Journal of Intelligent & Robotic Systems

, Volume 71, Issue 3–4, pp 303–317 | Cite as

Fast Path Re-planning Based on Fast Marching and Level Sets



We investigate path planning algorithms that are based on level set methods for applications in which the environment is static, but where an a priori map is inaccurate and the environment is sensed in real-time. Our principal contribution is not a new path planning algorithm, but rather a formal analysis of path planning algorithms based on level set methods. Computational costs when planning paths with level set methods are due to the creation of the level set function. Once the level set function has been computed, the optimal path is simply gradient descent down the level set function. Our approach rests on the formal analysis of how value of the level set function changes when the changes in the environment are detected. We show that in many practical cases, only a small domain of the level set function needs to be re-computed when the environment changes. Simulation examples are presented to validate the effectiveness of the proposed method.


Path planning Autonomous vehicle Autonomous navigation 


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  1. 1.
    Alton, K., Mitchell, I.M.: Optimal path planning under different norms continuous state spaces. In: Proc. of IEEE International Conf. on Robotics and Automation, pp. 866–872 (2006)Google Scholar
  2. 2.
    Choi, W., Zhu, D., Latombe, J.C.: Contingency-tolerant robot motion planning and control. In: Proc. of IEEE/RSJ International Workshop on Intelligent Robots and Systems, pp. 78–86 (1989)Google Scholar
  3. 3.
    Cohen, L.D., Kimmel, R.: Global minimum for active contours models: a minimal path approach. Int. J. Comput. Vis. 24(1), 57–78 (1997)CrossRefGoogle Scholar
  4. 4.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1989)Google Scholar
  5. 5.
    Elfes, A.: Using occupancy grids for mobile robot perception and navigation. Computer 22(6), 46–57 (1989)CrossRefGoogle Scholar
  6. 6.
    Ferguson, D., Likhachev, M., Stentz, A.: A guide to heuristic path planning. In: Proc. of the International Workshop on Planning under Uncertainty for Autonomous Systems, International Conference on Automated Planning and Scheduling (2005)Google Scholar
  7. 7.
    Hassouna, M.S., Abdel-Hakim, A.E., Farag, A.A.: Robust robotic path planning using level sets. In: Proc. of IEEE International Conf. on Image Processing, vol. 3, pp. 473–476 (2005)Google Scholar
  8. 8.
    Khatib, M., Jaouni, H., Chatila, R., Laumond, J.P.: Dynamic path modification for car-like nonholonomic mobile robots. In: Proc. of IEEE International Conf. on Robotics and Automation, pp. 2920–2925 (1997)Google Scholar
  9. 9.
    Kimmel, R., Sethian, J.A.: Optimal algorithm for shape from shading and path planning. J. Math. Imaging Vis. 14, 237–244 (2001)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Kimmel, R., Amir, A., Bruckstein, A.M.: Finding shortest paths on surfaces using level set methods. IEEE Trans. Pattern Anal. Mach. Intell. 17(6), 635–640 (1995)CrossRefGoogle Scholar
  11. 11.
    Koenig, S., Likhachev, M.: Improved fast replanning for robot navigation in unknown terrain. Technical Report GIT-COGSCI-2002/3, College of Computing, Georgia Institute of Technology, Atlanta, GA (2002)Google Scholar
  12. 12.
    Krogh, B.H., Thrope, C.E.: Integrated path planning and dynamic steering control for autonomous vehicles. In: Proc. of IEEE International Conf. on Robotics and Automation, pp. 1664–1669 (1986)Google Scholar
  13. 13.
    Lamiraux, F., Bonnafous, D., Lefebvre, O.: Reactive path deformation for nonholonomic mobile robots. IEEE Trans. Robot. 2(6), 967–977 (2004)CrossRefGoogle Scholar
  14. 14.
    Latombe, J.C.: Robot Motion Planning. Kluwer Academic, Norwell (1991)CrossRefGoogle Scholar
  15. 15.
    LaValle, S.: Planning Algorithms. Cambridge University Press, Cambridge (2006)MATHCrossRefGoogle Scholar
  16. 16.
    Lions, P.L.: Generalized Solutions of Hamilton–Jacobi Solutions. Pitman, New York (1982)MATHGoogle Scholar
  17. 17.
    Mitchell, I.M., Sastry, S.: Continuous path planning with multiple constraints. In: Proc. of the 42nd IEEE Conf. on Decision and Control, pp. 5502–5507 (2003)Google Scholar
  18. 18.
    Osher, S.J., Sethian, J.A.: Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Petres, C., Pailhas, Y., Patron, P., Petillot, Y., Evans, J., Lane, D.: Path planning for autonomous underwater vehicles. IEEE Trans. Robot. 23(2), 331–341 (2007)CrossRefGoogle Scholar
  20. 20.
    Phillippsen, R.: A light formulation of the E* interpolated path replanner. Technical Report, Autonomous Systems Lab, Ecole Polytechnique Federale de Lausanne, Switzerland (2006)Google Scholar
  21. 21.
    Quinlan, S., Khatib, O.: Elastic bands: connecting path planning and control. In: Proc. of IEEE International Conf. on Robotics and Automation, pp. 802–807 (1993)Google Scholar
  22. 22.
    Rouy, E., Tourin, A.: A viscosity solutions approach to shape-from-shading. SIAM J. Numer. Anal. 29(3), 867–884 (1992)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Sethian, J.A.: Fast marching method. SIAM Rev. 41(2), 199–235 (1999)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Sun, X., Yeoh, W., Koenig, S.: Dynamic fringe-saving A*. In: Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, pp. 891–898 (2009)Google Scholar
  25. 25.
    Tsitsiklis, J.N.: Efficient algorithm for globally optimal trajectories. IEEE Trans. Automat. Contr. 40(9), 1528–1538 (1995)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Xu, B., Stilwell, D.J., Kurdila, A.J.: Efficient computation of level sets for path planning. In: IEEE/RSJ International Conf. on Intelligent Robots and Systems (2009)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Bin Xu
    • 1
  • Daniel J. Stilwell
    • 1
  • Andrew J. Kurdila
    • 2
  1. 1.The Bradley Department of Electrical and Computer EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.The Department of Mechanical EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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