Skip to main content
Log in

Scalable and practical pursuit-evasion with networked robots

  • Special Issue
  • Published:
Intelligent Service Robotics Aims and scope Submit manuscript

Abstract

In this paper, we consider the design and implementation of practical pursuit-evasion games with networked robots, where a communication network provides sensing-at-a-distance as well as a communication backbone that enables tighter coordination between pursuers. We first develop, using the theory of zero-sum games, an algorithm that computes the minimal completion time strategy for pursuit-evasion when pursuers and evaders have same speed, and when all players make optimal decisions based on complete knowledge. Then, we extend this algorithm to when evader are significantly faster than pursuers. Unfortunately, these algorithms do not scale beyond a small number of robots. To overcome this problem, we design and implement a partition algorithm where pursuers capture evaders by decomposing the game into multiple multi-pursuer single-evader games. We show that the partition algorithm terminates, has bounded capture time, is robust, and is scalable in the number of robots. We then describe the design of a real-world mobile robot-based pursuit evasion game. We validate our algorithms by experiments in a moderate-scale testbed in a challenging office environment. Overall, our work illustrates an innovative interplay between robotics and communication.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aigner M, Fromme M (1984) A Game of cops and robber. Discrete Appl. Math 8: 1–12

    Article  MATH  MathSciNet  Google Scholar 

  2. Alankus G, Atay N, Lu C, Bayazit B (2007) Adaptive embedded roadmaps for sensor networks. In: IEEE international conference on robotics and automation

  3. Alspach B (2004) Searching and sweeping graphs: a brief survey. Le Matematiche (Catania) 59: 5–37

    MATH  MathSciNet  Google Scholar 

  4. Batalin MA, Sukhatme GS (2003) Coverage, exploration and deployment by a mobile robot and communication network. In: Telecommunication systems journal. Special issue on wireless sensor networks, pp 376–391

  5. Berarducci A, Intrigila B (1993) On the cop number of a graph. Adv Appl Math 14(4): 389–403. doi:10.1006/aama.1993.1019

    Article  MATH  MathSciNet  Google Scholar 

  6. Bhattacharya S, Candido S, Hutchinson S (2007) Motion strategies for surveillance. In: Robotics: science and systems. http://www.roboticsproceedings.org/rss03/p32.html

  7. Burkard RE, Çela E (1999) Linear assignment problems and extensions. handbook of combinatorial optimization, vol. 4, Kluwer Academic Publishers, pp. 75–149

  8. Cheung W (2005) Constrained pursuit-evasion problems in the plane. Master Thesis, University of British Columbia

  9. Corke PI, Hrabar SE, Peterson R, Rus D, Saripalli S, Sukhatme GS (2004) Deployment and connectivity repair of a sensor net. In: 9th international symposium on experimental robotics

  10. Corker P, Peterson R, Rus D (2005) Localization and navigation assisted by networked cooperating sensors and robots. Int J Robot Res 24(9): 771–786

    Article  Google Scholar 

  11. Gerkey BP, Vaughan RT, Støy K, Howard A, Sukhatme GS, Mataric MJ (2001) Most valuable player: a robot device server for distributed control. Maui, HI, USA, pp 1226–1231

  12. Gnawali O, Greenstein B, Jang KY, Joki A, Paek J, Vieira M, Estrin D, Govindan R, Kohler E (2006) The TENET architecture for tiered sensor networks. In: Proceedings of the ACM conference on embedded networked sensor systems. Boulder, Colorado

  13. Goldstein AS, Reingold EM (1995) The complexity of pursuit on a graph. Theor Comput Sci 143(1): 93–112. doi:10.1016/0304-3975(95)80012-3

    MATH  MathSciNet  Google Scholar 

  14. Guibas LJ, Latombe JC, LaValle SM, Lin D, Motwani R (1997) Visibility-based pursuit-evasion in a polygonal environment. In: WADS '97: proceedings of the 5th international workshop on algorithms and data structures. Springer-Verlag, London, UK, pp 17–30. ISBN:3-540-63307-3

  15. Howard A, Matarić MJ, Sukhatme GS (2002) An incremental self-deployment algorithm for mobile sensor networks. Auton Robots 13(2): 113–126

    Article  MATH  Google Scholar 

  16. Isler V, Kannan S, Khanna S (2005) Randomized pursuit-evasion in a polygonal environment. IEEE Trans Robot 5(21): 864–875

    Google Scholar 

  17. Jonker R, Volgenant A (1987) A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 38(4): 325–340. doi:10.1007/BF02278710

    Article  MATH  MathSciNet  Google Scholar 

  18. Kuipers B, Byun YT (1990) A robot exploration and mapping strategy based on a semantic hierarchy of spatial representations. Tech. Rep. AI90-120

  19. Li Q, Rus D (2005) Navigation protocols in sensor networks. ACM Trans Sensor Netw 1(1): 3–35

    Article  Google Scholar 

  20. Matarić MJ (1992) Integration of representation into goal-driven behavior-based robots. IEEE Trans Robot Autom 8(3): 304–312

    Article  Google Scholar 

  21. Matarić MJ (2007) The robotics primer. MIT Press, Cambridge

    Google Scholar 

  22. Maxim B, Gaurav SS (2007) The design and analysis of an efficient local algorithm for coverage and exploration based on sensor network deployment. IEEE Trans Robot 23(4): 661–675

    Article  Google Scholar 

  23. Murrieta-Cid R, Muppirala T, Sarmiento A, Bhattacharya S, Hutchinson S (2007) Surveillance strategies for a pursuer with finite sensor range. Int J Rob Res 26(3): 233–253. doi:10.1177/0278364907077083

    Article  Google Scholar 

  24. Neufeld E, Myrvold W (1997) Practical toroidality testing. In: SODA '97: Proceedings of the eighth annual ACM-SIAM symposium on discrete algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, pp 574–580. ISBN:0-89871-390-0

  25. Neufeld S, Nowakowski R (1998) A game of cops and robbers played on products of graphs. Discrete Math 186(1–3): 253–266. doi:10.1016/S0012-365X(97)00165-9

    Article  MATH  MathSciNet  Google Scholar 

  26. Nowakowski RJ, Winkler P (1983) Vertex-to-vertex pursuit in a graph. Discrete Math 43(2–3): 235–239

    Article  MATH  MathSciNet  Google Scholar 

  27. Oh S, Schenato L, Chen P, Sastry S (2007) Tracking and coordination of multiple agents using sensor networks: system design, algorithms and experiments. Proceedings IEEE 95(1):234–254. http://www.truststc.org/pubs/244.html

    Google Scholar 

  28. O’Hara KJ, Bigio V, Dodson E, Irani A, Walker D, Balch T (2005) Physical path planning using the gnats. In: IEEE international conference on robotics and automation

  29. Parsons TD (1978) Pursuit-evasion in a graph. Lect Notes Math 642: 426–441. doi:10.1007/BFb0070400

    Article  MathSciNet  Google Scholar 

  30. Pferschy U (1997) Solution methods and computational investigations for the linear bottleneck assignment problem. Computing 59(3): 237–258. doi:10.1007/BF02684443

    Article  MATH  MathSciNet  Google Scholar 

  31. Quilliot A (1985) A short note about pursuit games played on a graph with a given genus. J Comb Theory, Ser B 38(1): 89–92

    Article  MATH  MathSciNet  Google Scholar 

  32. Reich J, Misra V, Rubenstein D (2008) Roomba MADNeT: a mobile ad-hoc delay tolerant network testbed. In: MC2R: Mobile Computing and Communications Review. ACM Sigmobile

  33. Russell, Stuart J, Norvig, Peter (2003) Artificial Intelligence: A Modern Approach. http://portal.acm.org/citation.cfm?id=773294

  34. Seymour PD, Thomas R (1993) Graph searching and a min–max theorem for tree-width. J Comb Theory Ser B 58(1): 22–33. doi:10.1006/jctb.1993.1027

    Article  MATH  MathSciNet  Google Scholar 

  35. Sgall J (2001) Solution of David Gale’s lion and man problem. Theor Comput Sci 259(1–2): 663–670

    Article  MATH  MathSciNet  Google Scholar 

  36. Sumo Robot (2008) http://msdn2.microsoft.com/en-us/robotics/bb403184.aspx

  37. Tekdas O, Isler V (2008) Robotic routers. In: Proceeding of IEEE international conference on robotics and automation. http://www.cs.rpi.edu/%7Eisler/new/pub/pubs/icra08routers.pdf (to appear)

  38. The SmURV Robotics Platform. http://robotics.cs.brown.edu/projects/smurv/

  39. Vidal R, Shakernia O, Kim HJ, Shim DH, Sastry S (2002) Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation. IEEE Trans Robot Autom 18(5): 662–669

    Article  Google Scholar 

  40. Wang X, Jose B. Cruz J, Chen G, Pham K, Blasch E (2007) Formation control in multi-player pursuit evasion game with superior evaders, p 657811. SPIE. doi:10.1117/12.723300. http://link.aip.org/link/?PSI/6578/657811/1

  41. Wei M, Chen G, Cruz J, Hayes L, Chang MH (2006) A decentralized approach to pursuer-evader games with multiple superior evaders. Intelligent Transportation Systems Conference. ITSC '06. IEEE pp 1586–1591.doi:10.1109/ITSC.2006.1707450

  42. Weisstein EW. Grid graph. MathWorld—a wolfram web resource. http://mathworld.wolfram.com/GridGraph.html

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marcos A. M. Vieira.

Additional information

This material is based in part upon work supported by the National Science Foundation under Grants No. CCF-0820230, CNS-0540420, CNS-0325875 and CCR-0120778 and a gift from the Okawa Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author (s) and do not necessarily reflect the views of the National Science Foundation. Marcos Vieira was supported in part by Grant 2229/03–0 from CAPES, Brazil.

Electronic Supplementary Material

The Below is the Electronic Supplementary Material.

ESM 1 (mpg 17,392 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vieira, M.A.M., Govindan, R. & Sukhatme, G.S. Scalable and practical pursuit-evasion with networked robots. Intel Serv Robotics 2, 247–263 (2009). https://doi.org/10.1007/s11370-009-0050-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11370-009-0050-y

Keywords

Navigation