Autonomous Robots

, Volume 41, Issue 2, pp 311–331 | Cite as

Stochastic mobility prediction of ground vehicles over large spatial regions: a geostatistical approach

  • Ramón González
  • Paramsothy Jayakumar
  • Karl Iagnemma
Article

Abstract

This paper describes a stochastic approach to vehicle mobility prediction over large spatial regions [>\(5 \times 5\) (km\(^2\))]. The main source of uncertainty considered in this work derives from uncertainty in terrain elevation, which arises from sampling (at a finer resolution) a Digital Elevation Model. In order to account for such uncertainty, Monte Carlo simulation is employed, leading to a stochastic analysis of vehicle mobility properties. Experiments performed on two real data sets (namely, the Death Valley region and Sahara desert) demonstrate the advantage of stochastic analysis compared to classical deterministic mobility prediction. These results show the computational efficiency of the proposed methodology. The robotic simulator ANVEL has also been used to validate the proposed methodology.

Keywords

NATO Reference Mobility Model (NRMM) Mission planning  Geographical Information Systems (GIS) D* path planner  Statistical sampling 

Notes

Acknowledgments

The research described in this publication was carried out at the Massachusetts Institute of Technology, under the Army Research Project Grant W911NF-13-1-0063 funded by US Army TARDEC. The authors also thank Justin Crawford from Quantum Signal for his support with ANVEL. The authors thank anonymous reviewers for providing useful comments on the paper.

References

  1. AM General LLC specialized vehicles for commercial and military customers. http://www.amgeneral.com/vehicles/hmmwv; Visited: November, 2015.
  2. American Society for Testing and Materials (1996) Standard guide for analysis of spatial variation in geostatistical site investigations. In Annual book of ASTM standards. (vol. 04.08). West Conshohocken, PA: ASTM.Google Scholar
  3. Amidi, O. (1990). Integrated mobile robot control. Technical Report CMU–RI–TR–90–17, Robotics Institute, Carnegie Mellon University.Google Scholar
  4. Anderson, A., Wang, G., & Gertner, G. (2006). Local variability based sampling for mapping a soil erosion cover factor by co-simulation with landsat TM images. International Journal of Remote Sensing, 27(12), 2423–2447.CrossRefGoogle Scholar
  5. Arieira, J., Karssenberg, D., de Jong, S., Addink, E., Couto, E., da Cunha, C. N., et al. (2011). Integrating field sampling, geostatistics and remote sensing to map wetland vegetation in the Pantanal, Brazil. Biogeosciences, 8, 667–686.CrossRefGoogle Scholar
  6. Basaran, M., Erpul, G., Ozcan, A., Saygin, D., Kibar, M., Bayramin, I., et al. (2011). Spatial information of soil hydraulic conductivity and performance of Cokriging over Kriging in a semi-arid basin scale. Environ Earth Sci, 63, 827–838.CrossRefGoogle Scholar
  7. Bechler, A., Romary, T., Jeannee, N., & Desnoyers, Y. (2013). Geostatistical sampling optimization of contaminated facilities. Stochastic Environmental Research and Risk Assessment, 27(8), 1967–1974.CrossRefGoogle Scholar
  8. Bivand, R., Pebesma, E., & Gomez-Rubio, V. (2013). Use R (2nd ed.)., Applied spatial data analysis with R New York: Springer.MATHGoogle Scholar
  9. Bohling, G. (2005). Kriging. http://people.ku.edu/~gbohling/cpe940; Visited: November, 2015.
  10. Brus, D., & Gruijter, J. (1994). Estimation of non-ergodic variograms and their sampling variance by design-based sampling strategies. Mathematical Geology, 26(4), 437–454.CrossRefGoogle Scholar
  11. Chiles, J., & Delfiner, P. (2012). Geostatistics. modeling spatial uncertainty, probabily and statistics (2nd ed.). New York: Wiley.CrossRefMATHGoogle Scholar
  12. Corke, P. (2011). Robotics, vision and control., Fundamental algorithms in matlab. Springer Tracts in Advanced Robotics Dordrecht: Springer.CrossRefMATHGoogle Scholar
  13. Davis, T., & Keller, C. (1997). Modelling uncertainty in natural resource analysis using fuzzy sets and Monte Carlo simulation: Slope stability prediction. International Journal of Geographical Information Science, 11(5), 409–434.CrossRefGoogle Scholar
  14. Fisher, P. (1991). Modelling soil map-unit inclusions by Monte Carlo simulation. International Jornal of Geographical Information Systems, 5(2), 193–208.CrossRefGoogle Scholar
  15. Fisher, P., & Tate, N. (2006). Causes and consequences of error in digital elevation models. Progress in Physical Geography, 30(4), 467–489.CrossRefGoogle Scholar
  16. Goldberg, S., Maimone, M., & Matthies, L. (2002). Stereo vision and rover navigation software for planetary exploration. IEEE Aerospace Conference, 5, 2025–2036.Google Scholar
  17. Gorsich, D., & Genton, M. (2000). Variogram model selection via nonparametric derivative estimation. Mathematical Geology, 32(3), 249–270.CrossRefGoogle Scholar
  18. Haley, P. W., Jurkat, M. P., & Brady, P. M. (1979). NATO reference mobility model, Edition I. Technical Report 12503. US Army TARDEC, Warren, MI.Google Scholar
  19. Hadsell, R., Sermanet, P., Ben, J., Erkan, A., Scoffier, M., Kavukcuoglu, K., et al. (2009). Learning long-range vision for autonomous off-road driving. Journal of Field Robotics, 26(2), 120–144.CrossRefGoogle Scholar
  20. Helmick, D., Angelova, A., & Matthies, L. (2009). Terrain adaptive navigation for planetary rovers. Journal of Field Robotics, 26(4), 391–410.CrossRefGoogle Scholar
  21. Hosseini, S., Kappas, M., Bodaghabadi, M., Chahouki, M., & Khojasteh, E. (2014). Comparison of different geostatistical methods for soil mapping using remote sensing and environment variables in Pshtkouh rangelands, Iran. Polish Journal of Environmental Studies, 23(3), 737–751.Google Scholar
  22. Hunter, G., & Goodchild, M. (1997). Modeling the uncertainty of slope and aspect estimates derived from spatial databases. Geographical Analysis, 29(1), 35–49.CrossRefGoogle Scholar
  23. Isaaks, E., & Srivastava, R. (1989). An introduction to applied geostatistics. Oxford: Oxford University Press.MATHGoogle Scholar
  24. Ishigami, G., Nagatani, K., & Yoshida, K. (2009). Slope traversal controls for planetary exploration rover on sandy terrain. Journal of Field Robotics, 26(3), 264–286.CrossRefGoogle Scholar
  25. Karumachi, S., Allen, T., Bailey, T., & Scheding, S. (2010). Non-parametric learning to aid path planning over slopes. The International Journal of Robotics Research, 29(8), 997–1018.CrossRefGoogle Scholar
  26. Kweon, I. S., & Kanade, T. (1992). High-resolution terrain map from multiple sensor data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2), 278–292.CrossRefGoogle Scholar
  27. Kerry, R., Oliver, M., & Frogbrook, Z. (2010). Sampling in precision agriculture. Geostatistical applications for precision agriculture (pp. 35–63). Dordrecht: Springer.CrossRefGoogle Scholar
  28. Kulis, B., & Jordan, M. (2012). Revisiting K-means: New algorithms via Bayesian nonparametrics. In International conference on machine learning (pp. 513–520): International Machine Learning Society (IMLS).Google Scholar
  29. Kumar, J., Mills, R., Hoffman, F., & Hargrove, W. (2011). Parallel K-means clustering for quantitative ecoregion delineation using large data sets. Procedia Computer Science, 4, 1602–1611.CrossRefGoogle Scholar
  30. Lakhankar, T., Jones, A., Combs, C., Sengupta, M., Haar, T. V., & Khanbilvardi, R. (2010). Analysis of large scale spatial variability of soil moisture using a geostatistical method. Sensors, 10, 913–932.CrossRefGoogle Scholar
  31. LaValle, S. M. (2006). Planning algorithms. Cambridge: Cambridge University Press. http://planning.cs.uiuc.edu; Visited: November, 2015.
  32. Lessem, A., Mason, G., & Ahlvin, R. (1996). Stochastic vehicle mobility forecasts using the NATO reference mobility model. Journal of Terramechanics, 33(6), 273–280.CrossRefGoogle Scholar
  33. Li, J., & Heap, A. (2011). A review of comparative studies of spatial interpolation methods in environmental sciences: Performance and impact factors. Ecological Informatics, 6(3–4), 228–241.CrossRefGoogle Scholar
  34. mGstat: A geostatistical matlab toolbox. http://mgstat.sourceforge.net; Visited: November, 2015.
  35. Papadakis, P. (2013). Terrain traversability analysis methods for unmanned ground vehicles: A survey. Engineering Applicatons of Artificial Intelligence, 26(4), 1373–1385.CrossRefGoogle Scholar
  36. Pengelly, J. (2002). Monte Carlo methods. http://www.cs.otago.ac.nz/cosc453; Visited: November, 2015.
  37. Peynot, T., Lui, S., McAllister, R., Fitch, R., & Sukkarieh, S. (2014). Learned stochastic mobility prediction for planning with control uncertainty on unstructured terrain. Journal of Field Robotics, 31(6), 969–995.CrossRefGoogle Scholar
  38. Rubinstein, R., & Kroese, D. (2007). Simulation and the Monte Carlo method (2nd ed.)., Applied Probability and Statistics New York: Wiley.CrossRefMATHGoogle Scholar
  39. Stentz, A. (1995). The focussed D* algorithm for real-time replanning. In Proceedings of the international joint conference on artificial intelligence.Google Scholar
  40. Stentz, A., Kelly, A., Rander, P., Herman, H., Amidi, O., Mandelbaum, R., et al. (2003). Real-time, multi-perspective perception for unmanned ground vehicles. In Proceedings of of AUVSI unmanned systems symposium.Google Scholar
  41. Stentz,T., Kelly, A., Herman, H., Rander, P., & Amidi, O. (2002). Integrated air/ground vehicle system for semi-autonomous off-road navigation. In AUVSI symposium (pp. 1–15).Google Scholar
  42. Srivastava, R. (2013). Geostatistics: A toolkit for data analysis, spatial prediction and risk management in the coal industry. International Journal of Coal Geology, 112, 2–13.CrossRefGoogle Scholar
  43. Thompson, S. (2012). Sampling, probability and statistics (3rd ed.). New York: Wiley.Google Scholar
  44. Thrun, S., Montemerlo, M., et al. (2006). STANLEY, the robot that won the DARPA gran challenge. Journal of Field Robotics, 23(9), 661–692.CrossRefGoogle Scholar
  45. Tsui, O., Coops, N., Wulder, M., & Marshall, P. (2013). Integrating airborne LIDAR and space-borne radar via multivariable Kriging to estimate above-ground biomass. Remote Sensing of Environment, 139, 340–352.CrossRefGoogle Scholar
  46. Vandapel, N., Donamukkala, R., & Hebert, M. (2006). Unmanned ground vehicle navigation using aerial ladar data. International Journal of Robotics Research, 25(1), 31–51.CrossRefGoogle Scholar
  47. van der Meer, F. (2012). Remote-sensing image analysis and geostatistics. International Journal of Remote Sensing, 33(18), 5644–5676.CrossRefGoogle Scholar
  48. Vedaldi, A., Fulkerson, B. (2008). VLFeat: An open and portable library of computer vision algorithms. http://www.vlfeat.org; Visited: November, 2015.
  49. WebGIS. (2105). Geographic information systems resource. http://www.webgis.com; Visited: November, 2015.
  50. Webster, R., & Oliver, M. (2007). Geostatistics for environmental scientists (2nd ed.)., Statistics in Practice New York: Wiley.CrossRefMATHGoogle Scholar
  51. Willoughby, W., Jones, R., Mason, G., Shoop, S., & Lever, J. (2006). Application of historical mobility testing to sensor-based robotic performance. In: Proceedings of SPIE 6230, unmanned systems technology VIII (pp. 1–8).Google Scholar
  52. Wu, J. (2012). Advances in K-means clustering., Springer Theses Berlin: Springer.CrossRefMATHGoogle Scholar
  53. Zhou, Q., & Liu, X. (2004). Analysis of errors of derived slope and aspect related to DEM data properties. Journal of Computer & Geosciences, 30, 369–378.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Ramón González
    • 1
  • Paramsothy Jayakumar
    • 3
  • Karl Iagnemma
    • 2
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA
  3. 3.US Army RDECOM TARDECWarrenUSA

Personalised recommendations