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Potential functions based sampling heuristic for optimal path planning

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Abstract

Rapidly-exploring Random Tree star (RRT*) is a recently proposed extension of Rapidly-exploring Random Tree (RRT) algorithm that provides a collision-free, asymptotically optimal path regardless of obstacles geometry in a given environment. However, one of the limitation in the RRT* algorithm is slow convergence to optimal path solution. As a result it consumes high memory as well as time due to the large number of iterations utilised in achieving optimal path solution. To overcome these limitations, we propose the potential function based-RRT* that incorporates the artificial potential field algorithm in RRT*. The proposed algorithm allows a considerable decrease in the number of iterations and thus leads to more efficient memory utilization and an accelerated convergence rate. In order to illustrate the usefulness of the proposed algorithm in terms of space execution and convergence rate, this paper presents rigorous simulation based comparisons between the proposed techniques and RRT* under different environmental conditions. Moreover, both algorithms are also tested and compared under non-holonomic differential constraints.

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Notes

  1. The procedure \(\mu (\cdot )\) provides the Lebesgue measure of any given state space e.g. \(\mu (X)\) denotes the Lebesgue measure of the whole state space X. Lebesgue measure is also called d-dimensional volume of the given space.

References

  • Arya, S., Mount, D. M., Netanyahu, N. S., Silverman, R., & Wu, A. Y. (1998). An optimal algorithm for approximate nearest neighbor searching fixed dimensions. Journal of the ACM (JACM), 45(6), 891–923.

    Article  MathSciNet  MATH  Google Scholar 

  • Brooks, R. A., & Lozano-Perez, T. (1985). A subdivision algorithm in configuration space for findpath with rotation. IEEE Transactions on Systems Man and Cybernetics, 2, 224–233.

    Article  Google Scholar 

  • Canny, J. (1988). The complexity of robot motion planning. Cambridge: The MIT press.

    MATH  Google Scholar 

  • Goerzen, C., Kong, Z., & Mettler, B. (2010). A survey of motion planning algorithms from the perspective of autonomous uav guidance. Journal of Intelligent and Robotic Systems, 57(1–4), 65–100.

    Article  MATH  Google Scholar 

  • Karaman, S., & Frazzoli, E. (2010). Incremental sampling-based algorithms for optimal motion planning. arXiv preprint arXiv:1005.0416.

  • Karaman, S., & Frazzoli, E. (2011). Sampling-based algorithms for optimal motion planning. The International Journal of Robotics Research, 30(7), 846–894.

    Article  MATH  Google Scholar 

  • Kavraki, L. E., Svestka, P., Latombe, J.-C., & Overmars, M. H. (1996). Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation, 12(4), 566–580.

  • Khatib, O. (1986). Real-time obstacle avoidance for manipulators and mobile robots. The International Journal of Robotics Research, 5(1), 90–98.

    Article  MathSciNet  Google Scholar 

  • Koren, Y., & Borenstein, J. (1991). Potential field methods and their inherent limitations for mobile robot navigation. In IEEE international conference on robotics and automation (pp. 1398–1404).

  • Kuffner Jr, J., & Latombe, J.-C. (2000). Interactive manipulation planning for animated characters. In IEEE international conference on computer graphics and applications (pp. 417–418).

  • Lamiraux, F., & Laumond, J.-P. (1996). On the expected complexity of random path planning. In IEEE international conference on robotics and automation (pp. 3014–3019).

  • Latombe, J.-C. (1999). Motion planning: A journey of robots, molecules, digital actors, and other artifacts. The International Journal of Robotics Research, 18(11), 1119–1128.

    Article  Google Scholar 

  • LaValle, S. M. (1998). Rapidly-exploring random trees: A new tool for path planning. Report No. TR 98-11, Computer Science Department, Iowa State University.

  • LaValle, S. M. (2006). Planning algorithms. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Lee, M. C. & Park, M. G. (2003). Artificial potential field based path planning for mobile robots using a virtual obstacle concept. In IEEE/ASME international conference on advanced intelligent mechatronics (pp. 735–740).

  • Lin, M., Manocha, D., Cohen, J., & Gottschalk, S. (1996). Collision detection: Algorithms and applications. In Algorithms for Robotic Motion and Manipulation (WAFR96) (pp. 129–141).

  • Lozano-Pérez, T., & Wesley, M. A. (1979). An algorithm for planning collision-free paths among polyhedral obstacles. Communications of the ACM, 22(10), 560–570.

    Article  Google Scholar 

  • Matsumoto, K., Ishikawa, M., Inaba, M., & Shimoyama, I. (2012). Assistive robotic technologies for an aging society. In IEEE special issue on quality of life technology (pp. 2429–2441).

  • Perez, A., Karaman, S., Shkolnik, A., Frazzoli, E., Teller, S., & Walter, M. R. (2011). Asymptotically optimal path planning for manipulation using incremental sampling-based algorithms. In IEEE/RSJ international conference on intelligent robots and systems (pp. 4307–4313).

  • Qureshi, A. H., Iqbal, K. F., Qamar, S. M., Islam, F., Ayaz, Y., & Muhammad, N. (2013a). Potential guided directional-rrt* for accelerated motion planning in cluttered environments. In IEEE international conference mechatronics and automation (pp. 519–524).

  • Qureshi, A. H., Mumtaz, S., Iqbal, K. F., Ali, B., Ayaz, Y., Ahmed, F., Muhammad, M. S., Hasan, O., Kim, W. Y., & Ra, M. (2013b). Adaptive potential guided directional-rrt. In IEEE international conference on robotics and biomimetics (pp. 1887–1892).

  • Schwartz, J. T., & Sharir, M. (1983). On the piano movers problem II. General techniques for computing topological properties of real algebraic manifolds. Advances in Applied Mathematics, 4(3), 298–351.

    Article  MathSciNet  MATH  Google Scholar 

  • Taylor, R. H., & Stoianovici, D. (2003). Medical robotics in computer-integrated surgery. IEEE Transactions on Robotics and Automation, 19(5), 765–781.

    Article  Google Scholar 

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Authors and Affiliations

  1. Robotics and Intelligent Systems Engineering (RISE) Lab, School of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Ahmed Hussain Qureshi & Yasar Ayaz

  2. Department of System Innovation, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka, 560-8531, Japan

    Ahmed Hussain Qureshi

Authors
  1. Ahmed Hussain Qureshi
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  2. Yasar Ayaz
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Correspondence to Ahmed Hussain Qureshi.

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Qureshi, A.H., Ayaz, Y. Potential functions based sampling heuristic for optimal path planning. Auton Robot 40, 1079–1093 (2016). https://doi.org/10.1007/s10514-015-9518-0

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  • DOI: https://doi.org/10.1007/s10514-015-9518-0

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