Skip to main content
SpringerLink
Log in

Observability-based Optimization of Coordinated Sampling Trajectories for Recursive Estimation of a Strong, Spatially Varying Flowfield

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

Autonomous vehicles are effective environmental sampling platforms whose sampling performance can be optimized by path-planning algorithms that drive vehicles to specific regions of the operational domain containing the most informative data. In this paper, we apply tools from nonlinear observability, nonlinear control, and Bayesian estimation to derive a multi-vehicle control algorithm that steers vehicles to an optimal sampling formation in an estimated flowfield. Sampling trajectories are optimized using the empirical observability gramian, which quantifies the sensitivity of output measurements to variations of the flowfield parameters. We reconstruct the parameters of the flowfield from noisy flow measurements collected along the sampling trajectories using a recursive Bayesian filter.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Elston, J., Argrow, B., Frew, E., Houston, A.: Evaluation of UAS concepts of operation for severe storm penetration using hardware-in-the-loop simulations. In: AIAA Guidance, Navigation, and Control Conference, pp. 8178–8193. Toronto, Canada (2010)

  2. Leonard, N., Paley, D.A., Lekien, F., Sepulchre, R., Fratantoni, D., Davis, R.: Collective motion, sensor networks, and ocean sampling. In: Proceedings of the IEEE, vol. 95, no. 1, pp. 48–74 (2007)

  3. Lin, P.: Observations: The first successful typhoon eyewall-penetration reconnaissance flight mission conducted by the unmanned aerial vehicle, Aerosonde. Bull. Am. Meteorol. Soc. 87, 1481–1483 (2006)

    Article  Google Scholar 

  4. Hurricane basics: National Oceanographic and Atmospheric Administration (NOAA) (1999). http://hurricanes.noaa.gov/pdf/hurricanebook.pdf. Accessed 24 July 2012

  5. Ramp, S.R., Lermusiaux, P., Shulman, I., Chao, Y., Wolf, R.E., Bahr, F.L.: Oceanographic and atmospheric conditions on the continental shelf north of the Monterey bay during August 2006. Dyn. Atmos. Ocean. 52, 192–223 (2011)

    Article  Google Scholar 

  6. Krener, A.J.: Eulerian and Lagrangian observability of point vortex flows. Tellus 60, 1089–1102 (2008)

    Article  Google Scholar 

  7. Cortes, J., Martinez, S., Karatas, T., Bullo, F.: Coverage control for mobile sensing networks. IEEE Trans. Robot. Autom. 20(2), 243–255 (2004)

    Article  Google Scholar 

  8. Singh, A.K., Hahn, J.: Determining optimal sensor locations for state and parameter estimation for stable nonlinear systems. Ind. Eng. Chem. Res 44(15), 5645–5659 (2005)

    Article  Google Scholar 

  9. Lawrance, N.R., Sukkarieh, S.: Autonomous exploration of a wind field with a gliding aircraft. AIAA J. Guid. Control Dyn. 34(3), 719–733 (2011)

    Article  Google Scholar 

  10. Wouwer, A.V., Point, N., Porteman, S., Remy, M.: An approach to the selection of optimal sensor locations in distributed parameter systems. J. Process Control 10(4), 291–300 (2000)

    Article  Google Scholar 

  11. Lall, S., Marsden, J., Glavaski, S.A.: A subspace approach to balanced truncation for model reduction of nonlinear control systems. Int. J. Robust Nonlinear Control 12(6), 519–535 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Graham, R., Cortes, J.: Adaptive information collection by robotic sensor networks for spatial estimation. IEEE Trans. Automat. Contr. 57(6), 1404–1419 (2012)

    Article  MathSciNet  Google Scholar 

  13. Krener, A., Ide, K.: Measures of unobservability. In: IEEE Conference on Decision and Control, pp. 6401–6406. Shanghai, China (2009)

  14. Hermann, R., Krener, A.J.: Nonlinear controllability and observability. IEEE Trans. Automat. Contr. 22(5), 728–740 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  15. Salman, H., Kuznetsov, L., Jones, C., Ide, K.: A method of assimilating Lagrangian data into a shallow-water-equation ocean model. Mon. Weather Rev. 134, 1081–1101 (2006)

    Article  Google Scholar 

  16. Bergman, N.: Recursive Bayesian estimation navigation and tracking applications. Ph.D. dissertation, Department of Electrical Engineering, Linkoping University, Sweden (1999)

  17. Palanthandalam-Madapusi, H.J., Girard, A., Bernstein, D.S.: Wind-field reconstruction using flight data. In: Proc. of the 2008 American Control Conference, pp. 1863–1868 (2008)

  18. Langelaan, J.W., Alley, N., Neidhoefer, J.: Wind field estimation for small unmanned aerial vehicles. AIAA J. Guid. Control Dyn. 34(4), 1016–1030 (2011)

    Article  Google Scholar 

  19. Mulgund, S., Stengel, R.F.: Optimal nonlinear estimation for aircraft flight control in wind shear. Automatica 32(1), 3–13 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lynch, K.M., Schwartz, I.B., Yang, P., Freeman, R.A.: Decentralized environmental modeling by mobile sensor networks. IEEE Trans. Robot. 24(3), 710–724 (2008)

    Article  Google Scholar 

  21. DeVries, L., Paley, D.A.: Multi-vehicle control in a strong flowfield with application to hurricane sampling. J. Guid. Control Dyn. 35(3), 794–806 (2012)

    Article  Google Scholar 

  22. Paley, D.A., Peterson, C.: Stabilization of collective motion in a time-invariant flowfield. AIAA J. Guid. Control Dyn. 32, 771–779 (2009)

    Article  Google Scholar 

  23. Sepulchre, R., Paley, D.A., Leonard, N.E.: Stabilization of planar collective motion: all-to-all communication. IEEE Trans. Automat. Contr. 52, 811–824 (2007)

    Article  MathSciNet  Google Scholar 

  24. Techy, L., Paley, D.A., Woolsey, C.: UAV coordination on closed convex paths in wind. AIAA J. Guid. Control Dyn. 33, 1946–1951 (2010)

    Article  Google Scholar 

  25. Brinon Arranz, L., Seuret, A., Canudas De Wit, C.: Contraction control of a fleet circular formation of AUVs under limited communication range. In: Proc. of the 2010 American Control Conference, pp. 5991–5996. Baltimore, MD (2010)

  26. Sepulchre, R., Paley, D.A., Leonard, N.E.: Stabilization of planar collective motion with limited communication. IEEE Trans. Automat. Contr. 53, 706–719 (2008)

    Article  MathSciNet  Google Scholar 

  27. Brinon Arranz, L., Seuret, A., Canudas De Wit, C.: Translation control of a fleet circular formation of AUVs under finite communication range. In: Proc. of the 48th IEEE Conference on Decision and Control, pp. 8345–8350. Shanghai, China (2009)

  28. Paley, D.A., Leonard, N., Sepulchre, R.: Collective motion of self-propelled particles: Stabilizing symmetric formations on closed curves. In: Proc. 45th IEEE Conf. Decision and Control, pp. 5067–5072. San Diego, CA (2006)

  29. Ide, K., Ghil, M.: Extended Kalman filtering for vortex systems. part ii: rankine vortices. Dyn. Atmos. Ocean. 27, 333–350 (1997)

    Article  Google Scholar 

  30. Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control: Analysis and Design. John Wiley and Sons, West Sussex, England (1996)

    Google Scholar 

  31. Vaidya, U.: Observability gramian for nonlinear systems. In: Proc. of the 46th IEEE Conf. on Decision and Control (CDC), pp. 3357–3362. New Orleans, LA (2007)

  32. Hahn, J., Edgar, T.F.: A gramian based approach to nonlinear quantification and model classification. Ind. Eng. Chem. Res. 40, 5724–5731 (2001)

    Article  Google Scholar 

  33. Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall (2002)

  34. Peterson, C., Paley, D.A., Multi-vehicle coordination in an estimated time-varying flowfield. AIAA J. Guid. Control Dyn. 34, 177–191 (2011)

    Article  Google Scholar 

  35. Paley, D.A., Zhang, F., Leonard, N.E.: Cooperative control for ocean sampling: the Glider Coordinated Control System. IEEE Trans. Control Syst. Technol. 16(4), 735–744 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, University of Maryland, College Park, MD, USA

    Levi DeVries

  2. Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL, USA

    Sharanya J. Majumdar

  3. Department of Aerospace Engineering and Institute for Systems Research, University of Maryland, College Park, MD, USA

    Derek A. Paley

Authors
  1. Levi DeVries
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sharanya J. Majumdar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Derek A. Paley
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Levi DeVries.

Additional information

This work is supported by the National Science Foundation under CMMI Grant Nos. CMMI0928416 and CMMI0928198 and the Office of Naval Research under Grant No. N00014-09-1-1058.

Rights and permissions

Reprints and permissions

About this article

Cite this article

DeVries, L., Majumdar, S.J. & Paley, D.A. Observability-based Optimization of Coordinated Sampling Trajectories for Recursive Estimation of a Strong, Spatially Varying Flowfield. J Intell Robot Syst 70, 527–544 (2013). https://doi.org/10.1007/s10846-012-9718-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-012-9718-1

Keywords

Search

Navigation