Skip to main content
SpringerLink
Log in

Ellipsoid SLAM: a novel set membership method for simultaneous localization and mapping

  • Published:
Autonomous Robots Aims and scope Submit manuscript

Abstract

The extended Kalman filter (EKF) simultaneous localization and mapping (SLAM) requires the uncertainty to be Gaussian noise. This assumption can be relaxed to bounded noise by the set membership SLAM. However, the published set membership SLAMs are not suitable for large-scale and online problems. In this paper, we use ellipsoid algorithm for solving SLAM problem. The proposed ellipsoid SLAM has advantages over EKF SLAM and the other set membership SLAMs, in noise condition, online realization, and large-scale problem. By bounded ellipsoid technique, we analyze the convergence and stability of the ellipsoid SLAM. Simulation and experimental results show that the proposed ellipsoid SLAM is effective for online and large-scale problems such as Victoria Park dataset.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Borenstein, J., Everett, H. R., & Feng, L. (1997). Mobile robot positioning: sensors and techniques. Journal of Robotic Systems, 14(4), 231–249.

    Article  Google Scholar 

  • Correa, M. V., Aguirre, L. A., & Saldanha, R. R. (2002). Using steady-state prior knowledge to constrain parameter estimates in nonlinear system identification. IEEE Transactions on Circuits and Systems, Part I, 49(9), 1376–1381.

    Article  Google Scholar 

  • Di Marco, M., Garulli, A., Giannitrapani, A., & Vicino, A. (2004). A set theoretic approach to dynamic robot localization and mapping. Autonomous Robots, 16(1), 23–47.

    Article  Google Scholar 

  • Dissanayake, G., Newman, P., Clark, S., Durrant-Whyte, H., & Csorba, M. (2001). A solution to the simultaneous localization and map building (SLAM) problem. IEEE Transactions on Robotics and Automation, 17(3), 229–241.

    Article  Google Scholar 

  • Dissanayake, G., Williams, S. B., Durrant-Whyte, H., & Bailey, T. (2002). Map management for efficient simultaneous localization and mapping (SLAM). Autonomous Robots, 12(3), 267–286.

    Article  MATH  Google Scholar 

  • Fogel, E., & Huang, Y. F. (1982). On the value of information in system identification: Bounded noise case. Automatica, 18(2), 229–238.

    Article  MATH  MathSciNet  Google Scholar 

  • Folkesson, J., & Christensen, H. (2007). Closing the loop with graphical SLAM. IEEE Transactions on Robotics, 23(4), 731–741.

    Article  Google Scholar 

  • Garulli, A., & Vicino, A. (2001). Set membership localization of mobile robots via angle measurements. IEEE Transactions on Robotics and Automation, 17(4), 450–463.

    Article  Google Scholar 

  • Goodwin, G. C., & Sang Sin, K. (1984). Adaptive filtering prediction and control. Englewood Cliffs: Prentice-Hall.

    MATH  Google Scholar 

  • Guivant, J. E., & Nebot, E. M. (2001). Optimization of the simultaneous localization and map-building algorithm for real-time implementation. IEEE Transactions on Robotics and Automation, 17(3), 242–257.

    Article  Google Scholar 

  • Ho, K. L., & Newman, P. (2006). Loop closure detection in SLAM by combining visual and spatial appearance. Robotics and Autonomous Systems, 54(9), 740–749.

    Article  Google Scholar 

  • Jaulin, L. (2009). A nonlinear set membership approach for the localization and map building of underwater robots. IEEE Transactions on Robotics, 25(1), 88–98.

    Article  MathSciNet  Google Scholar 

  • Jaulin, L. (2011). Range-only SLAM with occupancy maps: a set-membership approach. IEEE Transactions on Robotics, 27(5), 1004–1010.

    Article  Google Scholar 

  • Kaess, M., Johannsson, H., Roberts, R., Ila, V., Leonard, J., & Dellaert, F. (2012). iSAM2: Incremental smoothing and mapping using the Bayes tree. International Journal of Robotics Research, 31, 216–235.

    Article  Google Scholar 

  • K-Team Corporation. (2013). http://www.k-team.com/contact-k-team.

  • Lorenz, R. G., & Boyd, S. P. (2005). Robust minimum variance beam-forming. IEEE Transactions on Signal Processing, 53(5), 1684–1696.

    Article  MathSciNet  Google Scholar 

  • Maksarov, D. G., & Norton, J. P. (1996). State bounding with ellipsoidal set description of the uncertainty. International Journal of Control, 65(5), 847–866.

    Article  MATH  MathSciNet  Google Scholar 

  • Montemerlo, M., & Thrun, S. (2007). FastSLAM, a scalable method for the simultaneous localization and mapping problem in robotics. Springer tracts in advanced robotics. New York: Springer.

  • Mullane, J., Ba-Ngu Vo, Adams, M., & Ba-Tuong Vo, (2011). A random-finite-set approach to Bayesian SLAM. IEEE Transactions on Robotics, 27(2), 268–282.

    Article  Google Scholar 

  • Natural Point Inc. (2013). http://www.naturalpoint.com/optitrack/.

  • Nazin, S.A. & Polyak, B.T. (2001). Limiting behavior of bounding ellipsoid for state estimation. Proceedings of the 5th IFAC symposium on nonlinear control systems. St.Petersburg, 585–589.

  • Neira, J., & Tardos, J. D. (2001). Data association in stochastic mapping using the joint compatibility test. IEEE Transactions on Robotics and Automation, 17(6), 890–897.

    Article  Google Scholar 

  • Nieto, J., Guivant, J., & Nebot, E. (2006). DenseSLAM: simultaneous localization and dense mapping. International Journal of Robotics Research, 25, 711–744.

    Article  Google Scholar 

  • Ros, L., Sabater, A., & Thomas, F. (2002). An ellipsoid calculus based on propagation and fusion. IEEE Transactions on Systems, Man and Cybernetics, 32(4), 430–442.

    Article  Google Scholar 

  • Scholte, E., & Campbell, M. E. (2003). A nonlinear set-membership filter for online applications. International Journal of Robust Nonlinear Control, 13, 1337–1358.

    Article  MATH  MathSciNet  Google Scholar 

  • Schweppe, F. C. (1968). Recursive state estimation: Unknown but bounded errors and system inputs. IEEE Transactions on Automatic Control, 13(1), 22–28.

    Article  Google Scholar 

  • Schweppe, F. C. (1973). Uncertain dynamic systems. Englewood cliffs: Prentice-Hall.

    Google Scholar 

  • Schweppe, F. C. (1973). Uncertain dynamic systems. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Sibley, G., Matthies, L., & Sukhatme, G. (2010). Sliding window filter with application to planetary landing. Journal of Field Robotics, 27(5), 587–608.

    Article  Google Scholar 

  • Thrun, S., Liu, Y., Koller, D., Ng, A. Y., Ghahramani, Z., & Durrant-Whyte, H. (2004). Simultaneous localization and mapping with sparse extended information filters. International Journal of Robotics Research, 23, 693–716.

    Article  Google Scholar 

  • Wang, Z., Huang, S., & Dissanayake, G. (2007). D-SLAM: A decoupled solution to simultaneous localization and mapping. International Journal of Robotics Research, 26(2), 187–204.

    Article  Google Scholar 

  • Weyer, E., & Campi, M.C. (2000). Non-asymptotic confidence ellipsoids for the least squares estimate, 39rd IEEE Conference on Decision and Control, Sydney, 2688–2693.

  • Williams, S.B. (2001). “Efficient solutions to autonomous mapping and navigation problems”, PhD Thesis, The University of Sidney.

  • Yu, W., & de Jesus Rubio, J. (2009). Recurrent neural networks training with stable bounding ellipsoid algorithm. IEEE Transactions on Neural Networks, 20(6), 983–991.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Control Automatico, CINVESTAV-IPN (National Polytechnic Institute), 07360, Mexico City, Mexico

    Wen Yu, Erik Zamora & Alberto Soria

Authors
  1. Wen Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik Zamora
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alberto Soria
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen Yu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, W., Zamora, E. & Soria, A. Ellipsoid SLAM: a novel set membership method for simultaneous localization and mapping. Auton Robot 40, 125–137 (2016). https://doi.org/10.1007/s10514-015-9447-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10514-015-9447-y

Keywords

Search

Navigation