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Adaptive Path Planning for Multiple Vehicles with Bounded Curvature

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Robotics (SBR 2014 2014, ROBOCONTROL 2014, LARS 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 507))

Abstract

In this paper we introduce the k-Dynamic Dubins TSP with Neighborhoods (k-DDTSPN), the problem consisting of planning efficient paths among a set of target regions dynamically selected in the environment for multiple robots with bounded curvature (Dubins vehicle). We propose a decentralized auction-based technique, which uses a greedy constructive strategy to dynamically calculate the cost of insertion of the new region to each path and selects the one with the minimum impact on the length. We provide a formal analysis of the proposed technique, presenting an upper bound for the length of the longest tour. Several trials were executed in a simulated environment, allowing for a statistical investigation of the results.

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Notes

  1. 1.

    This is not a restriction of the method – just a convenience to keep reasoning, implementation, and results visualization simple. The methodology proposed in this paper covers continuous, convex regions in general.

References

  1. Applegate, D.L., Bixby, R.E., Chvatal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics). Princeton University Press, Princeton (2007)

    Google Scholar 

  2. Arkin, E.M., Hassin, R.: Approximation algorithms for the geometric covering salesman problem. Discrete Appl. Math. 55, 197–218 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bhadauria, D., Tekdas, O., Isler, V.: Robotic data mules for collecting data over sparse sensor fields. J. Field Robot. 28(3), 388–404 (2011)

    Article  MATH  Google Scholar 

  4. Choi, H.L., Brunet, L., How, J.: Consensus-based decentralized auctions for robust task allocation. IEEE Trans. Robot. 25(4), 912–926 (2009)

    Article  Google Scholar 

  5. Comarela, G., Gonçalves, K., Pappa, G.L., Almeida, J., Almeida, V.: Robot routing in sparse wireless sensor networks with continuous ant colony optimization. In: Proceedings of the 13th Annual Conference Companion on Genetic and Evolutionary Computation (GECCO’ 2011), pp. 599–606. ACM, New York (2011)

    Google Scholar 

  6. Concorde TSP Solver (2013). http://www.tsp.gatech.edu/concorde/index.html. Accessed 17-10-2013

  7. Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manage. Sci. 6(1), 80–91 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dias, M.B., Zlot, R., Kalra, N., Stentz, A.: Market-based multirobot coordination: a survey and analysis. Proc. IEEE 94(7), 1257–1270 (2006)

    Article  Google Scholar 

  9. Dubins, L.E.: On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am. J. Math. 79(3), 497–516 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  10. Enright, J.J., Savla, K., Frazzoli, E., Bullo, F.: Stochastic and dynamic routing problems for multiple UAVs. AIAA J. Guidance, Control, Dyn. 32(4), 1152–1166 (2009)

    Google Scholar 

  11. Isaacs, J.T., Klein, D.J., Hespanha, J.P.: Algorithms for the traveling salesman problem with neighborhoods involving a dubins vehicle. In: Proceedings of the IEE American Control Conference (ACC’ 2011), pp. 1704–1709 (2011)

    Google Scholar 

  12. Larsen, A., Madsen, O.B., Solomon, M.M.: Recent developments in dynamic vehicle routing systems. In: Golden, B., Raghavan, S., Wasil, E., Sharda, R., Voß, S. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges, Operations Research/Computer Science Interfaces Series, vol. 43, pp. 199–218. Springer, US (2008)

    Chapter  Google Scholar 

  13. Le Ny, J., Frazzoli, E., Feron, E.: The curvature-constrained traveling salesman problem for high point densities. In: Proceedings of the 46th IEEE Conference on Decision and Control (CDC’ 2007), pp. 5985–5990 (2007)

    Google Scholar 

  14. Ma, X., Castañón, D.A.: Receding horizon planning for dubins traveling salesman problems. In: Proceedings of the 45th IEEE Conference on Decision and Control (CDC’ 2006), pp. 5453–5458 (2006)

    Google Scholar 

  15. Macharet, D.G., Alves Neto, A., da Camara Neto, V.F., Campos, M.F.M.: An evolutionary approach for the Dubins’ traveling salesman problem with neighborhoods. In: Proceedings of the 21th Genetic and Evolutionary Computation Conference (2012)

    Google Scholar 

  16. Macharet, D.G., Alves Neto, A., da Camara Neto, V.F., Campos, M.F.M.: Efficient target visiting path planning for multiple vehicles with bounded curvature. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3830–3836 (2013)

    Google Scholar 

  17. Michael, N., Zavlanos, M., Kumar, V., Pappas, G.: Distributed multi-robot task assignment and formation control. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA’ 2008), pp. 128–133 (2008)

    Google Scholar 

  18. Obermeyer, K.J., Oberlin, P., Darbha, S.: Sampling-based roadmap methods for a visual reconnaissance UAV. In: Proceedings of the AIAA Conference on Guidance, Navigation and Control, Toronto, ON, Canada (2010)

    Google Scholar 

  19. Rathinam, S., Sengupta, R., Darbha, S.: A resource allocation algorithm for multivehicle systems with nonholonomic constraints. IEEE Trans. Autom. Sci. Eng. 4(1), 98–104 (2007)

    Article  Google Scholar 

  20. Savla, K., Bullo, F., Frazzoli, E.: On traveling salesperson problems for Dubins’ vehicle: stochastic and dynamic environments. In: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC’ 2005), pp. 4530–4535 (2005)

    Google Scholar 

  21. Savla, K., Frazzoli, E., Bullo, F.: On the point-to-point and traveling salesperson problems for Dubins’ vehicle. In: Proceedings of the IEE American Control Conference (ACC’ 2005), vol. 2, pp. 786–791 (2005)

    Google Scholar 

  22. Savla, K., Frazzoli, E., Bullo, F.: Traveling salesperson problems for the Dubins vehicle. IEEE Trans. Autom. Control 53(6), 1378–1391 (2008)

    Article  MathSciNet  Google Scholar 

  23. Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)

    Article  MathSciNet  Google Scholar 

  24. Solomon, M.M.: Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35(2), 254–265 (1987). http://dx.doi.org/10.1287/opre.35.2.254

  25. Tang, Z., Özgüner, Ü.: Motion planning for multitarget surveillance with mobile sensor agents. IEEE Trans. Robot. 21(5), 898–908 (2005)

    Article  Google Scholar 

  26. Tekdas, O., Isler, V., Lim, J., Terzis, A.: Using mobile robots to harvest data from sensor fields. IEEE Wireless Commun. 16(1), 22–28 (2009)

    Article  Google Scholar 

  27. Toth, P., Vigo, D. (eds.): The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia (2001)

    Google Scholar 

  28. Yuan, B., Orlowska, M., Sadiq, S.: On the optimal robot routing problem in wireless sensor networks. IEEE Trans. Knowl. Data Eng. 19(9), 1252–1261 (2007)

    Article  Google Scholar 

  29. Zavlanos, M., Spesivtsev, L., Pappas, G.: A distributed auction algorithm for the assignment problem. In: Proceedings of the 47th IEEE Conference on Decision and Control (CDC’ 2008), pp. 1212–1217 (2008)

    Google Scholar 

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Acknowledgments

This work was developed with the support of the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG).

Author information

Authors and Affiliations

  1. Computer Vision and Robotics Laboratory, Computer Science Department, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil

    Douglas G. Macharet & Mario F. M. Campos

Authors
  1. Douglas G. Macharet
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  2. Mario F. M. Campos
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Corresponding author

Correspondence to Douglas G. Macharet .

Editor information

Editors and Affiliations

  1. Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Fernando S. Osório

  2. Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Denis Fernando Wolf

  3. Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Kalinka Castelo Branco

  4. Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Valdir Grassi Jr.

  5. Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Marcelo Becker

  6. Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Roseli Romero

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Macharet, D.G., Campos, M.F.M. (2015). Adaptive Path Planning for Multiple Vehicles with Bounded Curvature. In: Osório, F., Wolf, D., Castelo Branco, K., Grassi Jr., V., Becker, M., Romero, R. (eds) Robotics. SBR 2014 ROBOCONTROL LARS 2014 2014 2014. Communications in Computer and Information Science, vol 507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48134-9_9

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  • DOI: https://doi.org/10.1007/978-3-662-48134-9_9

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  • Print ISBN: 978-3-662-48133-2

  • Online ISBN: 978-3-662-48134-9

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