Algorithmic Foundations of Robotics XI pp 591-607

Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 107) | Cite as

Finding a Needle in an Exponential Haystack: Discrete RRT for Exploration of Implicit Roadmaps in Multi-robot Motion Planning

Chapter

Abstract

We present a sampling-basedframeworkfor multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated RRT algorithm for the discrete case of a graph, and it enables a rapid exploration of the high-dimensional configuration space by carefully walking through an implicit representation of a tensor product of roadmaps for the individual robots. We demonstrate our approach experimentally on scenarios of up to 60 degrees of freedom where our algorithm is faster by a factor of at least ten when compared to existing algorithms that we are aware of.

References

  1. 1.
    PQP—A Proximity Query Package. http://gamma.cs.unc.edu/SSV/
  2. 2.
    Graph Product: Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Graph_product (2013)
  3. 3.
    Adler, A., de Berg, M., Halperin, D., Solovey, K.: Efficient multi-robot motion planning for unlabeled discs in simple polygons. CoRR arXiv:1312.1038 (2013)
  4. 4.
    Aronov, B., de Berg, M., van der Stappen, A.F., Švestka, P., Vleugels, J.: Motion planning for multiple robots. Discret. Comput. Geom. 22(4), 505–525 (1999)CrossRefMATHGoogle Scholar
  5. 5.
    Auletta, V., Monti, A., Parente, M., Persiano, P.: A linear time algorithm for the feasibility of pebble motion on trees. In: SWAT, pp. 259–270 (1996)Google Scholar
  6. 6.
    van den Berg, J., Overmars, M.: Prioritized motion planning for multiple robots. In: IROS, pp. 430–435 (2005)Google Scholar
  7. 7.
    van den Berg, J., Snoeyink, J., Lin, M., Manocha, D.: Centralized path planning for multiple robots: optimal decoupling into sequential plans. In: RSS (2009)Google Scholar
  8. 8.
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications, 3rd edn. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Branicky, M.S., Curtiss, M.M., Levine, J.A., Morgan, S.B.: RRTs for nonlinear, discrete, and hybrid planning and control. In: Decision and Control, pp. 9–12 (2003)Google Scholar
  10. 10.
    Choset, H., Lynch, K., Hutchinson, S., Kantor, G., Burgard, G., Kavraki, L., Thrun, S.: Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press, Cambridge (2005)Google Scholar
  11. 11.
    Şucan, I.A., Moll, M., Kavraki, L.E.: The open motion planning library. IEEE Robot. Autom. Mag. 19(4), 72–82 (2012)CrossRefGoogle Scholar
  12. 12.
    Goraly, G., Hassin, R.: Multi-color pebble motion on graphs. Algorithmica 58(3), 610–636 (2010)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Hirsch, S., Halperin, D.: Hybrid motion planning: coordinating two discs moving among polygonal obstacles in the plane. In: WAFR, pp. 239–255. Springer, New York (2002)Google Scholar
  14. 14.
    Hopcroft, J., Schwartz, J., Sharir, M.: On the complexity of motion planning for multiple independent objects; PSPACE-hardness of the “Warehouseman’s Problem”. IJRR 3(4), 76–88 (1984)Google Scholar
  15. 15.
    Karaman, S., Frazzoli, E.: Sampling-based algorithms for optimal motion planning. IJRR 30(7), 846–894 (2011)Google Scholar
  16. 16.
    Kavraki, L.E., Švestka, P., Latombe, J.C., Overmars, M.: probabilistic roadmaps for path planning in high dimensional configuration spaces. IEEE Trans. Robot. Autom. 12(4), 566–580 (1996)CrossRefGoogle Scholar
  17. 17.
    Kloder, S., Hutchinson, S.: Path planning for permutation-invariant multi-robot formations. In: ICRA, pp. 1797–1802 (2005)Google Scholar
  18. 18.
    Kornhauser, D.: Coordinating Pebble motion on graphs, the diameter of permutation groups, and applications. M.Sc. thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (1984)Google Scholar
  19. 19.
    Kuffner, J.J., LaValle, S.M.: RRT-connect: an efficient approach to single-query path planning. In: ICRA, pp. 995–1001 (2000)Google Scholar
  20. 20.
    Kuffner, J.J.: Effective sampling and distance metrics for 3D rigid body path planning. In: ICRA, pp. 3993–3998 (2004)Google Scholar
  21. 21.
    LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006)Google Scholar
  22. 22.
    Leroy, S., Laumond, J.P., Simeon, T.: Multiple path coordination for mobile robots: a geometric algorithm. In: IJCAI, pp. 1118–1123 (1999)Google Scholar
  23. 23.
    Luna, R., Bekris, K.E.: Push and swap: fast cooperative path-finding with completeness guarantees. In: IJCAI, pp. 294–300 (2011)Google Scholar
  24. 24.
    Muja, M., Lowe, D.G.: Fast approximate nearest neighbors with automatic algorithm configuration. In: VISSAPP, pp. 331–340. INSTICC Press (2009)Google Scholar
  25. 25.
    Pearl, J.: Heuristics: Intelligent Search Strategies for Computer Problem Solving. Addison-Wesley, Reading (1984)Google Scholar
  26. 26.
    Salzman, O., Hemmer, M., Halperin, D.: On the power of manifold samples in exploring configuration spaces and the dimensionality of narrow passages. In: WAFR, pp. 313–329 (2012)Google Scholar
  27. 27.
    Sanchez, G., Latombe, J.C.: Using a PRM planner to compare centralized and decoupled planning for multi-robot systems. In: ICRA, pp. 2112–2119 (2002)Google Scholar
  28. 28.
    Schwartz, J.T., Sharir, M.: On the piano movers’ problem: III. Coordinating the motion of several independent bodies. IJRR 2(3), 46–75 (1983)Google Scholar
  29. 29.
    Sharir, M., Sifrony, S.: Coordinated motion planning for two independent robots. Ann. Math. Artif. Intell. 3(1), 107–130 (1991)CrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    Solovey, K., Halperin, D.: \(k\)-color multi-robot motion planning. In: WAFR, pp. 191–207 (2012)Google Scholar
  31. 31.
    Spirakis, P.G., Yap, C.K.: Strong NP-hardness of moving many discs. Inf. Process. Lett. 19(1), 55–59 (1984)CrossRefMATHMathSciNetGoogle Scholar
  32. 32.
    Turpin, M., Michael, N., Kumar, V.: Computationally efficient trajectory planning and task assignment for large teams of unlabeled robots. In: ICRA, pp. 834–840 (2013)Google Scholar
  33. 33.
    Švestka, P., Overmars, M.: Coordinated path planning for multiple robots. Robot. Auton. Syst. 23, 125–152 (1998)CrossRefGoogle Scholar
  34. 34.
    Wagner, G., Choset, H.: M*: a complete multirobot path planning algorithm with performance bounds. In: IROS, pp. 3260–3267. IEEE (2011)Google Scholar
  35. 35.
    Wagner, G., Kang, M., Choset, H.: Probabilistic path planning for multiple robots with subdimensional expansion. In: ICRA, pp. 2886–2892 (2012)Google Scholar
  36. 36.
    Yap, C.: Coordinating the motion of several discs. Technical report, Courant Institute of Mathematical Sciences, Michigan State University, New York (1984)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Blavatnik School of Computer ScienceTel-Aviv UniversityTel AvivIsrael

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