Autonomous Robots

, Volume 37, Issue 4, pp 401–415 | Cite as

Goal assignment and trajectory planning for large teams of interchangeable robots

  • Matthew TurpinEmail author
  • Kartik Mohta
  • Nathan Michael
  • Vijay Kumar


This paper presents Goal Assignment and Planning: a computationally tractable, complete algorithm for generating dynamically feasible trajectories for \(N\) interchangeable (identical) robots navigating through known cluttered environments to \(M\) goal states. This is achieved by assigning goal states to robots to minimize the maximum cost over all robot trajectories. The computational complexity of this algorithm is shown to be polynomial in the number of robots in contrast to the expected exponential complexity associated with planning in the joint state space. This algorithm can be used to plan trajectories for dozens of robots, each in a potentially high dimensional state space. A series of planar case studies are presented and finally, experimental trials are conducted with a team of six quadrotor robots navigating in a constrained three-dimensional environment.


Multiple robot Trajectory planning Task assignment Micro aerial robot 



Research supported by: ONR Grant N00014-07-1-0829, ONR MURI Grant N00014-08-1-0696, NSF CCF-1138847, ARL Grant W911NF-08-2-0004, ONR Grant N00014-09-1-1051, Matthew Turpin was supported by NSF Fellowship Grant DGE-0822.


  1. Burkard, R. E., & Rendl, F. (1991). Lexicographic bottleneck problems. Operations Research Letters, 10(5), 303–308.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269–271.MathSciNetCrossRefzbMATHGoogle Scholar
  3. Enright, J., & Wurman, P. R. (2011). Optimization and coordinated autonomy in mobile fulfillment systems. In Automated action planning for autonomous mobile robots.Google Scholar
  4. Erdmann, M., & Lozano-Perez, T. (1987). On multiple moving objects. Algorithmica, 2(1–4), 477–521.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Fredman, M. L., & Tarjan, R. E. (1987). Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM (JACM), 34(3), 596–615.MathSciNetCrossRefGoogle Scholar
  6. Gerkey, B. P., & Matarić, M. J. (2004). A formal analysis and taxonomy of task allocation in multi-robot systems. The International Journal of Robotics Research, 23(9), 939–954.CrossRefGoogle Scholar
  7. Kant, K., & Zucker, S. W. (1986). Toward efficient trajectory planning: The path-velocity decomposition. The International Journal of Robotics Research, 5(3), 72–89.CrossRefGoogle Scholar
  8. Kloder, S., & Hutchinson, S. (2006). Path planning for permutation-invariant multirobot formations. IEEE Transactions on Robotics, 22(4), 650–665.CrossRefGoogle Scholar
  9. Kuhn, H. W. (1955). The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2(1–2), 83–97.MathSciNetCrossRefGoogle Scholar
  10. LaValle, S. M. (2006). Planning algorithms. Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  11. LaValle, S. M., & Hutchinson, S. A. (1998). Optimal motion planning for multiple robots having independent goals. IEEE Transactions on Robotics and Automation, 14(6), 912–925.CrossRefGoogle Scholar
  12. Liu, L., & Shell, D. A. (2011). Multi-level partitioning and distribution of the assignment problem for large-scale multi-robot task allocation. In Proceedings of the robotics: Science and systems, Los Angeles, CA, June 2011.Google Scholar
  13. Liu, L., & Shell, D. A. (2012). A distributable and computation-flexible assignment algorithm: From local task swapping to global optimality. In Robotics: Science and systems.Google Scholar
  14. Loizou, S. G., & Kyriakopoulos, K. J. (2008). Navigation of multiple kinematically constrained robots. IEEE Transactions on Robotics, 24(1), 221–231.CrossRefGoogle Scholar
  15. Luna, R. & Bekris, K. E. (2011). Push and swap: Fast cooperative path-finding with completeness guarantees. In Proceedings of the twenty-second international joint conference on artificial intelligence-volume volume one (pp. 294–300). Menlo Park: AAAI Press.Google Scholar
  16. Mellinger, D., & Kumar, V. (2011). Minimum snap trajectory generation and control for quadrotors. In Proceedings of the IEEE international conference on robotics and automation (pp. 2520–2525), Shanghai, China.Google Scholar
  17. Michael, N., Mellinger, D., Lindsey, Q., & Kumar, V. (2010). The GRASP multiple micro UAV testbed. IEEE Robotics and Automation Magazine, 17(3), 56–65.CrossRefGoogle Scholar
  18. O’Hara, I., Paulos, J., Davey, J., Eckenstein, N., Doshi, N., Tosun, T., et al. (2014). Self-assembly of a swarm of autonomous boats self-assembly of a swarm of autonomous boats into floating structures. In Proceedings of the IEEE international conference on robotics and automation, Hong Kong.Google Scholar
  19. Peasgood, M., Clark, C. M., & McPhee, J. (2008). A complete and scalable strategy for coordinating multiple robots within roadmaps. IEEE Transactions on Robotics, 24(2), 283–292.Google Scholar
  20. Psaraftis, H. N. (1988). Dynamic vehicle routing problems. Vehicle Routing: Methods and Studies, 16, 223–248.MathSciNetGoogle Scholar
  21. Schüpbach, K., & Zenklusen, R. (2011). Approximation algorithms for conflict-free vehicle routing. In Algorithms-ESA 2011 (pp. 640–651). Berlin: Springer.Google Scholar
  22. Sharon, G., Stern, R., & Felner, A., Sturtevant, N. R. (2012). Meta-agent conflict-based search for optimal multi-agent path finding. In SOCS.Google Scholar
  23. Sokkalingam, P. T., & Aneja, Y. P. (1998). Lexicographic bottleneck combinatorial problems. Operations Research Letters, 23(1), 27–33.MathSciNetCrossRefzbMATHGoogle Scholar
  24. Solovey, K., & Halperin, D. (2014). \(k\)-Color multi-robot motion planning. The International Journal of Robotics Research, 33(1), 82–97.CrossRefGoogle Scholar
  25. Turpin, M., Michael, N. & Kumar, V. (2012). Trajectory planning and assignment in multirobot systems. In Algorithmic foundations of robotics X (pp. 175–190). Boston, MA: Springer.Google Scholar
  26. Turpin, M., Michael, N., & Kumar, V. (2013a). Concurrent assignment and planning of trajectories for large teams of interchangeable robots. In Proceedings of the IEEE International Conference on Robotics and Automation.Google Scholar
  27. Turpin, M., Mohta, K., Michael, N., & Kumar, V. (2013b). Goal assignment and trajectory planning for large teams of aerial robots. In Robotics science and systems, Berlin, Germany.Google Scholar
  28. Van Den Berg, J, Guy, S. J., Lin, M., & Manocha, D. (2011). Reciprocal n-body collision avoidance. In Robotics research (pp. 3–19). Berlin: SpringerGoogle Scholar
  29. van Den Berg, J., Snoeyink, J., Lin, M. C., & Manocha, D. (2009). Centralized path planning for multiple robots: Optimal decoupling into sequential plans. In Robotics: Science and systems, Citeseer (Vol. 2, pp. 2–3).Google Scholar
  30. Van Den Berg, J. P., & Overmars, M. H. (2005). Prioritized motion planning for multiple robots. In IEEE/RSJ international conference on intelligent robots and systems, 2005. (IROS 2005) (pp. 430–435).Google Scholar
  31. Van Nieuwstadt, M. J., & Murray, R. M. (1998). Real-time trajectory generation for differentially flat systems. International Journal of Robust and Nonlinear Control, 8(11), 995–1020.MathSciNetCrossRefzbMATHGoogle Scholar
  32. Wagner, G., & Choset, H. (2011). M\(^{\ast }\): A complete multirobot path planning algorithm with performance bounds. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, San Francisco, CA (pp. 3260–3267).Google Scholar
  33. Wagner, G., Kang, M., & Choset, H. (2012). Probabilistic path planning for multiple robots with subdimensional expansion. In IEEE International Conference on Robotics and Automation (ICRA) (pp. 2886–2892).Google Scholar
  34. Yu, J., & LaValle, S. M. (2012). Distance optimal formation control on graphs with a tight convergence time guarantee. In 2012 IEEE 51st annual conference on decision and control (CDC) (pp. 4023–4028).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Matthew Turpin
    • 1
    Email author
  • Kartik Mohta
    • 1
  • Nathan Michael
    • 2
  • Vijay Kumar
    • 1
  1. 1.University of PennsylvaniaPhiladelphiaUSA
  2. 2.Carnegie Mellon UniversityPittsburghUSA

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