Reliable robust path planning with application to mobile robots

Romain Pepy; Michel Kieffer; Eric Walter

International Journal of Applied Mathematics and Computer Science (2009)

  • Volume: 19, Issue: 3, page 413-424
  • ISSN: 1641-876X

Abstract

top
This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.

How to cite

top

Romain Pepy, Michel Kieffer, and Eric Walter. "Reliable robust path planning with application to mobile robots." International Journal of Applied Mathematics and Computer Science 19.3 (2009): 413-424. <http://eudml.org/doc/207945>.

@article{RomainPepy2009,
abstract = {This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.},
author = {Romain Pepy, Michel Kieffer, Eric Walter},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {interval analysis; path planning; robust control; state-space models},
language = {eng},
number = {3},
pages = {413-424},
title = {Reliable robust path planning with application to mobile robots},
url = {http://eudml.org/doc/207945},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Romain Pepy
AU - Michel Kieffer
AU - Eric Walter
TI - Reliable robust path planning with application to mobile robots
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 3
SP - 413
EP - 424
AB - This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.
LA - eng
KW - interval analysis; path planning; robust control; state-space models
UR - http://eudml.org/doc/207945
ER -

References

top
  1. Ackermann, J., Barlett, A., Kaesbauer, D., Sienel, W. and Steinhauser, R. (1993). Robust Control Systems with Uncertain Physical Parameters, Springer-Verlag, London. 
  2. Alamo, T., Bravo, J., Camacho, E. and de Sevilla, U. (2003). Guaranteed state estimation by zonotopes, Proceedings of the 42nd Conference on Decision and Control, Maui, Hi, pp. 1035-1043. Zbl1091.93038
  3. Berger, M. (1987). Geometry I and II, Springer-Verlag, Berlin. Zbl0606.51001
  4. Bouilly, B., Simeon, T. and Alami, R. (1995). A numerical technique for planning motion strategies of a mobile robot in presence of uncertainty, Proceedings of the IEEE International Conference on Robotics and Automation, Nagoya, Japan, pp. 1327-1332. 
  5. Collins, P. and Goldsztejn, A. (2008). The reach-and-evolve algorithm for reachability analysis of nonlinear dynamical systems, Electronic Notes in Theoretical Computer Science 223: 87-102. Zbl06418597
  6. Fraichard, T. and Mermond, R. (1998). Path planning with uncertainty for car-like robots, Proceedings of the IEEE International Conference on Robotics and Automation, Leuven, Belgium, pp. 27-32. 
  7. Francis, B. A. and Khargonekar, P. P. (Eds.) (1995). Robust Control Theory, IMA Volumes in Mathematics and Its Applications, Vol. 66, Springer-Verlag, New York, NY. 
  8. Gonzalez, J. P. and Stentz, A. (2004). Planning with uncertainty in position: An optimal planner, Technical Report CMURI-TR-04-63, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA. 
  9. Gonzalez, J. P. and Stentz, A. (2005). Planning with uncertainty in position: An optimal and efficient planner, Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Edmonton, Canada, pp. 2435-2442. 
  10. Gonzalez, J. P. and Stentz, A. (2007). Planning with uncertainty in position using high-resolution maps, Proceedings of the IEEE International Conference on Robotics and Automation, Rome, Italy, pp. 1015-1022. 
  11. Graham, R. L. (1972). An efficient algorithm for determining the convex hull of a finite planar set, Information Processing Letters 1(4): 132-133. Zbl0236.68013
  12. Jaulin, L. (2001). Path planning using intervals and graphs, Reliable Computing 7(1): 1-15. Zbl1021.65029
  13. Jaulin, L. (2002). Nonlinear bounded-error state estimation of continuous-time systems, Automatica 38(6): 1079-1082. Zbl1026.93015
  14. Jaulin, L., Kieffer, M., Didrit, O. and Walter, E. (2001). Applied Interval Analysis, Springer-Verlag, London. Zbl1023.65037
  15. Jaulin, L. and Walter, E. (1996). Guaranteed tuning, with application to robust control and motion planning, Automatica 32(8): 1217-1221. Zbl0875.93232
  16. Kieffer, M., Jaulin, L., Braems, I. and Walter, E. (2001). Guaranteed set computation with subpavings, in W. Kraemer and J. W. von Gudenberg (Eds.), Scientific Computing, Validated Numerics, Interval Methods, Kluwer Academic/Plenum Publishers, New York, NY, pp. 167-178. 
  17. Kieffer, M., Jaulin, L. and Walter, E. (2002). Guaranteed recursive nonlinear state bounding using interval analysis, International Journal of Adaptative Control and Signal Processing 6(3): 193-218. Zbl1006.93067
  18. Kieffer, M. and Walter, E. (2003). Nonlinear parameter and state estimation for cooperative systems in a bounded-error context, in R. Alt, A. Frommer, R. B. Kearfott and W. Luther (Eds.), Numerical Software with Result Verification (Platforms, Algorithms, Applications in Engineering, Physics, and Economics), Springer, New York, NY, pp. 107-123. Zbl1126.93339
  19. Kieffer, M. and Walter, E. (2006). Guaranteed nonlinear state estimation for continuous-time dynamical models from discrete-time measurements, Proceedings of the 6th IFAC Symposium on Robust Control, Toulouse, France, (on CDROM). 
  20. Kuffner, J. J. and LaValle, S. M. (2000). RRT-connect: An efficient approach to single-query path planning, Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA, USA, pp. 995-1001. 
  21. Lambert, A. and Gruyer, D. (2003). Safe path planning in an uncertain-configuration space, Proceedings of the IEEE International Conference on Robotics and Automation, Taipei, Taiwan, pp. 4185-4190. 
  22. Latombe, J. C. (1991). Robot Motion Planning, Kluwer Academic Publishers, Boston, MA. Zbl0817.93045
  23. LaValle, S. M. (1998). Rapidly-exploring Random Trees: A new tool for path planning, Technical report, Iowa State University, Ames, IO. 
  24. LaValle, S. M. (2006). Planning Algorithms, Cambridge University Press, Cambridge, Available at: http://planning.cs.uiuc.edu/. Zbl1100.68108
  25. LaValle, S. M. and Kuffner, J. J. (2001a). Randomized kinodynamic planning, International Journal of Robotics Research 20(5): 378-400. 
  26. LaValle, S. M. and Kuffner, J. J. (2001b). Rapidly-exploring random trees: Progress and Prospects, in B. R. Donald, K. M. Lynch and D. Rus (Eds.), Algorithmic and Computational Robotics: New Directions, A. K. Peters, Wellesley, MA, pp. 293-308. Zbl0986.68151
  27. Lazanas, A. and Latombe, J. C. (1995). Motion planning with uncertainty: A landmark approach, Artificial Intelligence 76(1-2): 287-317. Zbl0939.68863
  28. Lohner, R. (1987). Enclosing the solutions of ordinary initial and boundary value problems, in E. Kaucher, U. Kulisch and C. Ullrich (Eds.), Computer Arithmetic: Scientific Computation and Programming Languages, BG Teubner, Stuttgart, pp. 255-286. 
  29. Luenberger, D. (1966). Observers for multivariable systems, IEEE Transactions on Automatic Control 11(2): 190-197. 
  30. Moore, R. E. (1966). Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ. Zbl0176.13301
  31. Moore, R. E. (1979). Methods and Applications of Interval Analysis, SIAM, Philadelphia, PA. Zbl0417.65022
  32. Pepy, R. and Lambert, A. (2006). Safe path planning in an uncertain-configuration space using RRT, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, pp. 5376-5381. 
  33. Pepy, R., Lambert, A. and Mounier, H. (2006). Reducing navigation errors by planning with realistic vehicle model, Proceedings of the IEEE Intelligent Vehicle Symposium, Tokyo, Japan, pp. 300-307. 
  34. Raissi, T., Ramdani, N. and Candau, Y. (2004). Set membership state and parameter estimation for systems described by nonlinear differential equations, Automatica 40(10): 1771-1777. Zbl1067.93019
  35. Ramdani, N., Meslem, N. and Candau, Y. (2008). Reachability analysis of uncertain nonlinear systems using guaranteed set integration, Proceedings of the IFAC World Congress, Seoul, Korea. Zbl1144.93303
  36. Schweppe, F. C. (1973). Uncertain Dynamic Systems, PrenticeHall, Englewood Cliffs, NJ. 
  37. Yakey, J., LaValle, S. M. and Kavraki, L. E. (2001). Randomized path planning for linkages with closed kinematic chains, IEEE Transactions on Robotics and Automation 17(6): 951-958. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.