Reliable Robust Path Planning with Application to Mobile Robots

Open access

Reliable Robust Path Planning with Application to Mobile Robots

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.

Ackermann, J., Barlett, A., Kaesbauer, D., Sienel, W. and Steinhauser, R. (1993). Robust Control Systems with Uncertain Physical Parameters, Springer-Verlag, London.

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.

Berger, M. (1987). Geometry I and II, Springer-Verlag, Berlin.

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.

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.

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.

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.

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.

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.

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.

Graham, R. L. (1972). An efficient algorithm for determining the convex hull of a finite planar set, Information Processing Letters 1(4): 132-133.

Jaulin, L. (2001). Path planning using intervals and graphs, Reliable Computing 7(1): 1-15.

Jaulin, L. (2002). Nonlinear bounded-error state estimation of continuous-time systems, Automatica 38(6): 1079-1082.

Jaulin, L., Kieffer, M., Didrit, O. and Walter, E. (2001). Applied Interval Analysis, Springer-Verlag, London.

Jaulin, L. and Walter, E. (1996). Guaranteed tuning, with application to robust control and motion planning, Automatica 32(8): 1217-1221.

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.

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.

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.

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 CD-ROM).

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.

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.

Latombe, J. C. (1991). Robot Motion Planning, Kluwer Academic Publishers, Boston, MA.

LaValle, S. M. (1998). Rapidly-exploring Random Trees: A new tool for path planning, Technical report, Iowa State University, Ames, IO.

LaValle, S. M. (2006). Planning Algorithms, Cambridge University Press, Cambridge, Available at: http://planning.cs.uiuc.edu/

LaValle, S. M. and Kuffner, J. J. (2001a). Randomized kinodynamic planning, International Journal of Robotics Research 20(5): 378-400.

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.

Lazanas, A. and Latombe, J. C. (1995). Motion planning with uncertainty: A landmark approach, Artificial Intelligence 76(1-2): 287-317.

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.

Luenberger, D. (1966). Observers for multivariable systems, IEEE Transactions on Automatic Control 11(2): 190-197.

Moore, R. E. (1966). Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ.

Moore, R. E. (1979). Methods and Applications of Interval Analysis, SIAM, Philadelphia, PA.

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.

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.

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.

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.

Schweppe, F. C. (1973). Uncertain Dynamic Systems, Prentice-Hall, Englewood Cliffs, NJ.

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.

International Journal of Applied Mathematics and Computer Science

Journal of the University of Zielona Góra

Journal Information


IMPACT FACTOR 2017: 1.694
5-year IMPACT FACTOR: 1.712

CiteScore 2017: 2.20

SCImago Journal Rank (SJR) 2017: 0.729
Source Normalized Impact per Paper (SNIP) 2017: 1.604

Mathematical Citation Quotient (MCQ) 2017: 0.13

Cited By

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 232 230 13
PDF Downloads 69 68 5