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DARP: Divide Areas Algorithm for Optimal Multi-Robot Coverage Path Planning

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Abstract

This paper deals with the path planning problem of a team of mobile robots, in order to cover an area of interest, with prior-defined obstacles. For the single robot case, also known as single robot coverage path planning (CPP), an 𝓞(n) optimal methodology has already been proposed and evaluated in the literature, where n is the grid size. The majority of existing algorithms for the multi robot case (mCPP), utilize the aforementioned algorithm. Due to the complexity, however, of the mCPP, the best the existing mCPP algorithms can perform is at most 16 times the optimal solution, in terms of time needed for the robot team to accomplish the coverage task, while the time required for calculating the solution is polynomial. In the present paper, we propose a new algorithm which converges to the optimal solution, at least in cases where one exists. The proposed technique transforms the original integer programming problem (mCPP) into several single-robot problems (CPP), the solutions of which constitute the optimal mCPP solution, alleviating the original mCPP explosive combinatorial complexity. Although it is not possible to analytically derive bounds regarding the complexity of the proposed algorithm, extensive numerical analysis indicates that the complexity is bounded by polynomial curves for practical sized inputs. In the heart of the proposed approach lies the DARP algorithm, which divides the terrain into a number of equal areas each corresponding to a specific robot, so as to guarantee complete coverage, non-backtracking solution, minimum coverage path, while at the same time does not need any preparatory stage (video demonstration and standalone application are available on-line http://tinyurl.com/DARP-app).

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References

  1. irobot web site. http://www.irobot.com. Accessed: 2016-4-1

  2. Mixed integer linear programming (milp) solver, software. http://lpsolve.sourceforge.net/. Accessed: 2016-4-1

  3. The area partitioning problem. In: Proceedings of the 12th Canadian Conference on Computational Geometry, Fredericton, New Brunswick, Canada (2000)

  4. Acar, E., Zhang, Y., Choset, H., Schervish, M., Costa, A.G., Melamud, R., Lean, D.C., Graveline, A.: Path planning for robotic demining and development of a test platform. In: International Conference on Field and Service Robotics, vol. 1, pp 161–168 (2001)

  5. Agmon, N., Hazon, N., Kaminka, G., et al.: Constructing spanning trees for efficient multi-robot coverage. In: Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006, pp 1698–1703. IEEE (2006)

  6. Apostolopoulos, D.S., Pedersen, L., Shamah, B.N., Shillcutt, K., Wagner, M.D., Whittaker, W.L.: Robotic antarctic meteorite search: outcomes. In: IEEE International Conference on Robotics and Automation, 2001. Proceedings 2001 ICRA, vol. 4, pp 4174–4179. IEEE (2001)

  7. Aurenhammer, F.: Voronoi diagrams—a survey of a fundamental geometric data structure. ACM Comput. Surv. (CSUR) 23(3), 345–405 (1991)

    Article  Google Scholar 

  8. Barrientos, A., Colorado, J., del Cerro, J., Martinez, A., Rossi, C., Sanz, D., Valente, J.: Aerial remote sensing in agriculture: a practical approach to area coverage and path planning for fleets of mini aerial robots. J. Field Rob. 28(5), 667–689 (2011)

    Article  Google Scholar 

  9. Breitenmoser, A., Schwager, M., Metzger, J.-C., Siegwart, R., Rus, D.: Voronoi coverage of non-convex environments with a group of networked robots. In: IEEE International Conference on Robotics and Automation (ICRA), 2010, pp 4982–4989. IEEE (2010)

  10. Butler, Z.J., Rizzi, A.A., Hollis, R.L.: Contact sensor-based coverage of rectilinear environments. In: Proceedings of the 1999 IEEE International Symposium on Intelligent Control/Intelligent Systems and Semiotics, 1999, pp 266–271. IEEE (1999)

  11. Choset, H.: Coverage for robotics–a survey of recent results. Ann. Math. Artif. Intell. 31(1–4), 113–126 (2001)

    Article  MATH  Google Scholar 

  12. Cortés, J.: Coverage optimization and spatial load balancing by robotic sensor networks. IEEE Trans. Autom. Control 55(3), 749–754 (2010)

    Article  MathSciNet  Google Scholar 

  13. Cortes, J., Martinez, S., Karatas, T., Bullo, F.: Coverage control for mobile sensing networks. In: IEEE International Conference on Robotics and Automation, 2002. Proceedings. ICRA’02, vol. 2, pp 1327–1332. IEEE (2002)

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

    Article  Google Scholar 

  15. Du, Q., Emelianenko, M., Ju, L.: Convergence of the lloyd algorithm for computing centroidal voronoi tessellations. SIAM J. Numer. Anal. 44(1), 102–119 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Durham, J.W., Carli, R., Frasca, P., Bullo, F.: Discrete partitioning and coverage control for gossiping robots. IEEE Trans. Robot. 28(2), 364–378 (2012)

    Article  Google Scholar 

  17. Elmaliach, Y., Agmon, N., Kaminka, G.A.: Multi-robot area patrol under frequency constraints. Ann. Math. Artif. Intell. 57(3-4), 293–320 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. 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  MATH  Google Scholar 

  19. Galceran, E., Carreras, M.: A survey on coverage path planning for robotics. Robot. Auton. Syst. 61(12), 1258–1276 (2013)

    Article  Google Scholar 

  20. Goldberg, K.: Robotics: countering singularity sensationalism. Nature 526(7573), 320–321 (2015)

    Article  Google Scholar 

  21. Hazon, N., Kaminka, G., et al.: Redundancy, efficiency and robustness in multi-robot coverage. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 2005. ICRA 2005, pp 735–741. IEEE (2005)

  22. Kapoutsis, A., Chatzichristofis, S.A., Doitsidis, L., de Sousa, J.B., Kosmatopoulos, E.B., et al.: Autonomous navigation of teams of unmanned aerial or underwater vehicles for exploration of unknown static & dynamic environments. In: 21st Mediterranean Conference on Control & Automation (MED), 2013, pp 1181–1188. IEEE (2013)

  23. Kapoutsis, A. Ch., Chatzichristofis, S.A., Doitsidis, L., de Sousa, J.B., Pinto, J., Braga, J., Kosmatopoulos, E.B.: Real-time adaptive multi-robot exploration with application to underwater map construction. Auton. Robot. 40(6), 987–1015 (2016)

    Article  Google Scholar 

  24. Lloyd, S.P.: Least squares quantization in pcm. IEEE Trans. Inf. Theory 28(2), 129–137 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  25. Maza, I., Ollero, A.: Multiple uav cooperative searching operation using polygon area decomposition and efficient coverage algorithms. In: Distributed Autonomous Robotic Systems 6, pp 221–230. Springer (2007)

  26. Moloney, D., Suarez, O.D.: A vision for the future [soapbox]. IEEE Consumer Electronics Magazine 4(2), 40–45 (2015)

    Article  Google Scholar 

  27. Nandakumar, R., Ramana Rao, N.: Fair partitions of polygons: an elementary introduction. Proc. Math. Sci. 122(3), 459–467 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Ollis, M., Stentz, A.: Vision-based perception for an automated harvester. In: Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robots and Systems, 1997. IROS’97, vol. 3, pp 1838–1844. IEEE (1997)

  29. Puig, D., García, M.A., Wu, L.: A new global optimization strategy for coordinated multi-robot exploration: development and comparative evaluation. Robot. Auton. Syst. 59(9), 635–653 (2011)

    Article  Google Scholar 

  30. Rubinstein, A.: Perfect equilibrium in a bargaining model. Econometrica: Journal of the Econometric Society, 97–109 (1982)

  31. Scaramuzza, D., Achtelik, M.C., Doitsidis, L., Fraundorfer, F., Kosmatopoulos, E.B., Martinelli, A., Achtelik, M.W., Chli, M., Chatzichristofis, S.A., Kneip, L., et al.: Vision-controlled micro flying robots: from system design to autonomous navigation and mapping in gps-denied environments. IEEE Robot. Autom. Mag., 1–10 (2014)

  32. Schwager, M., Rus, D., Slotine, J.-J.: Decentralized, adaptive coverage control for networked robots. Int. J. Robot. Res. 28(3), 357–375 (2009)

    Article  Google Scholar 

  33. Tarjan, R.E.: Data Structures and Network Algorithms, vol. 14. SIAM (1983)

  34. Waharte, S., Trigoni, N.: Supporting search and rescue operations with uavs. In: International Conference on Emerging Security Technologies (EST), 2010, pp 142–147. IEEE (2010)

  35. Wright, S.J.: Coordinate descent algorithms. Math. Program. 151(1), 3–34 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  36. Xu, A., Viriyasuthee, C., Rekleitis, I.: Efficient complete coverage of a known arbitrary environment with applications to aerial operations. Auton. Robot. 36(4), 365–381 (2014)

    Article  Google Scholar 

  37. Xu, Y., Yin, W.: A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion. SIAM J. Imag. Sci. 6(3), 1758–1789 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  38. Yao, Z.: Finding efficient robot path for the complete coverage of a known space. In: 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp 3369–3374. IEEE (2006)

  39. Zheng, X., Jain, S., Koenig, S., Kempe, D.: Multi-robot forest coverage. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005. (IROS 2005). 2005, pp 3852–3857. IEEE (2005)

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Acknowledgments

This project is funded by the European Commission (FIRE+ challenge, Horizon 2020) that aims to provide for research, technological development and demonstration under grant agreement no 645220 (RAWFIE)

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Greece

    Athanasios Ch. Kapoutsis, Savvas A. Chatzichristofis & Elias B. Kosmatopoulos

  2. Information Technologies Institute, CERTH, Thessaloniki, Greece

    Athanasios Ch. Kapoutsis, Savvas A. Chatzichristofis & Elias B. Kosmatopoulos

Authors
  1. Athanasios Ch. Kapoutsis
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  2. Savvas A. Chatzichristofis
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  3. Elias B. Kosmatopoulos
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Correspondence to Athanasios Ch. Kapoutsis.

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Kapoutsis, A.C., Chatzichristofis, S.A. & Kosmatopoulos, E.B. DARP: Divide Areas Algorithm for Optimal Multi-Robot Coverage Path Planning. J Intell Robot Syst 86, 663–680 (2017). https://doi.org/10.1007/s10846-016-0461-x

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