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A framework for multi-robot node coverage in sensor networks

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Abstract

Area coverage is a well-known problem in robotics. Extensive research has been conducted for the single robot coverage problem in the past decades. More recently, the research community has focused its attention on formulations where multiple robots are considered. In this paper, a new formulation of the multi-robot coverage problem is proposed. The novelty of this work is the introduction of a sensor network, which cooperates with the team of robots in order to provide coordination. The sensor network, taking advantage of its distributed nature, is responsible for both the construction of the path and for guiding the robots. The coverage of the environment is achieved by guaranteeing the reachability of the sensor nodes by the robots. Two distributed algorithms for path construction are discussed. The first aims to speed up the construction process exploiting a concurrent approach. The second aims to provide an underlying structure for the paths by building a Hamiltonian path and then partitioning it. A statistical analysis has been performed to show the effectiveness of the proposed algorithms. In particular, three different indexes of quality, namely completeness, fairness, and robustness, have been studied.

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References

  1. Arkin, E., Fekete, S., Mitchell, J.: The lawnmower problem. In: 5th Canadian Conf. on Computational Geometry, Waterloo, August 1993

  2. Colegrave, J., Branch, A.: A case study of autonomous household vacuum cleaner. In: AIAA/NASA CIRFFSS, Houston, 20–24 March 1994

  3. Gage, D.W.: Randomized search strategies with imperfect sensors. In: Chun, W.H., Wolfe, W.J. (eds.) Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, Mobile Robots VIII, vol. 2058, pp. 270–279, Society of Photo-Optical Instrumentation Engineers, Bellingham, Feb. 1994

  4. Pearce, A.L., Rybski, P.E., Stoeter, S.A., Papanikolopoulos, N.: Dispersion behaviors for a team of multiple miniature robots. In: International Conference on Robotics and Automation, ICRA-2003, pp. 1158–1163, Taipei, September 2003

  5. Choset, H.: Coverage for robotics—a survey of recent results. Ann. Math. Artif. Intell. 31(1), 113–126 (2001)

    Article  Google Scholar 

  6. Arkin, E.M., Fekete, S.P., Mitchell, J.S.B.: Approximation algorithms for lawn mowing and milling. Comput. Geom. 17(1–2), 25–50 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Choset, H.: Coverage for robotics—a survey of recent results. Ann. Math. Artif. Intell. 31, 113–126 (2001)

    Article  Google Scholar 

  8. Gabriely, Y., Rimon, E.: Spanning-tree based coverage of continuous areas by a mobile robot. Ann. Math. Artif. Intell. 31(1–4), 77–98 (2001)

    Article  Google Scholar 

  9. Hazon, N., Kaminka, G.A.: Redundancy, efficiency, and robustness in multi-robot coverage. In: ICRA 2005, Barcelona, 18–22 April 2005

  10. Agmon, N., Hazon, N., Kaminka, G.A.: Constructing spanning trees for efficient multi-robot coverage. In: ICRA 2006, Orlando, 15–19 May 2006

  11. Kong, C.S., Peng, N.A., Rekleitis, I.: Distributed coverage with multi-robot system. In: IEEE International Conference on Robotics and Automation, ICRA-2006, pp. 2423–2429, Orlando, May 2006

  12. Shuzhi, S.G., Fua, C.: Complete multi-robot coverage of unknown environments with minimum repeated coverage. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp. 715–720, Barcelona, 18–22 April 2005

  13. Rogge, J., Aeyels, D.: A novel strategy for exploration with multiple robots. In: Proceedings of the 4th International Conference on Informatics in Control, Automation and Robotics, Angers (2007)

  14. Rekleitis, I., Lee-Shue, V., New, A.P., Choset, H.: Limited communication, multi-robot team based coverage. In: International Conference on Robotics and Automation, 2004. Proceedings, ICRA ‘04. 2004 IEEE, vol. 4, pp. 3462–3468. IEEE, Piscataway (2004)

  15. Kurabayashi, D., Ota, J., Yoshida, E.: An algorithm of dividing a work area to multiple mobile robots. In: IROS ’95: Proceedings of the International Conference on Intelligent Robots and Systems, vol. 2, p. 2286. IEEE Computer Society, Washington, DC (1995)

  16. Min, T.W., Yin, H.K.: A decentralized approach for cooperative sweeping by multiple mobile robots. In: International Conference on Intelligent Robots and Systems, 1998. Proceedings, 1998 IEEE/RSJ, pp. 380–385. IEEE, Piscataway (1998)

  17. Butler, Z., Rizzi, A., Hollis, R.: Distributed coverage of rectilinear environments. In: Peters, A.K. (eds.) Proc. of the Workshop on the Algorithmic Foundations of Robotics, January 2001

  18. Zheng, X., Jain, S., Koenig, S., Kempe, D.: Multi-robot forest coverage. In: IROS 2005, Edmonton, 2–6 August 2005

  19. Wagner, I., Lindenbaum, M., Bruckstein, A.: Distributed covering by ant-robots using evaporating traces. IEEE Trans. Robot. Autom. 15(5), 918–933 (1999)

    Article  Google Scholar 

  20. Batalin, M., Sukhatme, G.: Spreading out: a local approach to multi-robot coverage. In: 6th International Symposium on Distributed Autonomous Robotic Systems, pp. 373–382 (2002)

  21. Chaomin, L., Yang, S.: A real-time cooperative sweeping strategy for multiple cleaning robots. In: Proceedings of the 2002 IEEE International Symposium on Intelligent Control, pp. 660–665. IEEE, Piscataway (2002)

  22. Acar, E.U., Choset, H.: Sensor-based coverage of unknown environments: incremental construction of morse decompositions. Int. J. Rob. Res. 21(4), 345–366 (2002)

    Article  Google Scholar 

  23. Choset, H., Pignon, P.: Coverage path planning: the boustrophedon cellular decomposition. In: International Conference on Field and Service Robotics, Canberra, Australia (1997)

  24. Butler, Z., Rizzi, A., Hollis, R.: Contact sensor-based coverage of rectilinear environments. In: IEEE Int’l Symposium on Intelligent Control, September 1999, pp. 266–271. IEEE, Piscataway (1999)

  25. Bang-Jensen, J., Gutin, G. (eds.): Digraphs: Theory, Algorithms and Applications. Springer Monographs in Mathematics. Springer, London (2000)

    Google Scholar 

  26. Volgenant, T., Jonker, R.: A branch and bound algorithm for the symmetric traveling salesman problem based on the 1-tree relaxation. Eur. J. Oper. Res. 9, 83–89 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  27. Diaby, M.: The traveling salesman problem: a linear programming formulation. WSEAS Trans. Math. 6(6), 745–754 (2007)

    MATH  MathSciNet  Google Scholar 

  28. Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulation of traveling salesman problems. J. ACM 7(4), 326–329 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  29. Karg, L.L., Thompson, G.L.: A heuristic approach to traveling salesman problems. Manage. Sci. 10, 225–248 (1964)

    Article  Google Scholar 

  30. Rosenkrantz, D., Stearns, R., Lewis, P.: An analysis of several heuristics for the traveling salesman problem. SIAM J. Comput. 6(3), 563–581 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  31. Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. Graduate School of Industrial Administration, CMU, Tech. Rep. 388 (1976)

  32. Clarke, G., Wright, G.: Scheduling of vehicles from a central depot to number of delivery points. Oper. Res. 12, 568–581 (1964)

    Article  Google Scholar 

  33. Bock, F.: An algorithm for solving traveling-salesman and related network optimization problems. Unpublished Manuscript Associated with Talk Presented at the 14th ORSA National Meeting (1965)

  34. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  35. Muhlenbein, H., Georges-Schleuter, M., Kramer, O.: Evolution algorithms in combinatorial optimization. Parallel Comput. 7, 65–85 (1988)

    Article  Google Scholar 

  36. Budinich, M.: Neural networks for the travelling salesman problem. J. Artif. Neural Netw. 2(4), 431–435 (1995)

    MathSciNet  Google Scholar 

  37. Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1(1), 53–66 (1997)

    Article  Google Scholar 

  38. Allwright, J., Carpenter, D.: A distributed implementation of simulated annealing for the traveling salesman problem. Parallel Comput. 10, 335–338 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  39. Sena, G.A., Megherbi, D., Isern, G.: Implementation of a parallel genetic algorithm on a cluster of workstations: traveling salesman problem, a case study. Future Gener. Comput. Syst. 17(4), 477–488 (2001)

    Article  MATH  Google Scholar 

  40. Tschöke, S., Lüling, R., Monien, B.: Solving the traveling salesman problem with a distributed branch-and-bound algorithm on a 1024 processor network. In: IPPS ’95: Proceedings of the 9th International Symposium on Parallel Processing, pp. 182–189. IEEE Computer Society, Washington, DC (1995)

  41. Bektas, T.: The multiple traveling salesman problem: an overview of formulations and solution procedures. Omega Int. J. Manag. Sci. 34(3), 209–219 (2006)

    Article  Google Scholar 

  42. Batalin, M., Sukhatme, G.S.: Coverage, exploration and deployment by a mobile robot and communication network. Telecommun. Syst. J. 26(2), 181–196 (2004) (special issue on Wireless Sensor Networks)

    Article  Google Scholar 

  43. Batalin, M., Sukhatme, G.S.: 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 (2007)

    Article  Google Scholar 

  44. Gasparri, A., Panzieri, S., Pascucci, F., Ulivi, G.: An interlaced kalm filter for sensors networks localization. Int. J. Sens. Netw. (IJSNet) (2007) (special issue on Interdisciplinary Design of Algorithms and Protocols in Wireless Sensor Networks)

  45. Beasley, J.: Route first—cluster second methods for vehicle routing. Omega 11(4), 403–408 (1983)

    Article  Google Scholar 

  46. Kim, Y., Govindan, R., Karp, B., Shenker, S.: Geographic routing made practical. In: NSDI’05: Proceedings of the 2nd Conference on Symposium on Networked Systems Design & Implementation, pp. 16–16. USENIX Association, Berkeley (2005)

  47. Kim, Y.J., Govindan, R., Karp, B., Shenker, S.: Lazy cross-link removal for geographic routing. In: Proceedings of the ACM Conference on Embedded Networked Sensor Systems (Sensys), Boulder, November 2006

  48. Laporte, G.: Generalized subtour elimination constraints and connectivity constraints. J. Oper. Res. Soc. 37(5), 509–514 (1986)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Dip. di Informatica e Automazione, Università “Roma Tre”, Via della Vasca Navale, 79, 00146, Rome, Italy

    Andrea Gasparri

  2. Department of Electrical Engineering, University of Southern California, Los Angeles, CA, 90007, USA

    Bhaskar Krishnamachari

  3. Robotic Embedded Systems Laboratory, University of Southern California, Los Angeles, CA, 90089, USA

    Gaurav S. Sukhatme

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  1. Andrea Gasparri
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  2. Bhaskar Krishnamachari
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  3. Gaurav S. Sukhatme
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Correspondence to Andrea Gasparri.

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Gasparri, A., Krishnamachari, B. & Sukhatme, G.S. A framework for multi-robot node coverage in sensor networks. Ann Math Artif Intell 52, 281–305 (2008). https://doi.org/10.1007/s10472-009-9126-9

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