Skip to main content

Multi-agent Cooperative Pursuit-Evasion Strategies Under Uncertainty

  • Conference paper
  • First Online:

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 9))

Abstract

We present a method for a collaborative team of pursuing robots to contain and capture a single evading robot. The main challenge is that the pursuers do not know the position of the evader exactly nor do they know the policy of the evader. Instead, the pursuers maintain an estimate of the evader’s position over time from noisy online measurements. We propose a policy by which the pursuers move to maximally reduce the area of space reachable by the evader given the uncertainty in the evader’s position estimate. The policy is distributed in the sense that each pursuer only needs to know the positions of its closest neighbors. The policy guarantees that the evader’s reachable area is non-increasing between measurement updates regardless of the evader’s policy. Furthermore, we show in simulations that the pursuers capture the evader despite the position uncertainty provided that the pursuer’s measurement noise decreases with the distance to the evade.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    www.cnn.com/2015/01/26/technology/security/drone-white-house/.

  2. 2.

    www.bbc.com/news/uk-40476264.

  3. 3.

    www.cbsnews.com/news/dutch-police-use-eagles-to-take-down-illegal-drones/.

  4. 4.

    Videos of the simulations can be found here, https://youtu.be/3GUlEf0fjyc

References

  1. Allen, R.E., Clark, A.A., Starek, J.A., Pavone, M.: A machine learning approach for real-time reachability analysis. In: Intelligent Robots and Systems, pp. 2202–2208. IEEE (2014)

    Google Scholar 

  2. Anton, F., Mioc, D., Gold, C.: The Voronoi Diagram of Circles and Its Application to the Visualization of the Growth of Particles, pp. 20–54. Springer, Berlin, Heidelberg (2009). http://link.springer.com/10.1007/978-3-642-00212-0_2

    Chapter  Google Scholar 

  3. Basar, T., Olsder, G.: Dynamic Noncooperative Game Theory. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (1999). https://books.google.com/books?id=k1oF5AxmJlYC

  4. Becis-Aubry, Y., Boutayeb, M., Darouach, M.: A stable recursive state estimation filter for models with nonlinear dynamics subject to bounded disturbances. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 1321–1326, Dec 2006

    Google Scholar 

  5. Bertsekas, D., Rhodes, I.: Recursive state estimation for a set-membership description of uncertainty. IEEE Trans. Autom. Control 16(2), 117–128 (1971). http://ieeexplore.ieee.org/document/1099674/

    Article  MathSciNet  Google Scholar 

  6. Chung, T.H., Hollinger, G.A., Isler, V.: Search and pursuit-evasion in mobile robotics. Auton. Robots 31(4), 299–316 (2011). http://link.springer.com/10.1007/s10514-011-9241-4

    Article  Google Scholar 

  7. Durieu, C., Walter, É., Polyak, B.: Multi-input multi-output ellipsoidal state bounding. J. Optim. Theory Appl. 111(2), 273–303 (2001). http://link.springer.com/10.1023/A:1011978200643

    Article  MathSciNet  Google Scholar 

  8. Emiris, I.Z., Tsigaridas, E.P., Tzoumas, G.M.: The predicates for the Voronoi diagram of ellipses. In: Proceedings of the Twenty-second Annual Symposium on Computational Geometry—SCG ’06, p. 227. ACM Press, New York, New York, USA (2006). http://portal.acm.org/citation.cfm?doid=1137856.1137891

  9. Gerkey, B.P., Thrun, S., Gordon, G.: Visibility-based pursuit-evasion with limited field of view. Int. J. Robot. Res. 25(4), 299–315 (2004). http://www.cs.cmu.edu/~ggordon/aaai04/pe-real-robots.pdf

    Article  Google Scholar 

  10. Huang, H., Ding, J., Zhang, W., Tomlin, C.J.: A differential game approach to planning in adversarial scenarios: a case study on capture-the-flag. In: 2011 IEEE International Conference on Robotics and Automation, pp. 1451–1456, May 2011

    Google Scholar 

  11. Huang, H., Zhang, W., Ding, J., Stipanovii, D.M., Tomlin, C.J.: Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference, pp. 4835–4840, Dec 2011

    Google Scholar 

  12. Isaacs, R.: Differential Games. Courier Corporation, New York (1967)

    MATH  Google Scholar 

  13. Kantaros, Y., Zavlanos, M.M.: Communication-aware coverage control for robotic sensor networks. In: 53rd IEEE Conference on Decision and Control, pp. 6863–6868, Dec 2014

    Google Scholar 

  14. LaValle, S., Hinrichsen, J.: Visibility-based pursuit-evasion: the case of curved environments. IEEE Trans. Robot. Autom. 17(2), 196–202 (2001). http://ieeexplore.ieee.org/document/928565/

    Article  Google Scholar 

  15. Liu, Y., Zhao, Y., Wu, F.: Ellipsoidal state-bounding-based set-membership estimation for linear system with unknown-but-bounded disturbances. IET Control Theory Appl. 10(4), 431–442 (2016). http://digital-library.theiet.org/content/journals/10.1049/iet-cta.2015.0654

    Article  MathSciNet  Google Scholar 

  16. Ngeli, T., Conte, C., Domahidi, A., Morari, M., Hilliges, O.: Environment-independent formation flight for micro aerial vehicles. In: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1141–1146, Sep 2014

    Google Scholar 

  17. Okabe, A.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. Wiley (2000). https://books.google.com/books?hl=en&lr=&id=dT7YH3mjeeIC&oi=fnd&pg=PP2&dq=voronoi+tessellation+of+sets&ots=846A2nl6lf&sig=KywKxrvicvcIaduji7Gc2wSOtPk#v=onepage&q=hyperbolic&f=false

  18. Olfati-Saber, R.: Distributed Kalman filter with embedded consensus filters. In: Proceedings of the 44th IEEE Conference on Decision and Control, pp. 8179–8184, Dec 2005

    Google Scholar 

  19. Oyler, D.W.: Contributions to Pursuit-Evasion Game Theory. Ph.D. thesis, University of Michigan (2016). https://deepblue.lib.umich.edu/bitstream/handle/2027.42/120650/dwoyler_1.pdf?sequence=1&isAllowed=y

  20. Pan, S., Huang, H., Ding, J., Zhang, W., vii, D.M.S., Tomlin, C.J.: Pursuit, evasion and defense in the plane, pp. 4167–4173, June 2012

    Google Scholar 

  21. Pierson, A., Wang, Z., Schwager, M.: Intercepting rogue robots: an algorithm for capturing multiple evaders with multiple pursuers. IEEE Robot. Autom. Lett. 2(2), 530–537 (2017)

    Article  Google Scholar 

  22. Santos, M., Diaz-Mercado, Y., Egerstedt, M.: Coverage control for multirobot teams with heterogeneous sensing capabilities. IEEE Robot. Autom. Lett. 3(2), 919–925 (2018)

    Article  Google Scholar 

  23. Stipanović, D.M., Melikyan, A., Hovakimyan, N.: Guaranteed strategies for nosnlinear multi-player pursuit-evasion games. Int. Game Theory Rev. 12(01), 1–17 (2010)

    Article  MathSciNet  Google Scholar 

  24. Tron, R., Vidal, R., Terzis, A.: Distributed pose averaging in camera networks via consensus on SE(3). In: 2008 Second ACM/IEEE International Conference on Distributed Smart Cameras, pp. 1–10, Sep 2008

    Google Scholar 

  25. Vidal, R., Shakernia, O., Kim, H.J., Shim, D.H., Sastry, S.: Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation. IEEE Trans. Robot. Autom. 18(5), 662–669 (2002). http://ieeexplore.ieee.org/document/1067989/

    Article  Google Scholar 

  26. Zhou, Z., Zhang, W., Ding, J., Huang, H., Stipanović, D.M., Tomlin, C.J.: Cooperative pursuit with Voronoi partitions. Automatica 72, 64–72 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported in part by Ford Motor Company. We are grateful for this support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kunal Shah .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Shah, K., Schwager, M. (2019). Multi-agent Cooperative Pursuit-Evasion Strategies Under Uncertainty. In: Correll, N., Schwager, M., Otte, M. (eds) Distributed Autonomous Robotic Systems. Springer Proceedings in Advanced Robotics, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-030-05816-6_32

Download citation

Publish with us

Policies and ethics