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Observability-based consistent EKF estimators for multi-robot cooperative localization

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Abstract

In this paper, we investigate the consistency of extended Kalman filter (EKF)-based cooperative localization (CL) from the perspective of observability. We analytically show that the error-state system model employed in the standard EKF-based CL always has an observable subspace of higher dimension than that of the actual nonlinear CL system. This results in unjustified reduction of the EKF covariance estimates in directions of the state space where no information is available, and thus leads to inconsistency. To address this problem, we adopt an observability-based methodology for designing consistent estimators in which the linearization points are selected to ensure a linearized system model with observable subspace of correct dimension. In particular, we propose two novel observability-constrained (OC)-EKF estimators that are instances of this paradigm. In the first, termed OC-EKF 1.0, the filter Jacobians are calculated using the prior state estimates as the linearization points. In the second, termed OC-EKF 2.0, the linearization points are selected so as to minimize their expected errors (i.e., the difference between the linearization point and the true state) under the observability constraints. The proposed OC-EKFs have been tested in simulation and experimentally, and have been shown to significantly outperform the standard EKF in terms of both accuracy and consistency.

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References

  • Bahr, A., Walter, M. R., & Leonard, J. J. (2009). Consistent cooperative localization. In Proc. IEEE international conference on robotics and automation (pp. 3415–3422), Kobe, Japan, May 15–19, 2009.

  • Bailey, T., Nieto, J., Guivant, J., Stevens, M., & Nebot, E. (2006). Consistency of the EKF-SLAM algorithm. In Proc. IEEE/RSJ international conference on intelligent robots and systems (pp. 3562–3568), Beijing, China, October 9–15, 2006.

  • Bar-Shalom, Y., Li, X. R., & Kirubarajan, T. (2001). Estimation with applications to tracking and navigation. New York: Wiley.

    Book  Google Scholar 

  • Bertsekas, D. P. (1999). Nonlinear programming. Nashua: Athena Scientific.

    MATH  Google Scholar 

  • Castellanos, J. A., Neira, J., & Tardos, J. (2004). Limits to the consistency of EKF-based SLAM. In Proc. 5th IFAC symposium on intelligent autonomous vehicles (pp. 1244–1249), Lisbon, Portugal, July 5–7, 2004.

  • Chen, Z., Jiang, K., & Hung, J. C. (1990). Local observability matrix and its application to observability analyses. In Proc. 16th annual conference of IEEE (pp. 100–103), Pacific Grove, CA, November 27–30, 1990.

  • Dieudonne, Y., Labbani-Igbida, O., & Petit, F. (2010). Deterministic robot-network localization is hard. IEEE Transactions on Robotics, 26(2), 331–339.

    Article  Google Scholar 

  • Feng, Y., Zhu, Z., & Xiao, J. (2006). Heterogeneous multi-robot localization in unknown 3D space. In Proc. IEEE/RSJ international conference on intelligent robots and systems (pp. 4533–4538), Beijing, China, October 9–15, 2006.

  • Fox, D., Burgard, W., Kruppa, H., & Thrun, S. (2000). A probabilistic approach to collaborative multi-robot localization. Autonomous Robots, 8(3), 325–344.

    Article  Google Scholar 

  • Hermann, R., & Krener, A. (1977). Nonlinear controllability and observability. IEEE Transactions on Automatic Control, 22(5), 728–740.

    Article  MATH  MathSciNet  Google Scholar 

  • Howard, A., Mataric, M. J., & Sukhatme, G. S. (2002). Localization for mobile robot teams using maximum likelihood estimation. In Proc. IEEE/RSJ international conference on intelligent robots and systems (pp. 434–439), Lausanne, Switzerland, September 30–October 4, 2002.

  • Howard, A., Mataric, M. J., & Sukhatme, G. S. (2003). Putting the ‘I’ in ‘team’: an ego-centric approach to cooperative localization. In Proc. IEEE international conference on robotics and automation (pp. 868–874), Taipei, Taiwan, September 14–19, 2003.

  • Huang, S., & Dissanayake, G. (2006). Convergence analysis for extended Kalman filter based SLAM. In Proc. IEEE international conference on robotics and automation (pp. 412–417), Orlando, FL, May 15–19, 2006.

  • Huang, S., & Dissanayake, G. (2007). Convergence and consistency analysis for extended Kalman filter based SLAM. IEEE Transactions on Robotics, 23(5), 1036–1049.

    Article  Google Scholar 

  • Huang, G. P., Mourikis, A. I., & Roumeliotis, S. I. (2008a). Analysis and improvement of the consistency of extended Kalman filter-based SLAM. In Proc. IEEE international conference on robotics and automation (pp. 473–479), Pasadena, CA, May 12–17, 2008.

  • Huang, G. P., Mourikis, A. I., & Roumeliotis, S. I. (2008b). A first-estimates Jacobian EKF for improving SLAM consistency. In Proc. 11th international symposium on experimental robotics (pp. 373–382), Athens, Greece, July 14–17, 2008.

  • Huang, G. P., Trawny, N., Mourikis, A. I., & Roumeliotis, S. I. (2009). On the consistency of multi-robot cooperative localization (Technical report). MARS Lab, University of Minnesota, Minnapolis, MN. www.cs.umn.edu/~ghuang/paper/TR_CL_Consistency.pdf

  • Huang, G. P., Trawny, N., Mourikis, A. I., & Roumeliotis, S. I. (2009). On the consistency of multi-robot cooperative localization. In Proc. robotics: science and systems (pp. 65–72), Seattle, WA, June 28–July 1, 2009.

  • Huang, G. P., Mourikis, A. I., & Roumeliotis, S. I. (2010). Observability-based rules for designing consistent EKF SLAM estimators. International Journal of Robotics Research, 29(5), 502–528.

    Article  Google Scholar 

  • Huntsberger, T. L., Trebi-Ollennu, A., Aghazarian, H., Schenker, P. S., & Pirjanian, P. (2004). Distributed control of multi-robot systems engaged in tightly coupled tasks. Autonomous Robots, 17(1), 79–92.

    Article  Google Scholar 

  • Julier, S., & Uhlmann, J. (2001). A counter example to the theory of simultaneous localization and map building. In Proc. IEEE international conference on robotics and automation (pp. 4238–4243), Seoul, Korea, May 21–26, 2001.

  • Karam, N., Chausse, F., Aufrere, R., & Chapuis, R. (2006). Localization of a group of communicating vehicles by state exchange. In Proc. IEEE/RSJ international conference on intelligent robots and systems (pp. 519–524), Beijing, China, October 9–15, 2006.

  • Kurazume, R., & Hirose, S. (2000). An experimental study of a cooperative positioning system. Autonomous Robots, 8(1), 43–52.

    Article  Google Scholar 

  • Martinelli, A. (2007). Improving the precision on multi robot localization by using a series of filters hierarchically distributed. In Proc. IEEE/RSJ international conference on intelligent robots and systems (pp. 1053–1058), San Diego, CA, October 29–November 2, 2007.

  • Martinelli, A., & Siegwart, R. (2005). Observability analysis for mobile robot localization. In Proc. IEEE/RSJ international conference on intelligent robots and systems (pp. 1471–1476), Alberta, Canada, August 2–6, 2005.

  • Meyer, C. (2001). Matrix analysis and applied linear algebra. Philadelphia: SIAM.

    Google Scholar 

  • Mourikis, A. I., & Roumeliotis, S. I. (2006). Performance analysis of multirobot cooperative localization. IEEE Transactions on Robotics, 22(4), 666–681.

    Article  Google Scholar 

  • Mourikis, A. I., & Roumeliotis, S. I. (2006). Optimal sensor scheduling for resource-constrained localization of mobile robot formations. IEEE Transactions on Robotics, 22(5), 917–931.

    Article  Google Scholar 

  • Nerurkar, E. D., Roumeliotis, S. I., & Martinelli, A. (2009). Distributed maximum a posteriori estimation for multi-robot cooperative localization. In Proc. IEEE international conference on robotics and automation (pp. 1402–1409), Kobe, Japan, May 12–17, 2009.

  • Panzieri, S., Pascucci, F., & Setola, R. (2006). Multirobot localization using interlaced extended Kalman filter. In Proc. IEEE/RSJ international conference on intelligent robots and systems (pp. 2816–2821), Beijing, China, October 9–15, 2006.

  • Rekleitis, I. M., Dudek, G., & Milios, E. E. (2002). Multi-robot cooperative localization: a study of trade-offs between efficiency and accuracy. In Proc. IEEE/RSJ international conference on intelligent robots and systems (pp. 2690–2695), Lausanne, Switzerland, September 30–October 4, 2002.

  • Roumeliotis, S. I., & Bekey, G. A. (2002). Distributed multirobot localization. IEEE Transactions on Robotics and Automation, 18(5), 781–795.

    Article  Google Scholar 

  • Roumeliotis, S. I., & Rekleitis, I. M. (2004). Propagation of uncertainty in cooperative multirobot localization: Analysis and experimental results. Autonomous Robots, 17(1), 41–54.

    Article  Google Scholar 

  • Tews, A. D., Sukhatme, G. S., & Mataric, M. J. (2004). A multi-robot approach to stealthy navigation in the presence of an observer. In Proc. IEEE international conference on robotics and automation (pp. 2379–2385), New Orleans, LA, April 26–May 1, 2004.

  • Trawny, N., & Roumeliotis, S. I. (2010). On the global optimum of planar, range-based robot-to-robot relative pose estimation. In Proc. IEEE international conference on robotics and automation (pp. 3200–3206), Anchorage, AK, May 3–8, 2010.

  • Trawny, N., Zhou, X. S., & Roumeliotis, S. I. (2009). 3D relative pose estimation from six distances. In Proc. robotics: science and systems (pp. 233–240), Seattle, WA, June 28–July 1, 2009.

  • Trawny, N., Zhou, X. S., Zhou, K., & Roumeliotis, S. I. (2010). Interrobot transformations in 3-D. IEEE Transactions on Robotics, 26(2), 226–243.

    Article  Google Scholar 

  • Zhou, X. S., & Roumeliotis, S. I. (2008). Robot-to-robot relative pose estimation from range measurements. IEEE Transactions on Robotics, 24(6), 1379–1393.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Guoquan P. Huang, Nikolas Trawny & Stergios I. Roumeliotis

  2. Department of Electrical Engineering, University of California, Riverside, CA, 92521, USA

    Anastasios I. Mourikis

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  1. Guoquan P. Huang
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  2. Nikolas Trawny
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  3. Anastasios I. Mourikis
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  4. Stergios I. Roumeliotis
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Correspondence to Guoquan P. Huang.

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Huang, G.P., Trawny, N., Mourikis, A.I. et al. Observability-based consistent EKF estimators for multi-robot cooperative localization. Auton Robot 30, 99–122 (2011). https://doi.org/10.1007/s10514-010-9207-y

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