Autonomous Robots

, Volume 42, Issue 4, pp 895–907 | Cite as

Locally-optimal multi-robot navigation under delaying disturbances using homotopy constraints

  • Jean GregoireEmail author
  • Michal Čáp
  • Emilio Frazzoli
Part of the following topical collections:
  1. Special Issue: Online Decision Making in Multi-Robot Coordination


We study the problem of reliable motion coordination strategies for teams of mobile robots when any of the robots can be temporarily stopped by an exogenous disturbance at any time. We assume that an arbitrary multi-robot planner initially provides coordinated trajectories computed without considering such disturbances. We are interested in designing a control strategy that handles delaying disturbance such that collisions and deadlocks are provably avoided, and the travel time is minimized. The problem is analyzed in a coordination space framework, in which each dimension represents the position of a single robot along its planned trajectory. We demonstrate that to avoid deadlocks, the trajectory of the system in the coordination space must be homotopic to the trajectory corresponding to the planned solution. We propose a controller that abides this homotopy constraint while minimizing the travel time. Besides being provably deadlock-free, our experiments show that travel time is significantly smaller with our method than than with a reactive method.


Autonomous robots Planning Coordination Control Homotopy classes 


  1. Alonso-Mora, J., Gohl, P., Watson, S., Siegwart, R., & Beardsley, P. (2014). Shared control of autonomous vehicles based on velocity space optimization. In: Proceedings of the IEEE international conference on robotics and automation, IEEE (pp. 1639–1645).Google Scholar
  2. Brock, O., & Khatib, O. (2002). Elastic strips: A framework for motion generation in human environments. The International Journal of Robotics Research, 21(12), 1031–1052.CrossRefGoogle Scholar
  3. Čáp, M., Gregoire, J., & Frazzoli, E. (2016) Provably safe and deadlock-free execution of multi-robot plans under delaying disturbances. In: Proceedings of the IEEE conference on intelligent robots and systems (pp. 5113–5118).
  4. Čáp, M., Novák, P., Kleiner, A., & Selecký, M. (2015). Prioritized planning algorithms for trajectory coordination of multiple mobile robots. IEEE transactions on automation science and engineering, 12(3), 835–849. Scholar
  5. Čáp, M., Vokřínek, J., & Kleiner, A. (2015b). Complete decentralized method for on-line multi-robot trajectory planning in well-formed infrastructures. In: Proceedings of the international conference on automated planning and scheduling (pp. 324–332).Google Scholar
  6. Dresner, K., & Stone, P. (2008). A multiagent approach to autonomous intersection management. Journal of Artificial Intelligence Research, 31, 591–656.Google Scholar
  7. Erdmann, M., & Lozano-Pérez, T. (1987). On multiple moving objects. Algorithmica, 2, 1419–1424.MathSciNetCrossRefzbMATHGoogle Scholar
  8. Ghrist, R., & Lavalle, S. M. (2006). Nonpositive curvature and pareto optimal coordination of robots. SIAM Journal on Control and Optimization, 45, 1697–1713.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Ghrist, R., O’Kane, J. M., & LaValle, S. M. (2005). Computing pareto optimal coordinations on roadmaps. The International Journal of Robotics Research, 12, 997–1012.CrossRefGoogle Scholar
  10. Gregoire, J. (2014). Priority-based coordination of mobile robots. arXiv preprint arXiv:14100879.
  11. Guizzo, E. (2008). Three engineers, hundreds of robots, one warehouse. Spectrum, IEEE, 45(7), 26–34.CrossRefGoogle Scholar
  12. Guy, S. J., Chhugani, J., Kim, C., Satish, N., Lin, M., Manocha, D., et al. (2009). Clearpath: Highly parallel collision avoidance for multi-agent simulation. In: Proceedings of the 2009 ACM SIGGRAPH/Eurographics symposium on computer animation, ACM, New York, NY, USA, SCA ’09 (pp. 177–187).Google Scholar
  13. Kant, K., & Zucker, S. W. (1986). Toward efficient trajectory planning: The path-velocity decomposition. International Journal of Robotics Research, 5(3), 72–89.CrossRefGoogle Scholar
  14. Kowshik, H., Caveney, D., & Kumar, P. (2011). Provable systemwide safety in intelligent intersections. IEEE Transactions on Vehicular Technology, 60(3), 804–818.CrossRefGoogle Scholar
  15. LaValle, S. M. (2006). Planning algorithms. Cambridge University Press, Cambridge. Available at
  16. Lumelsky, V. J., & Harinarayan, K. (1997). Decentralized motion planning for multiple mobile robots: The cocktail party model. In: Robot colonies (pp. 121–135). Berlin: Springer.Google Scholar
  17. O’Donnell, P., & Lozano-Perez, T. (1989). Deadlock-free and collision-free coordination of two robot manipulators. In: Proceedings of the IEEE international conference on robotics and automation (pp. 484 –489, Vol. 1).Google Scholar
  18. Pallottino, L., Scordio, V. G., Bicchi, A., & Frazzoli, E. (2007). Decentralized cooperative policy for conflict resolution in multivehicle systems. IEEE Transactions on Robotics, 23(6), 1170–1183.CrossRefGoogle Scholar
  19. Quinlan, S., & Khatib, O. (1993). Elastic bands: Connecting path planning and control. In: Proceedings of the IEEE international conference on robotics and automation (pp. 802–807), IEEE.Google Scholar
  20. Solovey, K., & Halperin, D. (2016). On the hardness of unlabeled multi-robot motion planning. The International Journal of Robotics Research, 35(14), 1750–1759. Scholar
  21. Solovey, K., Yu, J., Zamir, O., & Halperin, D. (2015). Motion planning for unlabeled discs with optimality guarantees. In: Proceedings of robotics: Science and systems, Rome, Italy.
  22. Spirakis, P. G., & Yap, C. K. (1984). Strong NP-hardness of moving many discs. Information Processing Letters, 19(1), 55–59.MathSciNetCrossRefzbMATHGoogle Scholar
  23. Turpin, M., Mohta, K., Michael, N., & Kumar, V. (2014). Goal assignment and trajectory planning for large teams of interchangeable robots. Autonomous Robots, 37(4), 401–415. Scholar
  24. Van Den Berg, J., Guy, S., Lin, M., & Manocha, D. (2011). Reciprocal n-body collision avoidance. Robotics Research, 70, 3–19.Google Scholar
  25. Van den Berg, J., Lin, M., & Manocha, D. (2008). Reciprocal velocity obstacles for real-time multi-agent navigation. In: Proceedings of the IEEE international conference on robotics and automation, IEEE (pp. 1928–1935).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.MIT Senseable City LabMITBostonUSA
  2. 2.Artificial Intelligence CenterCzech Technical UniversityPragueCzech Republic
  3. 3.Department of Mechanical and Process EngineeringETH ZurichZurichSwitzerland

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