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Analyzing the Multiple-target-multiple-agent Scenario Using Optimal Assignment Algorithms

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Abstract

This work considers the problem of maximum utilization of a set of mobile robots with limited sensor-range capabilities and limited travel distances. The robots are initially in random positions. A set of robots properly guards or covers a region if every point within the region is within the effective sensor range of at least one vehicle. We wish to move the vehicles into surveillance positions so as to guard or cover a region, while minimizing the maximum distance traveled by any vehicle. This problem can be formulated as an assignment problem, in which we must optimally decide which robot to assign to which slot of a desired matrix of grid points. The cost function is the maximum distance traveled by any robot. Assignment problems can be solved very efficiently. Solution times for one hundred robots took only seconds on a Silicon Graphics Crimson workstation. The initial positions of all the robots can be sampled by a central base station and their newly assigned positions communicated back to the robots. Alternatively, the robots can establish their own coordinate system with the origin fixed at one of the robots and orientation determined by the compass bearing of another robot relative to this robot. This paper presents example solutions to the multiple-target-multiple-agent scenario using a matching algorithm. Two separate cases with one hundred agents in each were analyzed using this method. We have found these mobile robot problems to be a very interesting application of optimal assignment algorithms, and we expect this to be a fruitful area for future research.

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References

  1. Ahuja, R., Magnanti, J., and Orlin, J.: Network Flows: Theory, Algorithms, and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1993.

    Google Scholar 

  2. Ahuja, R. and Orlin, J.: The scaling network simplex algorithms, Oper. Res. 40,Supplement 1 (1992), S5–S13.

    Google Scholar 

  3. Akgul, M.: A genuinely polynomial primal simplex algorithm for the assignment problem, Discrete Appl. Math. 45 (1993), 93–115.

    Google Scholar 

  4. Arkin, R. C.: Cooperation without communication: Multiagent schema-based robot navigation, J. Robotic Systems 9(3) (1992), 351–364.

    Google Scholar 

  5. Bertsekas, D. P.: The auction algorithm: A distributed relaxation method for the assignment problems, Ann. Oper. Res. 14 (1988), 105–123.

    Google Scholar 

  6. Brooks, R. A.: A robust layered control system for a mobile robot, IEEE J. Robotics Automat. 2(1) (1986), 14–23.

    Google Scholar 

  7. Brooks, R. A. and Flynn, A. M.: Fast, cheap and out of control: A robot invasion of the solar system, J. British Interplanetary Soc. 42 (1989), 478–485.

    Google Scholar 

  8. Chen, Q. and Luh, J. Y. S.: Coordination and control of a group of small mobile robots, in: IEEE Internat. Conf. on Robotics and Automation, Vol. 3, 1994, pp. 2315–2320.

    Google Scholar 

  9. Chvatal, V.: Linear Programming, Freeman, New York, 1980.

    Google Scholar 

  10. Duston, B. M. and Chatterjee, C.: Multi-sensor combination for vehicle-based mine detection, in: Proc. of the SPIE, Vol. 3374, 1998, pp. 309–316.

    Google Scholar 

  11. Edmonds: Maximum matching and a polyhedron with 0,1-vertices, J. Res. Nat. Bur. Standards 65B (1965), 125–130.

    Google Scholar 

  12. Gabow, H.: Implementations of algorithms for maximum matching on nonbipartite graphs, PhD Thesis, Computer Science Department, Stanford University, 1973.

  13. Gabow, H.: An efficient implementation for Edmonds’ algorithm for maximum matching on graphs, J. Assoc. Comput. Mach. 23(2) (1976), 221–334.

    Google Scholar 

  14. Gabow, H.: Data structures for weighted matching and nearest common ancestors with linking, in: Proc. of the 1st ACM/SIAM Symposium on Discrete Algorithms, 1990, pp. 434–443.

  15. Healey, A. J. and Kim, J.: Modeling and simulation methodology for reconnaissance in VSW minefields with multiple autonomous vehicles, in: Proc. of the SPIE, Vol. 3711, 1999, pp. 184–194.

    Google Scholar 

  16. Ignizio, J. and Cavalier, T.: Linear Programming, Prentice-Hall, Englewood Cliffs, NJ, 1994.

    Google Scholar 

  17. Jun, J.-H., Lee, D.-W., and Sim, K.-B.: Realization of cooperative strategies and swarm behavior in distributed autonomous robotic systems using artificial immune system, in: IEEE Internat. Conf. on Systems, Man, and Cybernetics, Vol. 6, 1999, pp. 614–619.

    Google Scholar 

  18. Krieger, M. J. B., Billeter, J.-B., and Keller, L.: Ant-like task allocation and recruitment in cooperative robots, Nature 406 (2000), 992–995.

    Google Scholar 

  19. Kube, R. C. and Zhang, H.: Collective robotics: From social insects to robots, Adaptive Behavior 2(2) (1993), 189–218.

    Google Scholar 

  20. Kuc, R. and Barshan, B.: Bat-like sonar for guiding mobile robots, IEEE Control Systems 12(4) (1992), 4–12.

    Google Scholar 

  21. Leeuwen, J.: Graph algorithms, in: J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Vol. A, MIT Press, Cambridge, MA, 1990, pp. 525–632.

    Google Scholar 

  22. McMichael, D. W.: Data fusion for vehicle-borne mine detection, in: Eurel Internat. Conf., No. 431, 1996, pp. 167–171.

  23. Micali, S. and Vazirani, V.: An O(V E) algorithm for finding maximum matching in general graphs, in: Proc. of the 21st Annual IEEE Symposium on Foundations of Computer Science, 1980, pp. 17–27.

  24. Miyata et al.: Cooperative transport in unknown environment - application of real-time task assignment, IEEE Internat. Conf. on Robotics and Automation, Vol. 4, 2000, pp. 3176–3182.

    Google Scholar 

  25. Nelson, B. N., Gader, P. D., and Keller, J. M.: Fuzzy set information fusion in landmine detection, in: Proc. of the SPIE, Vol. 3710, 1999, pp. 1168–1178.

    Google Scholar 

  26. Noreils, F. R.: Toward a robot architecture integrating cooperation between mobile robots: Application to indoor environment, Internat. J. Robotics Res. 12(1) (1993), 79–98.

    Google Scholar 

  27. Orlin, J.: A polynomial-time primal network simplex algorithm for minimum cost flows, in: Proc. of the 7th Annual ACM/SIAM Symposium on Discrete Algorithms, 1996, pp. 474–481.

  28. Parker, L. E.: Current state of the art in distributed autonomous mobile robotics, in: Distributed Autonomous Robotic Systems 4, Springer, Berlin, 2000, pp. 3–12.

    Google Scholar 

  29. Reynolds, C. W.: Flocks, herds, and schools, Computer Graphics 21(4) (1987), 25–34.

    Google Scholar 

  30. Sokkalingam, P., Sharma, P., and Ahuja, R.: A new primal simplex algorithm for network flow problem, in: NET-FLOW’ 93, to appear in Mathematical Programming B.

  31. Spires, S. V. and Goldsmith, S. Y.: Exhaustive geographic search with mobile robots along space-filling curves, in: Proc. of the Collective Robotics Workshop, July 1998, pp. 1–12.

  32. Wein, J. and Zenios, S. A.: Massively parallel auction algorithms for the assignment problem, in: Proc. of the 3rd Symposium on Frontiers of Massively Parallel Computation, November 1990, pp. 90–99.

  33. Yamaguchi, H. and Arai, T.: Distributed and autonomous control method for generating shape of multiple mobile robot group, in: IEEE Internat. Conf. on Intelligent Robots and Systems, Vol. 2, 1994, pp. 800–807.

    Google Scholar 

  34. Yoshida, E., Arai, T., Ota, J., and Miki, T.: Effect of grouping in local communication system of multiple mobile robots, in: IEEE Internat. Conf. on Intelligent Robots and Systems, Vol. 2, 1994, pp. 808–815.

    Google Scholar 

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Authors and Affiliations

  1. Sandia National Laboratories, Albuquerque, NM, 87185-1003, U.S.A.

    Kwan S. Kwok, Brian J. Driessen & Cynthia A. Phillips

  2. Georgia Institute of Technology, Atlanta, GA, 30332, U.S.A.

    Craig A. Tovey

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  1. Kwan S. Kwok
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  2. Brian J. Driessen
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  3. Cynthia A. Phillips
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  4. Craig A. Tovey
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Kwok, K.S., Driessen, B.J., Phillips, C.A. et al. Analyzing the Multiple-target-multiple-agent Scenario Using Optimal Assignment Algorithms. Journal of Intelligent and Robotic Systems 35, 111–122 (2002). https://doi.org/10.1023/A:1020238115592

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