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Path Planning on Hierarchical Bundles with Differential Evolution

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10941))

Abstract

Computing hierarchical routing networks in polygonal maps is significant to realize the efficient coordination of agents, robots and systems in general; and the fact of considering obstacles in the map, makes the computation of efficient networks a relevant need for cluttered environments. In this paper, we present an approach to compute the minimal-length hierarchical topologies in polygonal maps by Differential Evolution and Route Bundling Concepts. Our computational experiments in scenarios considering convex and non-convex configuration of polygonal maps show the feasibility of the proposed approach.

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References

  1. Chazelle, B.: A theorem on polygon cutting with applications. In: Proceedings of 23rd IEEE Symposium on Foundations of Computer Science, pp. 339–349 (1982)

    Google Scholar 

  2. Chiang, H.T., Malone, N., Lesser, K., Oishi, M., Tapia, L.: Path-guided artificial potential fields with stochastic reachable sets for motion planning in highly dynamic environments, pp. 2347–2354, May 2015

    Google Scholar 

  3. Chow, W., Li, L., Young, E., Sham, C.: Obstacle-avoiding rectilinear Steiner tree construction in sequential and parallel approach. Integr. VLSI J. 47, 105–114 (2014)

    Article  Google Scholar 

  4. Cormen, T., Leiserson, C., Rivest, R.: Introduction to Algorithms. MIT Press, Cambridge (1993)

    MATH  Google Scholar 

  5. Cui, W., Zhou, H., Qu, H., Wong, P.C., Li, X.: Geometry-based edge clustering for graph visualization. IEEE Trans. Visual. Comput. Graph. 14, 1277–1284 (2008)

    Article  Google Scholar 

  6. Davoodi, M., Panahi, F., Mohades, A., Hashemi, S.N.: Clear and smooth path planning. Appl. Soft Comput. 32, 568–579 (2015)

    Article  Google Scholar 

  7. Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)

    Article  MathSciNet  Google Scholar 

  8. Duan, H., Huang, L.: Imperialist competitive algorithm optimized artificial neural networks for UCAV global path planning. Neurocomputing, 125, 166–171 (2014). Advances in Neural Network Research and Applications Advances in Bio-Inspired Computing: Techniques and Applications

    Article  Google Scholar 

  9. exedesign: Factory. http://www.blendswap.com/blends/view/55233

  10. Gansner, E.R., Hu, Y., North, S., Scheidegger, C.: Multilevel agglomerative edge bundling for visualizing large graphs. In: IEEE Pacific Visualization Symposium, pp. 187–194 (2011)

    Google Scholar 

  11. Ghita, N., Kloetzer, M.: Trajectory planning for a car-like robot by environment abstraction. Robot. Auton. Syst. 60(4), 609–619 (2012)

    Article  Google Scholar 

  12. Holten, D.: Hirerarchical edge bundles: visualization of adjacency relations in hierarchical data. In: IEEE Pacific Visualization Symposium, pp. 187–194 (2006)

    Article  Google Scholar 

  13. Holten, D., van Wijk, J.J.: Force-directed edge bundling for graph visualization. In: Eurographics, Symposium on Visualization (2009)

    Article  Google Scholar 

  14. Jing, T.T., Hu, Y., Feng, Z., Hong, X., Hu, X., Yan, G.: A full-scale solution to the rectilinear obstacle-avoiding Steiner problem. Integr. VLSI J. 41, 413–425 (2008)

    Article  Google Scholar 

  15. Kavraki, L.E., Svestka, P., Latombe, J.C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. Robot. Autom. 12(4), 566–580 (1996)

    Article  Google Scholar 

  16. LaValle, S.M.: Rapidly-exploring random trees: a new tool for path planning. Technical report. Computer Science Department, Iowa State University (TR 98–11)

    Google Scholar 

  17. LaValle, S.M., Kuffner Jr., J.J.: Rapidly-exploring random trees: progress and prospects (2000)

    Google Scholar 

  18. Lee, D.T., Preparata, F.P.: Euclidean shortest paths in the presence of rectilinear barriers. Networks 14(3), 393–410 (1984)

    Article  MathSciNet  Google Scholar 

  19. Lozano-Pérez, T., Wesley, M.A.: An algorithm for planning collision-free paths among polyhedral obstacles. Commun. ACM 22(10), 560–570 (1979)

    Article  Google Scholar 

  20. LWP23D: Game map: Factory. https://www.blendswap.com/blends/view/81600

  21. Mac, T.T., Copot, C., Tran, D.T., Keyser, R.D.: A hierarchical global path planning approach for mobile robots based on multi-objective particle swarm optimization. Appl. Soft Comput. 59, 68–76 (2017)

    Article  Google Scholar 

  22. Mohanan, M., Salgoankar, A.: A survey of robotic motion planning in dynamic environments. Robot. Auton. Syst. 100, 171–185 (2018)

    Article  Google Scholar 

  23. Müller-Hannemann, M., Tazari, S.: A near linear time approximation scheme for Steiner tree among obstacles in the plane. Comput. Geom. Theory Appl. 43, 395–409 (2010)

    Article  MathSciNet  Google Scholar 

  24. Parque, V., Kobayashi, M., Higashi, M.: Bijections for the numeric representation of labeled graphs. In: IEEE International Conference on Systems, Man and Cybernetics, pp. 447–452 (2014)

    Google Scholar 

  25. Parque, V., Kobayashi, M., Higashi, M.: Searching for machine modularity using Explorit. In: IEEE International Conference on Systems, Man and Cybernetics, pp. 2599–2604 (2014)

    Google Scholar 

  26. Parque, V., Miura, S., Miyashita, T.: Optimization of route bundling via differential evolution with a convex representation. In: 2017 IEEE International Conference on Real-time Computing and Robotics (RCAR), pp. 727–732, July 2017

    Google Scholar 

  27. Parque, V., Miyashita, T.: On k-subset sum using enumerative encoding. In: IEEE International Symposium on Signal Processing and Information Technology, pp. 81–86 (2016)

    Google Scholar 

  28. Parque, V., Miyashita, T.: On succinct representation of directed graphs. In: IEEE International Conference on Big Data and Smart Computing, pp. 199–205 (2017)

    Google Scholar 

  29. Parque, V., Kobayashi, M., Higashi, M.: Optimisation of bundled routes. In: 16th International Conference on Geometry and Graphics, pp. 893–902 (2014)

    Google Scholar 

  30. Parque, V., Kobayashi, M., Higashi, M.: Neural computing with concurrent synchrony. In: Loo, C.K., Yap, K.S., Wong, K.W., Teoh, A., Huang, K. (eds.) ICONIP 2014, Part I. LNCS, vol. 8834, pp. 304–311. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12637-1_38

    Chapter  Google Scholar 

  31. Parque, V., Miura, S., Miyashita, T.: Computing path bundles in bipartite networks. In: 7th International Conference on Simulation and Modelling Methodologies, Technologies and Applications, pp. 422–427, Madrid, Spain (2017)

    Google Scholar 

  32. Parque, V., Miura, S., Miyashita, T.: Route bundling in polygonal domains using differential evolution. Robot. Biomimetics 4(1), 22 (2017)

    Article  Google Scholar 

  33. Parque, V., Miyashita, T.: Bundling n-Stars in polygonal maps. In: 29th IEEE International Conference on Tools with Artificial Intelligence, 6–8 November, Boston, USA (2017)

    Google Scholar 

  34. Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)

    Article  Google Scholar 

  35. Robbins, H., Courant, R.: What is Mathematics?. Oxford University Press, Oxford (1941)

    MATH  Google Scholar 

  36. Šter, B.: An integrated learning approach to environment modelling in mobile robot navigation. Neurocomputing 57, 215–238 (2004). New Aspects in Neurocomputing: 10th European Symposium on Artificial Neural Networks 2002

    Google Scholar 

  37. Selassie, D., Heller, B., Heer, J.: Divided edge bundling for directional network data. IEEE Trans. Visual. Comput. Graph. 17(12), 2354–2363 (2011)

    Article  Google Scholar 

  38. Souissi, O., Benatitallah, R., Duvivier, D., Artiba, A., Belanger, N., Feyzeau, P.: Path planning: a 2013 survey. In: Proceedings of 2013 International Conference on Industrial Engineering and Systems Management (IESM), pp. 1–8, October 2013

    Google Scholar 

  39. Vojtěch, J., Kössler, M.: O minimálních grafech, obsahujících \(n\) daných bodů. Časopis pro pěstování matematiky a fysiky 063(8), 223–235 (1934)

    Google Scholar 

  40. Wang, M., Luo, J., Fang, J., Yuan, J.: Optimal trajectory planning of free-floating space manipulator using differential evolution algorithm. Adv. Space Res. 61(6), 1525–1536 (2018)

    Article  Google Scholar 

  41. Winter, P.: Euclidean Steiner minimal trees with obstacles and Steiner visibility graphs. Discrete Appl. Math. 47, 187–206 (1993)

    Article  MathSciNet  Google Scholar 

  42. Winter, P., Zachariasen, M., Nielsen, J.: Short trees in Polygons. Discrete Appl. Math. 118, 55–72 (2002)

    Article  MathSciNet  Google Scholar 

  43. Zhang, H., Ye, D., Guo, W.: A heuristic for constructing a rectilinear Steiner tree by reusing routing resources over obstacles. Integr. VLSI J. 55, 162–175 (2016)

    Article  Google Scholar 

  44. Zhang, X., Chen, J., Xin, B., Fang, H.: Online path planning for UAV using an improved differential evolution algorithm. IFAC Proc. Vol. 44(1), 6349–6354 (2011). 18th IFAC World Congress

    Article  Google Scholar 

  45. Zhang, Y., Gong, D.W., Zhang, J.H.: Robot path planning in uncertain environment using multi-objective particle swarm optimization. Neurocomputing 103, 172–185 (2013)

    Article  Google Scholar 

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Parque, V., Miyashita, T. (2018). Path Planning on Hierarchical Bundles with Differential Evolution. In: Tan, Y., Shi, Y., Tang, Q. (eds) Advances in Swarm Intelligence. ICSI 2018. Lecture Notes in Computer Science(), vol 10941. Springer, Cham. https://doi.org/10.1007/978-3-319-93815-8_25

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  • DOI: https://doi.org/10.1007/978-3-319-93815-8_25

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  • Online ISBN: 978-3-319-93815-8

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