About this Journal Submit a Manuscript Table of Contents 
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 613964, 9 pages
http://dx.doi.org/10.1155/2013/613964
Research Article

Path Planning for Mobile Objects in Four-Dimension Based on Particle Swarm Optimization Method with Penalty Function

Yong Ma,1 M. Zamirian,2 Yadong Yang,1 Yanmin Xu,1 and Jing Zhang3

1Navigation College, Wuhan University of Technology, Wuhan, Hubei 430063, China
2Department of Mathematics, Islamic Azad University, Bojnourd Branch, Bojnourd 94186-54145, Iran
3Chutian College, Huazhong Agricultural University, Wuhan, Hubei 430205, China

Received 4 December 2012; Accepted 1 January 2013

Academic Editor: Yang Tang

Copyright © 2013 Yong Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Frazzoli, Z. H. Mao, J. H. Oh, and E. Feron, “Resolution of conflicts involving many aircraft via semidefinite programming,” Journal of Guidance, Control, and Dynamics, vol. 24, no. 1, pp. 79–86, 2001. View at Publisher · View at Google Scholar · View at Scopus
  2. W. Powell, Approximate Dynamic Programming: Solving the Curses of Dimensionality, vol. 703, Wiley-Blackwell, 2007.
  3. Y. Kim, D.-W. Gu, and I. Postlethwaite, “Real-time path planning with limited information for autonomous unmanned air vehicles,” Automatica, vol. 44, no. 3, pp. 696–712, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  4. Y. Wang, D. M. Lane, and G. J. Falconer, “Two novel approaches for unmanned underwater vehicle path planning: constrained optimization and semi-infinite constrained optimization,” Robotica, vol. 18, no. 2, pp. 123–142, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. C. Pêtrès, Y. Pailhas, P. Patrón, Y. Petillot, J. Evans, and D. Lane, “Path planning for autonomous underwater vehicles,” IEEE Transactions on Robotics, vol. 23, no. 2, pp. 331–341, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. P. P. Y. Wu, D. Campbell, and T. Merz, “Multi-objective four-dimensional vehicle motion planning in large dynamic environments,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 41, no. 3, pp. 621–634, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. Y. Ma, H. Wang, and M. Zamirian, “A novel approach for multiple mobile objects path planning: parametrization method and conflict resolution strategy,” Physics Letters A, vol. 376, no. 4, pp. 377–386, 2012. View at Publisher · View at Google Scholar
  8. H. Wang, Y. Ma, Y. Xie, and M. Guo, “Mobile robot optimal path planning based on smoothing A* algorithm,” Journal of Tongji University, vol. 38, no. 11, pp. 1647–1655, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. Y. Guo and L. E. Parker, “A distributed and optimal motion planning approach for multiple mobile robots,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA ’02), vol. 3, pp. 2612–2619, IEEE, May 2002. View at Scopus
  10. J. E. Hopcroft, J. T. Schwartz, and M. Sharir, “On the complexity of motion planning for multiple independent objects; pspace-hardness of the warehouseman’s problem,” International Journal of Robotics Research, vol. 3, no. 4, pp. 76–88, 1984. View at Scopus
  11. T. Berglund, A. Brodnik, H. Jonsson, M. Staffanson, and I. Söderkvist, “Planning smooth and obstacle-avoiding B-spline paths for autonomous mining vehicles,” IEEE Transactions on Automation Science and Engineering, vol. 7, no. 1, pp. 167–172, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. I. Skrjanc and G. Klancar, “Optimal cooperative collision avoidance between multiple robots based on bernstein-bézier curves,” Robotics and Autonomous Systems, vol. 58, no. 1, pp. 1–9, 2010. View at Publisher · View at Google Scholar
  13. M. Zamirian, A. V. Kamyad, and M. H. Farahi, “A novel algorithm for solving optimal path planning problems based on parametrization method and fuzzy aggregation,” Physics Letters A, vol. 373, no. 38, pp. 3439–3449, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948, December 1995. View at Scopus
  15. M. Saska, M. Macas, L. Preucil, and L. Lhotská, “Robot path planning using particle swarm optimization of ferguson splines,” in Proceedings of the IEEE Conference on Emerging Technologies and Factory Automation (ETFA ’06), pp. 833–839, IEEE, 2006.
  16. A. W. Mohemmed, N. C. Sahoo, and T. K. Geok, “Solving shortest path problem using particle swarm optimization,” Applied Soft Computing Journal, vol. 8, no. 4, pp. 1643–1653, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Tang, Z. Wang, and J. Fang, “Controller design for synchronization of an array of delayed neural networks using a controllable probabilisticpso,” Information Sciences, vol. 181, no. 20, pp. 4715–4732, 2011. View at Publisher · View at Google Scholar
  18. Y. Tang, Z. Wang, and J. Fang, “Feedback learning particle swarm optimization,” Applied Soft Computing, vol. 11, no. 8, pp. 4713–4725, 2011. View at Publisher · View at Google Scholar
  19. Y. Tang, Z. Wang, and J. A. Fang, “Parameters identification of unknown delayed genetic regulatory networks by a switching particle swarm optimization algorithm,” Expert Systems with Applications, vol. 38, no. 3, pp. 2523–2535, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. R. Abiyev, D. Ibrahim, and B. Erin, “Navigation of mobile robots in the presence of obstacles,” Advances in Engineering Software, vol. 41, no. 10-11, pp. 1179–1186, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. M. A. P. Garcia, O. Montiel, O. Castillo, R. Sepúlveda, and P. Melin, “Path planning for autonomous mobile robot navigation with ant colony optimization and fuzzy cost function evaluation,” Applied Soft Computing Journal, vol. 9, no. 3, pp. 1102–1110, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, vol. 12 of Texts in Applied Mathematics, Springer, New York, NY, USA, 3rd edition, 2002. View at MathSciNet
  23. J. A. Joines and C. R. Houck, “On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's,” in Proceedings of the 1st IEEE Conference on Evolutionary Computation, pp. 579–584, June 1994. View at Scopus
  24. J. Yang, Y. Chen, J. Horng, and C. Kao, “Applying family competition to evolution strategies for constrained optimization,” in Proceedings of the 6th International Conference on Evolutionary Programming, pp. 201–211, Springer, 1997.
  25. K. Parsopoulos and M. Vrahatis, “Particle swarm optimization method for constrained optimization problems,” in Intelligent Technologies-Theory and Application: New Trends in Intelligent Technologies, pp. 214–220, IOS Press, 2002.
  26. C. F. Juang and Y. C. Chang, “Evolutionary-group-based particle-swarm-optimized fuzzy controller with application to mobile-robot navigation in unknown environments,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 2, pp. 379–392, 2011. View at Publisher · View at Google Scholar · View at Scopus