Skip to main content
SpringerLink
Log in

BSplines Properties with Interval Analysis for Constraint Satisfaction Problem: Application in Robotics

  • Conference paper
  • First Online:
Intelligent Autonomous Systems 15 (IAS 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 867))

Included in the following conference series:

  • 1345 Accesses

Abstract

Interval Analysis is a mathematical tool that could be used to solve Constraint Satisfaction Problem. It guarantees solutions, and deals with uncertainties. However, Interval Analysis suffers from an overestimation of the solutions, i.e. the pessimism. In this paper, we initiate a new method to reduce the pessimism based on the convex hull properties of BSplines and the Kronecker product. To assess our method, we compute the feasible workspace of a 2D manipulator taking into account joint limits, stability and reachability constraints: a classical Constraint Satisfaction Problem in robotics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Tay, N.N.W., Saputra, A.A., Botzheim, J., Kubota, N.: Service robot planning via solving constraint satisfaction problem. ROBOMECH J. 3(1), 17 (2016)

    Article  Google Scholar 

  2. Lozano-Pérez, T., Kaelbling, L.P.: A constraint-based method for solving sequential manipulation planning problems. In: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3684–3691, September 2014

    Google Scholar 

  3. Fromherz, M.P., Hogg, T., Shang, Y., Jackson, W.B.: Modular robot control and continuous constraint satisfaction. In: Proceedings of IJCAI-01 Workshop on Modelling and Solving Problems with Constraints, pp. 47–56 (2001)

    Google Scholar 

  4. Lengagne, S., Ramdani, N., Fraisse, P.: Planning and fast replanning safe motions for humanoid robots. IEEE Trans. Robot. 27(6), 1095–1106 (2011)

    Article  Google Scholar 

  5. Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis with Examples in Parameter and State Estimation, Robust Control and Robotics. Springer, London (2001)

    MATH  Google Scholar 

  6. Lengagne, S., Vaillant, J., Yoshida, E., Kheddar, A.: Generation of whole-body optimal dynamic multi-contact motions. Int. J. Robot. Res. 17 (2013)

    Google Scholar 

  7. Merlet, J.-P.: Interval analysis and reliability in robotics. Int. J. Reliab. Saf. 3(1–3), 104–130 (2009)

    Article  Google Scholar 

  8. Yokoo, M., Hirayama, K.: Algorithms for distributed constraint satisfaction: a review. Auton. Agents Multi-Agent Syst. 3(2), 185–207 (2000)

    Article  Google Scholar 

  9. Gelle, E., Faltings, B.: Solving mixed and conditional constraint satisfaction problems. Constraints 8(2), 107–141 (2003)

    Article  MathSciNet  Google Scholar 

  10. Sunaga, T.: Theory of interval algebra and its application to numerical analysis. RAAG Mem. Ggujutsu Bunken Fukuy-kai 2, 547–564 (1958)

    MATH  Google Scholar 

  11. Moore, R.E., Bierbaum, F.: Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics (Siam Studies in Applied Mathematics). Siam Studies in Applied Mathematics, vol. 2. Soc for Industrial & Applied Math, Philadelphia (1979)

    Google Scholar 

  12. Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  13. Pérez-Galván, C., Bogle, I.D.L.: Global optimisation for dynamic systems using interval analysis. Comput. Chem. Eng. 107, 343–356 (2017)

    Article  Google Scholar 

  14. Jiang, C., Han, X., Guan, F., Li, Y.: An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method. Eng. Struct. 29(11), 3168–3177 (2007)

    Article  Google Scholar 

  15. Ma, H., Xu, S., Liang, Y.: Global optimization of fuel consumption in J2 rendezvous using interval analysis. Adv. Space Res. 59(6), 1577–1598 (2017)

    Article  Google Scholar 

  16. Merlet, J.P.: Interval Analysis and Robotics, pp. 147–156. Springer, Heidelberg (2011)

    Google Scholar 

  17. Jaulin, L.: Interval analysis and robotics. In: SCAN 2012, Russia, Novosibirsk (2012)

    Google Scholar 

  18. Rohou, S., Jaulin, L., Mihaylova, L., Le Bars, F., Veres, S.M.: Guaranteed computation of robot trajectories. Robot. Auton. Syst. 93, 76–84 (2017)

    Article  Google Scholar 

  19. Desrochers, B., Jaulin, L.: Minkowski operations of sets with application to robot localization. In: SNR 2017, Uppsala (2017)

    Google Scholar 

  20. Benoît, D., Luc, J.: Computing a guaranteed approximation of the zone explored by a robot. IEEE Trans. Autom. Control 62(1), 425–430 (2017)

    Article  MathSciNet  Google Scholar 

  21. Le Bars, F., Bertholom, A., Sliwka, J., Jaulin, L.: Interval SLAM for underwater robots; a new experiment. In: NOLCOS 2010, France, p. XX, September 2010

    Article  Google Scholar 

  22. Wu, J.: Uncertainty analysis and optimization by using the orthogonal polynomials, Ph.D. dissertation (2015)

    Google Scholar 

  23. Netz, L.: Using horner schemes to improve the efficiency and precision of interval constraint propagation (2015)

    Google Scholar 

  24. Schäcke, K.: On the kronecker product (2013)

    Google Scholar 

  25. Loan, C.F.: The ubiquitous kronecker product. J. Comput. Appl. Math. 123(1), 85–100 (2000). Numerical Analysis 2000. Vol. III: Linear Algebra

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS, UMR 6602, Pascal Institute, 63171, Aubiére, France

    Rawan Kalawoun, Sébastien Lengagne & Youcef Mezouar

  2. SIGMA Clermont, Pascal Institute, BP10448, 63000, Clermont-Ferrand, France

    Rawan Kalawoun & Youcef Mezouar

  3. Clermont-Auvergne University, Pascal Institute, BP10448, 63000, Clermont-Ferrand, France

    Sébastien Lengagne

  4. Clermont-Auvergne University, Laboratory of Mathematics Blaise Pascal, BP10448, 63000, Clermont-Ferrand, France

    François Bouchon

Authors
  1. Rawan Kalawoun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sébastien Lengagne
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. François Bouchon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Youcef Mezouar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rawan Kalawoun .

Editor information

Editors and Affiliations

  1. Baden-Wuerttemberg Cooperative State University, Karlsruhe, Germany

    Marcus Strand

  2. Humanoids and Intelligence Systems Lab, KIT - Karlsruher Institut für Technologie, Karlsruhe, Germany

    Rüdiger Dillmann

  3. University of Padua , Padua, Italy

    Emanuele Menegatti

  4. University of Padua, Padua, Italy

    Stefano Ghidoni

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kalawoun, R., Lengagne, S., Bouchon, F., Mezouar, Y. (2019). BSplines Properties with Interval Analysis for Constraint Satisfaction Problem: Application in Robotics. In: Strand, M., Dillmann, R., Menegatti, E., Ghidoni, S. (eds) Intelligent Autonomous Systems 15. IAS 2018. Advances in Intelligent Systems and Computing, vol 867. Springer, Cham. https://doi.org/10.1007/978-3-030-01370-7_39

Download citation

Publish with us

Policies and ethics

Search

Navigation