)

    MATH  Google Scholar 

  17. Latombe, J.C.: Robot Motion Planning. Kluwer Academic, Norwell (1991)

    Google Scholar 

  18. Lim, J., Shim, E.Y., Takahashi, T.: A study on static and dynamic path planning for autonomous vehicle. In: Proc. RO-MAN’97, IEEE Int. Workshop on Robot and Human Communication, pp. 22–27 (1997)

  19. Lumelsky, V., Stepanov, A.A.: Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shapes. Algoritmica 2, 403–430 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  20. Paliouras, J.D., Meadows, D.S.: Complex Variables for Scientists and Engineers. McMillan, New York (1992)

    Google Scholar 

  21. Jing, R., McIsaac, K.A., Patel, R.V.: Modified Newton’s method applied to potential filed-based navigation for mobile robots. IEEE Trans. Robot. 22(2), 384–391 (2006)

    Article  Google Scholar 

  22. Solkonikoff, I.S., Redheffer, R.M.: Mathematics of Physics and Modern Engineering. McGraw-Hill, Hightstown (1966)

    Google Scholar 

  23. Tan, C.L.: The Boundary Element Method, a Short Course Monograph. Dept. of Mechanical and Aeronautical Engineering, Carleton University, Ottawa (1987)

  24. Zelek, J.S.: Dynamic path planning. In: Proc. of the IEEE Int. Conf. on Cybernatics Man and Systems (1995)

  25. Zu, L., Chen, L., Zuojun, L., Peng, Y.: Research on path planning method of multiple mobile robot in dynamic environment. In: Proceedings of the 2007 World Congress on Intelligent Control and Automation, Chongqing, China, 25–27 July 2008, pp. 5286–5291

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Authors and Affiliations

  1. Institute for Aerospace Research (IAR), National Research Council Canada (NRC), 5145 Decelles Ave., Montreal, QC, Canada, H9C 1T2

    Iraj Mantegh

  2. Department of Computer Science and Engineering, York University, Toronto, ON, Canada

    Michael R. M. Jenkin

  3. Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada

    Andrew A. Goldenberg

Authors
  1. Iraj Mantegh
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  2. Michael R. M. Jenkin
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  3. Andrew A. Goldenberg
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Corresponding author

Correspondence to Iraj Mantegh.

Additional information

This research was supported by the Canadian Institute for Robotics and Intelligent Systems (IRIS) and NSERC Canada, Grant No. A4664.

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Mantegh, I., Jenkin, M.R.M. & Goldenberg, A.A. Path Planning for Autonomous Mobile Robots Using the Boundary Integral Equation Method. J Intell Robot Syst 59, 191–220 (2010). https://doi.org/10.1007/s10846-010-9394-y

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  • DOI: https://doi.org/10.1007/s10846-010-9394-y

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