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Reciprocal n-Body Collision Avoidance

  • Conference paper

Part of the Springer Tracts in Advanced Robotics book series (STAR,volume 70)

Abstract

In this paper, we present a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace. In our formulation, each robot acts fully independently, and does not communicate with other robots. Based on the definition of velocity obstacles [5], we derive sufficient conditions for collision-free motion by reducing the problem to solving a low-dimensional linear program. We test our approach on several dense and complex simulation scenarios involving thousands of robots and compute collision-free actions for all of them in only a few milliseconds. To the best of our knowledge, this method is the first that can guarantee local collision-free motion for a large number of robots in a cluttered workspace.

Keywords

  • Mobile Robot
  • Current Velocity
  • Collision Avoidance
  • Obstacle Avoidance
  • Optimization Velocity

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.

This research is supported in part by ARO Contracts W911NF-04-1-0088, NSF award 0636208, DARPA/RDECOM Contracts N61339-04-C-0043 and WR91CRB-08-C-0137, Intel, and Microsoft.

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References

  1. Abe, Y., Yoshiki, M.: Collision avoidance method for multiple autonomous mobile agents by implicit cooperation. In: IEEE RSJ Int. Conf. Intell. Robot. Syst., pp. 1207–1212 (2001)

    Google Scholar 

  2. Borenstein, J., Koren, Y.: The vector field histogram - fast obstacle avoidance for mobile robots. IEEE Journal of Robotics and Automation 7(3), 278–288 (1991)

    CrossRef  Google Scholar 

  3. de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  4. Faverjon, B., Tournassoud, P.: A local based approach for path planning of manipulators with a high number of degrees of freedom. In: IEEE Int. Conf. Robot. Autom., pp. 1152–1159 (1987)

    Google Scholar 

  5. Fiorini, P., Shiller, Z.: Motion planning in dynamic environments using Velocity Obstacles. Int. Journal of Robotics Research 17(7), 760–772 (1998)

    CrossRef  Google Scholar 

  6. Fox, D., Burgard, W., Thrun, S.: The dynamic window approach to collision avoidance. IEEE Robot. Autom. Mag. 4, 23–33 (1997)

    CrossRef  Google Scholar 

  7. Fraichard, T., Asama, H.: Inevitable collision states - a step towards safer robots? Advanced Robotics 18(10), 1001–1024 (2004)

    CrossRef  Google Scholar 

  8. Fulgenzi, C., Spalanzani, A., Laugier, C.: Dynamic obstacle avoidance in uncertain environment combining PVOs and occupancy grid. In: IEEE Int. Conf. Robot. Autom., pp. 1610–1616 (2007)

    Google Scholar 

  9. Gil de Lamadrid, J.: Avoidance of Obstacles With Unknown Trajectories: Locally Optimal Paths and Periodic Sensor Readings. Int. Journal of Robotics Research 13(6), 496–507 (1994)

    CrossRef  Google Scholar 

  10. Guy, S., Chhugani, J., Kim, C., Satish, N., Dubey, P., Lin, M., Manocha, D.: Highly parallel collision avoidance for multi-agent simulation. In: ACM Symposium on Computer Animation (2009)

    Google Scholar 

  11. Helbing, D., Farkas, I., Vicsek, T.: Simulating dynamical features of escape panic. Nature 407, 487–490 (2000)

    CrossRef  Google Scholar 

  12. Hsu, D., Kindel, R., Latombe, J., Rock, S.: Randomized kinodynamic motion planning with moving obstacles. Int. J. Robot. Res. 21(3), 233–255 (2002)

    CrossRef  Google Scholar 

  13. Kanehiro, F., Lamiraux, F., Kanoun, O., Yoshida, E., Laumond, J.-P.: A local collision avoidance method for non-strictly convex polyhedra. In: Robotics: Science and Systems (2008)

    Google Scholar 

  14. Khatib, O.: Real-Time Obstacle Avoidance for Manipulators and Mobile Robots. Int. Journal of Robotics Research 5(1), 90–98 (1986)

    CrossRef  MathSciNet  Google Scholar 

  15. Kluge, B., Prassler, E.: Reflective navigation: Individual behaviors and group behaviors. In: IEEE Int. Conf. Robot. Autom., pp. 4172–4177 (2004)

    Google Scholar 

  16. Kuchar, J., Chang, L.: Survey of conflict detection and resolution modeling methods. In: AIAA Guidance, Navigation, and Control Conf. (1997)

    Google Scholar 

  17. Lin, M.: Efficient collision detection for animation and robotics. PhD thesis, University of California, Berkeley (1993)

    Google Scholar 

  18. LaValle, S.: Planning Algorithms. Cambridge University Press, Cambridge (2006)

    CrossRef  MATH  Google Scholar 

  19. Martinez-Gomez, L., Fraichard, T.: Collision avoidance in dynamic environments: an ICS-based solution and its comparative evaluation. In: IEEE Int. Conf. on Robotics and Automation (2009)

    Google Scholar 

  20. McLurkin, J., Demaine, E.: A Distributed Boundary Detection Algorithm for Multi-Robot Systems (2009) (under review)

    Google Scholar 

  21. Pettré, J., de Heras Ciechomski, P., Maïm, J., Yershin, B., Laumond, J.-P., Thalmann, D.: Real-time navigating crowds: scalable simulation and rendering. Computer Animation and Virtual Worlds 17, 445–455 (2006)

    CrossRef  Google Scholar 

  22. Petti, S., Fraichard, T.: Safe motion planning in dynamic environments. In: IEEE RSJ Int. Conf. Intell. Robot. Syst., pp. 2210–2215 (2005)

    Google Scholar 

  23. Reynolds, C.: Flocks, herds and schools: A distributed behavioral model. In: Int. Conf. on Computer Graphics and Interactive Techniques, pp. 25–34 (1987)

    Google Scholar 

  24. Simmons, R.: The curvature-velocity method for local obstacle avoidance. In: IEEE Int. Conf. on Robotics and Automation, pp. 3375–3382 (1996)

    Google Scholar 

  25. Snape, J., van den Berg, J., Guy, S., Manocha, D.: Independent navigation of multiple mobile robots with hybrid reciprocal velocity obstacles. In: IEEE/RSJ Int. Conf. Intell. Robot. Syst. (2009)

    Google Scholar 

  26. van den Berg, J., Lin, M., Manocha, D.: Reciprocal Velocity Obstacles for real-time multi-agent navigation. In: IEEE Int. Conf. on Robotics and Automation, pp. 1928–1935 (2008)

    Google Scholar 

  27. Wilkie, D., van den Berg, J., Manocha, D.: Generalized velocity obstacles. In: IEEE RSJ Int. Conf. Intell. Robot. Syst. (2009)

    Google Scholar 

  28. Zucker, M., Kuffner, J., Branicky, M.: Multipartite RRTs for rapid replanning in dynamic environments. In: IEEE Int. Conf. on Robotics and Automation, pp. 1603–1609 (2007)

    Google Scholar 

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van den Berg, J., Guy, S.J., Lin, M., Manocha, D. (2011). Reciprocal n-Body Collision Avoidance. In: Pradalier, C., Siegwart, R., Hirzinger, G. (eds) Robotics Research. Springer Tracts in Advanced Robotics, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19457-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-19457-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19456-6

  • Online ISBN: 978-3-642-19457-3

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