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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Chazelle, B.: A theorem on polygon cutting with applications. In: Proceedings of 23rd IEEE Symposium on Foundations of Computer Science, pp. 339–349 (1982)
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
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)
Cormen, T., Leiserson, C., Rivest, R.: Introduction to Algorithms. MIT Press, Cambridge (1993)
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)
Davoodi, M., Panahi, F., Mohades, A., Hashemi, S.N.: Clear and smooth path planning. Appl. Soft Comput. 32, 568–579 (2015)
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)
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
exedesign: Factory. http://www.blendswap.com/blends/view/55233
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)
Ghita, N., Kloetzer, M.: Trajectory planning for a car-like robot by environment abstraction. Robot. Auton. Syst. 60(4), 609–619 (2012)
Holten, D.: Hirerarchical edge bundles: visualization of adjacency relations in hierarchical data. In: IEEE Pacific Visualization Symposium, pp. 187–194 (2006)
Holten, D., van Wijk, J.J.: Force-directed edge bundling for graph visualization. In: Eurographics, Symposium on Visualization (2009)
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)
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)
LaValle, S.M.: Rapidly-exploring random trees: a new tool for path planning. Technical report. Computer Science Department, Iowa State University (TR 98–11)
LaValle, S.M., Kuffner Jr., J.J.: Rapidly-exploring random trees: progress and prospects (2000)
Lee, D.T., Preparata, F.P.: Euclidean shortest paths in the presence of rectilinear barriers. Networks 14(3), 393–410 (1984)
Lozano-Pérez, T., Wesley, M.A.: An algorithm for planning collision-free paths among polyhedral obstacles. Commun. ACM 22(10), 560–570 (1979)
LWP23D: Game map: Factory. https://www.blendswap.com/blends/view/81600
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)
Mohanan, M., Salgoankar, A.: A survey of robotic motion planning in dynamic environments. Robot. Auton. Syst. 100, 171–185 (2018)
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)
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)
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)
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
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)
Parque, V., Miyashita, T.: On succinct representation of directed graphs. In: IEEE International Conference on Big Data and Smart Computing, pp. 199–205 (2017)
Parque, V., Kobayashi, M., Higashi, M.: Optimisation of bundled routes. In: 16th International Conference on Geometry and Graphics, pp. 893–902 (2014)
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
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)
Parque, V., Miura, S., Miyashita, T.: Route bundling in polygonal domains using differential evolution. Robot. Biomimetics 4(1), 22 (2017)
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)
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)
Robbins, H., Courant, R.: What is Mathematics?. Oxford University Press, Oxford (1941)
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
Selassie, D., Heller, B., Heer, J.: Divided edge bundling for directional network data. IEEE Trans. Visual. Comput. Graph. 17(12), 2354–2363 (2011)
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
Vojtěch, J., Kössler, M.: O minimálních grafech, obsahujících \(n\) daných bodů. Časopis pro pěstování matematiky a fysiky 063(8), 223–235 (1934)
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)
Winter, P.: Euclidean Steiner minimal trees with obstacles and Steiner visibility graphs. Discrete Appl. Math. 47, 187–206 (1993)
Winter, P., Zachariasen, M., Nielsen, J.: Short trees in Polygons. Discrete Appl. Math. 118, 55–72 (2002)
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)
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
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)
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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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