k-Color Multi-robot Motion Planning

  • Kiril SoloveyEmail author
  • Dan Halperin
Conference paper
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 86)


We present a simple and natural extension of the multi-robot motion planning problem where the robots are partitioned into groups (colors), such that in each group the robots are interchangeable. Every robot is no longer required to move to a specific target, but rather to some target placement that is assigned to its group. We call this problem k-color multi-robot motion planning and provide a sampling-based algorithm specifically designed for solving it. At the heart of the algorithm is a novel technique where the k-color problem is reduced to several discrete multi-robot motion planning problems. These reductions amplify basic samples into massive collections of free placements and paths for the robots. We demonstrate the performance of the algorithm by an implementation for the case of disc robots in the plane and show that it successfully and efficiently copes with a variety of challenging scenarios, involving many robots, while a straightforward extension of prevalent sampling-based algorithms for the k-color case, fails even on simple scenarios. Interestingly, our algorithm outperforms a state-of-the- art implementation for the standard multi-robot problem, in which each robot has a distinct color.


Motion Planning Path Planning Multiple Robot Connection Generator Robot Motion Planning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Amato, N.M., Bayazit, O.B., Dale, L.K., Jones, C., Vallejo, D.: Choosing good distance metrics and local planners for probabilistic roadmap methods. In: ICRA, pp. 630–637 (1998)Google Scholar
  2. 2.
    Aronov, B., de Berg, M., van der Stappen, A.F., Švestka, P., Vleugels, J.: Motion planning for multiple robots. In: SCG, pp. 374–382 (1998)Google Scholar
  3. 3.
    van den Berg, J., Overmars, M.: Prioritized motion planning for multiple robots. In: IROS, pp. 430–435 (2005)Google Scholar
  4. 4.
    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
  5. 5.
    Calinescu, G., Dumitrescu, A., Pach, J.: Reconfigurations in graphs and grids. SIAM J. Discrete Math. 22(1), 124–138 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Choset, H., Lynch, K., Hutchinson, S., Kantor, G., Burgard, G., Kavraki, L., Thrun, S.: Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press (2005)Google Scholar
  7. 7.
    Fogel, E., Halperin, D., Wein, R.: CGAL Arrangements and Their Applications: A Step-by-Step Guide. In: Geometry and Computing. Springer (2012)Google Scholar
  8. 8.
    Goraly, G., Hassin, R.: Multi-color pebble motion on graphs. Algorithmica 58(3), 610–636 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Hirsch, S., Halperin, D.: Hybrid Motion Planning: Coordinating Two Discs Moving Among Polygonal Obstacles in the Plane. In: Boissonat, J.-D., Burdick, J., Goldberg, K., Hutchinson, S. (eds.) Algorithmic Foundation of Robotics V. STAR, vol. 7, pp. 239–255. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Kavraki, L.E., Svestka, P., Latombe, J.C., Overmars, M.: Probabilistic roadmaps for path planning in high dimensional configuration spaces. IEEE Transactions on Robotics and Automation 12(4), 566–580 (1996)CrossRefGoogle Scholar
  12. 12.
    Kavraki Lab: The open motion planning library, OMPL (2010),
  13. 13.
    Kornhauser, D.: Coordinating pebble motion on graphs, the diameter of permutation groups, and applications. M.Sc. thesis, Department of Electrical Engineering and Computer Scienec, Massachusetts Institute of Technology (1984)Google Scholar
  14. 14.
    Kornhauser, D., Miller, G., Spirakis, P.: Coordinating pebble motion on graphs, the diameter of permutation groups, and applications. In: FOCS, pp. 241–250. IEEE Computer Society (1984)Google Scholar
  15. 15.
    Kuffner, J.J., Lavalle, S.M.: RRT-Connect: An efficient approach to single-query path planning. In: ICRA, pp. 995–1001 (2000)Google Scholar
  16. 16.
    LaValle, S.M.: Planning Algorithms. Cambridge University Press (2006)Google Scholar
  17. 17.
    Leroy, S., Laumond, J.P., Simeon, T.: Multiple path coordination for mobile robots: A geometric algorithm. In: IJCAI, pp. 1118–1123 (1999)Google Scholar
  18. 18.
    Loyd, S.: Mathematical Puzzles of Sam Loyd. Dover (1959)Google Scholar
  19. 19.
    Luna, R., Bekris, K.E.: Efficient and complete centralized multi-robot path planning. In: IROS (2011)Google Scholar
  20. 20.
    Plaku, E., Bekris, K.E., Kavraki, L.E.: OOPS for motion planning: An online open-source programming system. In: ICRA, pp. 3711–3716. IEEE (2007)Google Scholar
  21. 21.
    Sanchez, G., Claude Latombe, J.: Using a PRM planner to compare centralized and decoupled planning for multi-robot systems. In: ICRA (2002)Google Scholar
  22. 22.
    Schwartz, J.T., Sharir, M.: On the piano movers’ problem: III. Coordinating the motion of several independent bodies. IJRR 2(3), 46–75 (1983)MathSciNetGoogle Scholar
  23. 23.
    Siek, J.G., Lee, L.Q., Lumsdaine, A.: The Boost Graph Library User Guide and Reference Manual (2002)Google Scholar
  24. 24.
    Solovey, K., Halperin, D.: Supplementary online material,
  25. 25.
    Svestka, P., Overmars, M.H.: Coordinated path planning for multiple robots. Robotics and Autonomous Systems 23, 125–152 (1998)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

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

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