Intelligent Bézier curve-based path planning model using Chaotic Particle Swarm Optimization algorithm

  • Alaa Tharwat
  • Mohamed ElhosenyEmail author
  • Aboul Ella Hassanien
  • Thomas Gabel
  • Arun Kumar


Path planning algorithms have been used in different applications with the aim of finding a suitable collision-free path which satisfies some certain criteria such as the shortest path length and smoothness; thus, defining a suitable curve to describe path is essential. The main goal of these algorithms is to find the shortest and smooth path between the starting and target points. This paper makes use of a Bézier curve-based model for path planning. The control points of the Bézier curve significantly influence the length and smoothness of the path. In this paper, a novel Chaotic Particle Swarm Optimization (CPSO) algorithm has been proposed to optimize the control points of Bézier curve, and the proposed algorithm comes in two variants: CPSO-I and CPSO-II. Using the chosen control points, the optimum smooth path that minimizes the total distance between the starting and ending points is selected. To evaluate the CPSO algorithm, the results of the CPSO-I and CPSO-II algorithms are compared with the standard PSO algorithm. The experimental results proved that the proposed algorithm is capable of finding the optimal path. Moreover, the CPSO algorithm was tested against different numbers of control points and obstacles, and the CPSO algorithm achieved competitive results.


Particle Swarm Optimization (PSO) Bézier curve Path planning Chaos 


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.


  1. 1.
    Elhoseny, M., Tharwat, A., Farouk, A., Hassanien, A.E.: K-coverage model based on genetic algorithm to extend wsn lifetime. IEEE sensors letters 1(4), 1–4 (2017)CrossRefGoogle Scholar
  2. 2.
    Li, R., Wu, W., Qiao, H.: The compliance of robotic hands-from functionality to mechanism. Assem. Autom. 35(3), 281–286 (2015)CrossRefGoogle Scholar
  3. 3.
    Robinson, D.C., Sanders, D.A., Mazharsolook, E.: Ambient intelligence for optimal manufacturing and energy efficiency. Assem. Autom. 35(3), 234–248 (2015)CrossRefGoogle Scholar
  4. 4.
    Manikas, T.W., Ashenayi, K., Wainwright, R.L.: Genetic algorithms for autonomous robot navigation. IEEE Instrum. Meas. Mag. 10(6), 26–31 (2007)CrossRefGoogle Scholar
  5. 5.
    Metawa, N., Hassan, M.K., Elhoseny, M.: Genetic algorithm based model for optimizing bank lending decisions. Expert Syst. Appl. 80, 75–82 (2017)CrossRefGoogle Scholar
  6. 6.
    Elhoseny, M., Shehab, A., Yuan, X.: Optimizing robot path in dynamic environments using genetic algorithm and bezier curve. J. Intell. Fuzzy Syst. 33(4), 2305–2316 (2017)CrossRefzbMATHGoogle Scholar
  7. 7.
    Tharwat, A.: Linear vs. quadratic discriminant analysis classifier: a tutorial. Int. J. Appl. Pattern Recognit. 3(2), 145–180 (2016)CrossRefGoogle Scholar
  8. 8.
    Elhoseny, M., Tharwat, A., Hassanien, A.E.: Bezier curve based path planning in a dynamic field using modified genetic algorithm. J. Comput. Sci. (2017).
  9. 9.
    Roberge, V., Tarbouchi, M., Labonté, G.: Comparison of parallel genetic algorithm and particle swarm optimization for real-time uav path planning. IEEE Trans. Ind. Inform. 9(1), 132–141 (2013)CrossRefGoogle Scholar
  10. 10.
    Contreras-Cruz, M.A., Ayala-Ramirez, V., Hernandez-Belmonte, U.H.: Mobile robot path planning using artificial bee colony and evolutionary programming. Appl. Soft Comput. 30, 319–328 (2015)CrossRefGoogle Scholar
  11. 11.
    Das, P., Behera, H., Panigrahi, B.: A hybridization of an improved particle swarm optimization and gravitational search algorithm for multi-robot path planning. Swarm Evol. Comput. 28, 14–28 (2016)CrossRefGoogle Scholar
  12. 12.
    Gálvez, A., Iglesias, A., Cabellos, L.: Tabu search-based method for Bézier curve parameterization. Int. J. Softw. Eng. Appl. 7, 283–296 (2013)Google Scholar
  13. 13.
    Li, B., Liu, L., Zhang, Q., Lv, D., Zhang, Y., Zhang, J., Shi, X.: Path planning based on firefly algorithm and Bezier curve. In: IEEE International Conference on Information and Automation (ICIA), IEEE, pp. 630–633 (2014)Google Scholar
  14. 14.
    Arana-Daniel, N., Gallegos, A.A., López-Franco, C., Alanis, A.Y.: Smooth global and local path planning for mobile robot using particle swarm optimization, radial basis functions, splines and Bezier curves. In: IEEE Congress on Evolutionary Computation (CEC), IEEE, pp. 175–182 (2014)Google Scholar
  15. 15.
    Ziolkowski, M., Gratkowski, S.: Genetic algorithm coupled with Bézier curves applied to the magnetic field on a solenoid axis synthesis. Arch. Electr. Eng. 65(2), 361–370 (2016)Google Scholar
  16. 16.
    Kennedy, J.: Particle swarm optimization. In: Encyclopedia of Machine Learning. Springer, New York, pp. 760–766 (2010)Google Scholar
  17. 17.
    Maitra, M., Chatterjee, A.: A hybrid cooperative-comprehensive learning based pso algorithm for image segmentation using multilevel thresholding. Expert Syst. Appl. 34(2), 1341–1350 (2008)CrossRefGoogle Scholar
  18. 18.
    Ibrahim, A., Tharwat, A., Gaber, T., Hassanien, A.E.: Optimized superpixel and adaboost classifier for human thermal face recognition. Signal Image Video Process. (2017).
  19. 19.
    Tharwat, A., Hassanien, A.E., Elnaghi, B.E.: A ba-based algorithm for parameter optimization of support vector machine. Pattern Recogn. Lett. 93, 13–22 (2017)CrossRefGoogle Scholar
  20. 20.
    Tharwat, A., Gaber, T., Ibrahim, A., Hassanien, A.E.: Linear discriminant analysis: a detailed tutorial. AI Commun. 30(2), 169–190 (2017)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Subasi, A.: Classification of emg signals using pso optimized svm for diagnosis of neuromuscular disorders. Comput. Biol. Med. 43(5), 576–586 (2013)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Van der Merwe, D., Engelbrecht, A.P.: Data clustering using particle swarm optimization. In: The 2003 Congress on Evolutionary Computation, CEC’03, vol. 1., IEEE, pp. 215–220 (2003)Google Scholar
  23. 23.
    Tharwat, A.: Principal component analysis-a tutorial. Int. J. Appl. Pattern Recogn. 3(3), 197–240 (2016)CrossRefGoogle Scholar
  24. 24.
    Vesterstrom, J., Thomsen, R.: A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In: Congress on Evolutionary Computation, CEC2004, vol. 2, IEEE, pp. 1980–1987 (2004)Google Scholar
  25. 25.
    Miyatake, M., Veerachary, M., Toriumi, F., Fujii, N., Ko, H.: Maximum power point tracking of multiple photovoltaic arrays: a pso approach. IEEE Trans. Aerosp. Electron. Syst. 47(1), 367–380 (2011)CrossRefGoogle Scholar
  26. 26.
    Molazei, S., Ghazizadeh-Ahsaee, M.: Mopso algorithm for distributed generator allocation. In: Fourth International Conference on Power Engineering, Energy and Electrical Drives (POWERENG), IEEE, pp. 1340–1345 (2013)Google Scholar
  27. 27.
    Gandomi, A.H., Yang, X.S.: Chaotic bat algorithm. J. Comput. Sci. 5(2), 224–232 (2014)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Wang, G.G., Guo, L., Gandomi, A.H., Hao, G.S., Wang, H.: Chaotic krill herd algorithm. Inf. Sci. 274, 17–34 (2014)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Gharooni-fard, G., Moein-darbari, F., Deldari, H., Morvaridi, A.: Scheduling of scientific workflows using a chaos-genetic algorithm. Proc. Comput. Sci. 1(1), 1445–1454 (2010)CrossRefGoogle Scholar
  30. 30.
    Talatahari, S., Azar, B.F., Sheikholeslami, R., Gandomi, A.: Imperialist competitive algorithm combined with chaos for global optimization. Commun. Nonlinear Sci. Numer. Simul. 17(3), 1312–1319 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Gandomi, A., Yang, X.S., Talatahari, S., Alavi, A.: Firefly algorithm with chaos. Commun. Nonlinear Sci. Numer. Simul. 18(1), 89–98 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Ma, Y., Zamirian, M., Yang, Y., Xu, Y., Zhang, J.: Path planning for mobile objects in four-dimension based on particle swarm optimization method with penalty function. In: Mathematical Problems in Engineering (2013)Google Scholar
  33. 33.
    Liang, J., Song, H., Qu, B., Liu, Z.: Comparison of three different curves used in path planning problems based on particle swarm optimizer. In: Mathematical Problems in Engineering (2014)Google Scholar
  34. 34.
    Sahingoz, O.K.: Generation of Bezier curve-based flyable trajectories for multi-uav systems with parallel genetic algorithm. J. Intell. Robotic Syst. 74(1–2), 499–511 (2014)CrossRefGoogle Scholar
  35. 35.
    Gardner, B., Selig, M.: Airfoil design using a genetic algorithm and an inverse method. In: 41st Aerospace Sciences Meeting and Exhibit, pp. 1–12 (2003)Google Scholar
  36. 36.
    Jolly, K., Kumar, R.S., Vijayakumar, R.: A Bezier curve based path planning in a multi-agent robot soccer system without violating the acceleration limits. Robot. Auton. Syst. 57(1), 23–33 (2009)CrossRefGoogle Scholar
  37. 37.
    Giannakoglou, K.: A design method for turbine-blades using genetic algorithms on parallel computers. Comput. Fluid Dyn. 98(1), 1–2 (1998)Google Scholar
  38. 38.
    Chen, L., Wang, S., Hu, H., McDonald-Maier, K.: Bézier curve based trajectory planning for an intelligent wheelchair to pass a doorway. In: International Conference on Control (CONTROL), IEEE, pp. 339–344 (2012)Google Scholar
  39. 39.
    Choi, J.w., Curry, R., Elkaim, G.: Path planning based on Bézier curve for autonomous ground vehicles. In: Advances in Electrical and Electronics Engineering-IAENG Special Edition of the World Congress on Engineering and Computer Science, (WCECS’08), IEEE, pp. 158–166 (2008)Google Scholar
  40. 40.
    Wagner, R., Birbach, O., Frese, U.: Rapid development of manifold-based graph optimization systems for multi-sensor calibration and slam. In: 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, pp. 3305–3312 (2011)Google Scholar
  41. 41.
    Heppner, F., Grenander, U.: A stochastic nonlinear model for coordinated bird flocks. Ubiquity Chaos 99, 233–238 (1990)Google Scholar
  42. 42.
    Reynolds, C.W.: Flocks, herds and schools: a distributed behavioral model. ACM Siggraph Comput. Graph. 21(4), 25–34 (1987)CrossRefGoogle Scholar
  43. 43.
    Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the 6th International Symposium on Micro Machine and Human Science, vol. 1., New York, pp. 39–43 (1995)Google Scholar
  44. 44.
    Yang, X.S.: Nature-Inspired Optimization Algorithms, 1st edn. Elsevier, Amsterdam (2014)zbMATHGoogle Scholar
  45. 45.
    Ren, B., Zhong, W.: Multi-objective optimization using chaos based pso. Inf. Technol. J. 10(10), 1908–1916 (2011)CrossRefGoogle Scholar
  46. 46.
    Vohra, R., Patel, B.: An efficient chaos-based optimization algorithm approach for cryptography. Commun. Netw. Secur. 1(4), 75–79 (2012)Google Scholar
  47. 47.
    Demšar, J.: Statistical comparisons of classifiers over multiple data sets. J. Mach. Learn. Res. 7, 1–30 (2006)MathSciNetzbMATHGoogle Scholar
  48. 48.
    Masehian, E., Sedighizadeh, D.: A multi-objective pso-based algorithm for robot path planning. In: Proceedings of IEEE International Conference on Industrial Technology (ICIT), IEEE, pp. 465–470 (2010)Google Scholar

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Authors and Affiliations

  1. 1.Faculty of Computer Science and EngineeringFrankfurt University of Applied SciencesFrankfurt am MainGermany
  2. 2.Faculty of Computers and InformationMansoura UniversityMansouraEgypt
  3. 3.Faculty of Computers and InformationCairo UniversityCairoEgypt
  4. 4.Scientific Research Group in Egypt (SRGE)CairoEgypt
  5. 5.School of EEESASTRA UniversityThanjavurIndia

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