Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2016, Article ID 2539761, 12 pages
http://dx.doi.org/10.1155/2016/2539761
Research Article

Path Planning and Replanning for Mobile Robot Navigation on 3D Terrain: An Approach Based on Geodesic

Institute of Information Science, Academia Sinica, Nangang, Taipei 11529, Taiwan

Received 31 December 2015; Revised 11 April 2016; Accepted 26 May 2016

Academic Editor: Mustapha Zidi

Copyright © 2016 Kun-Lin Wu 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. S. M. LaValle, Planning Algorithms, Cambridge University Press, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. P. K.-C. Wang, Visibility-Based Optimal Path and Motion Planning, Springer, New York, NY, USA, 2015.
  3. S. Alatartsev, S. Stellmacher, and F. Ortmeier, “Robotic task sequencing problem: a survey,” Journal of Intelligent and Robotic Systems: Theory and Applications, vol. 80, no. 2, pp. 279–298, 2015. View at Publisher · View at Google Scholar · View at Scopus
  4. L. Yang, J. Qi, J. Xiao, and X. Yong, “A literature review of UAV 3D path planning,” in Proceedings of the 11th World Congress on Intelligent Control and Automation (WCICA '14), pp. 2376–2381, IEEE, Shenyang, China, July 2014. View at Publisher · View at Google Scholar · View at Scopus
  5. O. Hachour, “A three dimensional collision-free path planning,” International Journal of Systems Applications, Engineering & Development, vol. 3, no. 4, pp. 117–126, 2009. View at Google Scholar
  6. K. G. Shin and N. D. Mckay, “Selection of near-minimum time geometric paths for robotic manipulators,” IEEE Transactions on Automatic Control, vol. 31, no. 6, pp. 501–511, 1986. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Liu, “Robotic online path planning on point cloud,” IEEE Transactions on Cybernetics, vol. 46, no. 5, pp. 1217–1228, 2016. View at Publisher · View at Google Scholar · View at Scopus
  8. L. D. Zhang and C. J. Zhou, “Robot optimal trajectory planning based on geodesics,” in Proceedings of the IEEE International Conference on Control and Automation (ICCA '07), pp. 2433–2436, June 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. P. Coelho and U. Nunes, “Lie algebra application to mobile robot control: a tutorial,” Robotica, vol. 21, no. 5, pp. 483–493, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. Chen, L. Li, and X. Ji, “Smooth and accurate trajectory planning for industrial robots,” Advances in Mechanical Engineering, vol. 6, Article ID 342137, 8 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  11. L. Zhang and C. Zhou, “Kuka youBot arm shortest path planning based on geodesics,” in Proceedings of the IEEE International Conference on Robotics and Biomimetics (ROBIO '13), pp. 2317–2321, IEEE, Shenzhen, China, December 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. Hu, F. Bao, B. Li, and Z. Gu, “Path planning based on geodesic for mobile robots,” in Proceedings of the 27th Chinese Control and Decision Conference (CCDC '15), pp. 4315–4320, IEEE, Qingdao, China, May 2015. View at Publisher · View at Google Scholar · View at Scopus
  13. R.-J. Yan, J. Wu, J. Y. Lee, and C.-S. Han, “Representation of 3D environment map using B-spline surface with two mutually perpendicular LRFs,” Mathematical Problems in Engineering, vol. 2015, Article ID 690310, 14 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. Z. Shiller and Y.-R. Gwo, “Dynamic motion planning of autonomous vehicles,” IEEE Transactions on Robotics and Automation, vol. 7, no. 2, pp. 241–249, 1991. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Huptych and S. Röck, “Online path planning in dynamic environments using the curve shortening flow method,” Production Engineering, vol. 9, no. 5-6, pp. 613–621, 2015. View at Publisher · View at Google Scholar · View at Scopus
  16. Y. Kitamura, T. Tanaka, F. Kishino, and M. Yachida, “3-D path planning in a dynamic environment using an octree and an artificial potential field,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 2, pp. 474–481, August 1995. View at Scopus
  17. Y. Wang and W. Cao, “A global path planning method for mobile robot based on a three-dimensional-like map,” Robotica, vol. 32, no. 4, pp. 611–624, 2014. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Ataei and A. Yousefi-Koma, “Three-dimensional optimal path planning for waypoint guidance of an autonomous underwater vehicle,” Robotics and Autonomous Systems, vol. 67, pp. 23–32, 2015. View at Publisher · View at Google Scholar · View at Scopus
  19. S.-R. Chang and U.-Y. Huh, “Curvature-continuous 3D path-planning using QPMI method,” International Journal of Advanced Robotic Systems, vol. 12, 2015. View at Publisher · View at Google Scholar
  20. L. Jaillet and J. M. Porta, “Efficient asymptotically-optimal path planning on manifolds,” Robotics and Autonomous Systems, vol. 61, no. 8, pp. 797–807, 2013. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Aalbers, Obstacle avoidance using limit cycles [M.S. thesis], Delft University of Technology, Delft, Netherlands, 2013.
  22. S. M. Khansari-Zadeh and A. Billard, “A dynamical system approach to realtime obstacle avoidance,” Autonomous Robots, vol. 32, no. 4, pp. 433–454, 2012. View at Publisher · View at Google Scholar · View at Scopus
  23. J. Lu, Y. Diaz-Mercado, M. Egerstedt, H. Zhou, and S.-N. Chow, “Shortest paths through 3-dimensional cluttered environments,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA '14), pp. 6579–6585, Hong Kong, June 2014. View at Publisher · View at Google Scholar · View at Scopus
  24. M. P. do Carmo, Riemannian Geometry, Birkhäuser, 1992.
  25. H. Yu, J. J. Zhang, and Z. Jiao, “Geodesics on point clouds,” Mathematical Problems in Engineering, vol. 2014, Article ID 860136, 12 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. I. Arvanitakis, A. Tzes, and M. Thanou, “Geodesic motion planning on 3D-terrains satisfying the robot's kinodynamic constraints,” in Proceedings of the 39th Annual Conference of the IEEE Industrial Electronics Society (IECON '13), pp. 4144–4149, Vienna, Austria, November 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. I. R. Manchester and J. J. E. Slotine, “Control contraction metrics: convex and intrinsic criteria for nonlinear feedback design,” https://arxiv.org/abs/1503.03144
  28. S. Arimoto, “Modeling and control of multi-body mechanical systems: part i a riemannian geometry approach,” in Advances in the Theory of Control, Signals and Systems with Physical Modeling, vol. 407 of Lecture Notes in Control and Information Sciences, pp. 3–16, Springer, Berlin, Germany, 2011. View at Google Scholar
  29. B. K. Ghosh and I. B. Wijayasinghe, “Dynamics of human head and eye rotations under Donders' constraint,” IEEE Transactions on Automatic Control, vol. 57, no. 10, pp. 2478–2489, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976. View at MathSciNet
  31. V. A. Toponogov, Differential Geometry of Curves and Surfaces: A Concise Guide, Birkhäauser, 2006. View at MathSciNet
  32. B. O'Neill, Elementary Differential Geometry, Academic Press, Amsterdam, The Netherlands, 2nd edition, 2006. View at MathSciNet
  33. N. M. Patrikalakis and T. Maekawa, Shape Interrogation for Computer Aided Design and Manufacturing, Springer, 2002. View at MathSciNet
  34. D. M. Morera and P. C. P. Carvalho, Geodesic-Based Modeling on Manifold Triangulations, Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil, 2006.
  35. Z. T. Zheng and S. G. Chen, “The general orthogonal projection on a regular surface,” in Proceedings of the 5th European Conference on European Computing Conference (ECC '11), pp. 116–119, World Scientific and Engineering Academy and Society (WSEAS), Orlando, Fla, USA, 2011.
  36. K.-L. Wu, C.-W. Lo, Y.-C. Lin, and J.-S. Liu, “3D Path planning based on nonlinear geodesic equation,” in Proceedings of the 11th IEEE International Conference on Control and Automation, pp. 342–347, Taichung, Taiwan, June 2014.
  37. R. E. Deakin and M. N. Hunter, Geodesics on an Ellipsoid-Bessels Method, School of Mathematical Geospatial Sciences, RMIT University, Melbourne, Australia, 2009.
  38. N. Ganganath, C.-T. Cheng, and C. K. Tse, “A constraint-aware heuristic path planner for finding energy-efficient paths on uneven terrains,” IEEE Transactions on Industrial Informatics, vol. 11, no. 3, pp. 601–611, 2015. View at Publisher · View at Google Scholar · View at Scopus