Journal of Intelligent & Robotic Systems

, Volume 66, Issue 4, pp 505–522 | Cite as

Multiresolution Hierarchical Path-Planning for Small UAVs Using Wavelet Decompositions

  • Panagiotis Tsiotras
  • Dongwon Jung
  • Efstathios Bakolas


We present an algorithm for solving the shortest (collision-free) path planning problem for an agent (e.g., a small UAV) with limited on-board computational resources. The agent has detailed knowledge of the environment and the obstacles only in the vicinity of its current position. Far away obstacles are only partially known and may even change dynamically. The algorithm makes use of the wavelet transform to construct an approximation of the environment at different levels of resolution. We associate with this multiresolution representation of the environment a graph, whose dimension can be made commensurate to the on-board computational resources of the agent. The adjacency list of the graph can be efficiently constructed directly from the approximation and detail wavelet coefficients, thus further speeding up the whole process. Simulations are presented to test the efficiency of the algorithm using non-trivial scenarios.


Path-planning Wavelets Multiresolution UAV 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bakolas, E., Tsiotras, P.: Multiresolution path planning via sector decompositions compatible to on-board sensor data. In: AIAA Guidance, Navigation, and Control Conference. Honolulu, HI, 18–21 August 2008. AIAA Paper 2008-7238Google Scholar
  2. 2.
    Behnke, S.: Local Multiresolution Path Planning. Lecture Notes in Computer Science, pp. 332–343 (2004)Google Scholar
  3. 3.
    Bi, Z., Yimin, Y., Wei, Y.: Hierarchical path planning approach for mobile robot navigation under the dynamic environment. In: IEEE International Conference on Industrial Informatics, Daejeon, Korea, pp. 372–376 (2008). doi: 10.1109/INDIN.2008.4618127
  4. 4.
    Broz, P., Kolingerova, I., Apu, R.A., Gavrilova, M., Zitka, P.: Path planning in dynamic environment using an adaptive mesh. In: Spring Conference on Computer Graphics SCCG 2007, pp. 172–178 (2007)Google Scholar
  5. 5.
    Burrus, C.S., Gopinath, R.A., Guo, H.: Introduction to Wavelets and Wavelet Transforms. Prentice Hall, New Jersey (1998)Google Scholar
  6. 6.
    Calderbank, A.R., Daubechies, I., Sweldens, W., Yeo, B.L.: Wavelet transforms that map integers to integers. Appl. Comput. Harmon. Anal. 5(3), 332–369 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  8. 8.
    Cowlagi, R., Tsiotras, P.: Beyond quadtrees: cell decomposition for path planning using the wavelet transform. In: 46th IEEE Conference on Decision and Control, New Orleans, pp. 1392–1397 (2007)Google Scholar
  9. 9.
    Cowlagi, R., Tsiotras, P.: Multiresolution path planning with wavelets: a local replanning approach. In: American Control Conference, Seattle, pp. 1220–1225 (2008)Google Scholar
  10. 10.
    Cowlagi, R., Tsiotras, P.: Multi-resolution path planning: theoretical analysis, efficient implementation, and extensions to dynamic environments. In: 49th IEEE Conference on Decision and Control, Atlanta, pp. 1384–1390 (2010)Google Scholar
  11. 11.
    Daubechies, I., Sweldens, W.: Factoring wavelets transforms into lifting steps. J. Fourier Anal. Appl. 4(3), 247–269 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Freeden, W., Windheuser, U.: Spherical wavelet transform and its discretization. Adv. Comput. Math. 5(1), 51–94 (1996). doi: 10.1007/BF02124735 MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Hwang, J.Y., Kim, J.S., Lim, S.S., Park, K.H.: A fast path planning by path graph optimization. IEEE Trans. Syst. Man Cybern. 33(1), 121–127 (2003)CrossRefGoogle Scholar
  14. 14.
    Jung, D.: Hierarchical path planning and control of a small fixed-wing UAV: theory and experimental validation. Ph.D. Thesis, Georgia Institute of Technology, Atlanta (2007)Google Scholar
  15. 15.
    Jung, D., Ratti, J., Tsiotras, P.: Real-time implementation and validation of a new hierarchical path planning scheme for UAVs via hardware-in-the-loop simulation. J. Intell. Robot. Syst. 54(1), 163–181 (2009). doi: 10.1007/s10846-008-9255-0 CrossRefGoogle Scholar
  16. 16.
    Jung, D., Tsiotras, P.: Multiresolution on-line path planning for small unmanned aerial vehicles. In: American Control Conference, Seattle, pp. 2744–2749 (2008)Google Scholar
  17. 17.
    Kambhampati, S., Davis, L.S.: Multiresolution path planning for mobile robots planning. IEEE J. Robot. Autom. 2(3), 135–145 (1986)CrossRefGoogle Scholar
  18. 18.
    Kim, C.T., Lee, J.J.: Mobile robot navigation using multi-resolution electrostatic potential field. In: 32nd Annual Conference of IEEE Industrial Electronics Society, 2005, IECON 2005 (2005)Google Scholar
  19. 19.
    Koenig, A.: Agent-centered search. Artif. Intell. Mag. 22(4), 109–131 (2001)MathSciNetGoogle Scholar
  20. 20.
    Koenig, S., Likhachev, M., Furcy, D.: Lifelong planning A*. Artif. Intell. J. 155(1–2), 93–146 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Latombe, J.C.: Robot Motion Planning. Kluwer Academic Publishers, Boston (1991)CrossRefGoogle Scholar
  22. 22.
    LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006)zbMATHCrossRefGoogle Scholar
  23. 23.
    Li, T.H.: Multiscale representation and analysis of spherical data by spherical wavelets. SIAM J. Sci. Comput. 21(3), 924–953 (1999). do 10.1137/S1064827598341463 MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Li, Y., Li, C., Zhang, Z.: Q-learning based method of adaptive path planning for mobile robot. In: 2006 IEEE International Conference on Information Acquisition, Shandong, China, pp. 983–987 (2006). doi: 10.1109/ICIA.2006.305871
  25. 25.
    Longega, L., Panzieri, S., Pascucci, F., Ulivi, G.: Indoor robot navigation using log-polar local maps. In: Robot Control 2003 (SYROCO’03): a Proceedings Volume from the 7th IFAC Symposium, Wrocław, Poland, 1–3 September 2003, Pergamon, p. 213 (2004)Google Scholar
  26. 26.
    Lu, Y., Huo, X., Tsiotras, P.: Beamlet-like data processing for accelerated path-planning using multiscale information of the environment. In: 49th IEEE Conference on Decision and Control, Atlanta, pp. 3808–3813 (2010)Google Scholar
  27. 27.
    Noborio, H., Naniwa, T., Arimoto, S.: A quadtree-based path planning algorithm for a mobile robot. J. Robot. Syst. 7(44), 555–574 (1990)zbMATHCrossRefGoogle Scholar
  28. 28.
    Pai, D.K., Reissell, L.M.: Multiresolution rough terrain motion planning. IEEE Trans. Robot. Autom. 14, 19–33 (1998)CrossRefGoogle Scholar
  29. 29.
    Prazenica, R.J., Kurdila, A.J., Sharpley, R.C., Evers, J.: Multiresolution and adaptive path planning for maneuver of micro-air-vehicles in urban environments. In: AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco (2005)Google Scholar
  30. 30.
    Sermanet, P., Hadsell, R., Scoffier, M., Muller, U., LeCun, Y.: Mapping and planning under uncertainty in mobile robots with long-range perception. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2525–2530 (2008). doi: 10.1109/IROS.2008.4651203
  31. 31.
    Sinopoli, B., Micheli, M., Donato, G., Koo, T.J.: Vision based navigation for an unmanned aerial vehicle. In: Proceedings of 2001 IEEE Conference on Robotics and Automation, pp. 1757–64 (2001)Google Scholar
  32. 32.
    Stentz, A.: Optimal and efficient path planning for partially-known environments. In: Proceedings of the IEEE International Conference on Robotics and Automation, vol. 4, pp. 3310–3317 (1994)Google Scholar
  33. 33.
    Sweldens, W.: The lifting scheme: a construction of second generation wavelets. SIAM J. Math. Anal. 29(2), 511–546 (1997)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Tsiotras, P., Bakolas, E.: A hierarchical on-line path-planning scheme using wavelets. In: European Control Conference, Kos, Greece, pp. 2806–2812 (2007)Google Scholar
  35. 35.
    Yu, H., Beard, R., Byrne, J.: Vision-based local multi-resolution mapping and path planning for miniature air vehicles. In: American Control Conference, St. Louis, pp. 5247–5252. (2009). doi: 10.1109/ACC.2009.5160065
  36. 36.
    Zhu, D., Latombe, J.: New heuristic algorithms for efficient hierarchical path planning. IEEE Trans. Robot. Autom. 7(1), 9–20 (1991)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Panagiotis Tsiotras
    • 1
  • Dongwon Jung
    • 1
  • Efstathios Bakolas
    • 1
  1. 1.School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations