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Mobile Robotic Sensors for Environmental Monitoring using Gaussian Markov Random Field

Published online by Cambridge University Press:  01 September 2020

Linh Nguyen Open the ORCID record for Linh Nguyen [Opens in a new window] ,
Sarath Kodagoda ,
Ravindra Ranasinghe  and
Gamini Dissanayake
Linh Nguyen*
Affiliation:
School of Engineering, Information Technology and Physical Sciences, Federation University Australia, Churchill, VIC 3842, Australia
Sarath Kodagoda
Affiliation:
Centre for Autonomous Systems, University of Technology Sydney, Ultimo, NSW 2007, Australia E-mails: sarath.kodagoda@uts.edu.au, ravindra.ranasinghe@uts.edu.au, gamini.dissanayake@uts.edu.au
Ravindra Ranasinghe
Affiliation:
Centre for Autonomous Systems, University of Technology Sydney, Ultimo, NSW 2007, Australia E-mails: sarath.kodagoda@uts.edu.au, ravindra.ranasinghe@uts.edu.au, gamini.dissanayake@uts.edu.au
Gamini Dissanayake
Affiliation:
Centre for Autonomous Systems, University of Technology Sydney, Ultimo, NSW 2007, Australia E-mails: sarath.kodagoda@uts.edu.au, ravindra.ranasinghe@uts.edu.au, gamini.dissanayake@uts.edu.au
*
*Corresponding author. E-mail: l.nguyen@federation.edu.au
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Summary

This paper addresses the issue of monitoring spatial environmental phenomena of interest utilizing information collected by a network of mobile, wireless, and noisy sensors that can take discrete measurements as they navigate through the environment. It is proposed to employ Gaussian Markov random field (GMRF) represented on an irregular discrete lattice by using the stochastic partial differential equations method to model the physical spatial field. It then derives a GMRF-based approach to effectively predict the field at unmeasured locations, given available observations, in both centralized and distributed manners. Furthermore, a novel but efficient optimality criterion is then proposed to design centralized and distributed adaptive sampling strategies for the mobile robotic sensors to find the most informative sampling paths in taking future measurements. By taking advantage of conditional independence property in the GMRF, the adaptive sampling optimization problem is proven to be resolved in a deterministic time. The effectiveness of the proposed approach is compared and demonstrated using pre-published data sets with appealing results.

Keywords

Environmental monitoringMobile robotic sensorsSensor networksSpatial predictionGaussian Markov random field

Information

Type
Articles
Information
Robotica , Volume 39 , Issue 5 , May 2021 , pp. 862 - 884
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

Leonard, N. E., Paley, D., Lekien, F., Sepulchre, R., Fratantoni, D. M. and Davis, R., “Collective motion, sensor networks and ocean sampling,” Proc. IEEE 95(1), 48–74 (2007).CrossRefGoogle Scholar
Mysorewala, M., Popa, D. and Lewis, F., “Multi-scale adaptive sampling with mobile agents for mapping of forest fires,” J. Intell. Robot. Syst. 54(4), 535–565 (2009).CrossRefGoogle Scholar
Le, D. V., Oh, H. and Yoon, S., “Environment learning-based coverage maximization with connectivity constraints in mobile sensor networks,” IEEE Sens. J. 16(10), 3958–3971 (2016).CrossRefGoogle Scholar
Susca, S., Bullo, F. and Martínez, S., “Monitoring environmental boundaries with a robotic sensor network,” IEEE Trans. Syst, Control. Tech. 16(2), 288–296 (2008).Google Scholar
Jadaliha, M. and Choi, J., “Environmental monitoring using autonomous aquatic robots: Sampling algorithms and experiments,” IEEE Trans. Syst, Control. Tech. 21(3), 899–905 (2013).Google Scholar
Choi, J., Lee, J. and Oh, S., “Swarm Intelligence for Achieving the Global Maximum Using Spatio-Temporal Gaussian Processes,” Proceedings of the American Control Conference, Washington, USA, June 2008, pp. 135–140.Google Scholar
Graham, R. and Cortes, J., “A Cooperative Deployment Strategy for Optimal Sampling in Spatiotemporal Estimation,” Proceedings of the IEEE Conference on Decision and Control, Cancun, Mexico (2008) pp. 2432–2437.Google Scholar
Graham, R. and Cortes, J., “Distributed Sampling of Random Fields with Unknown Covariance,” Proceedings of the American Control Conference, MI, USA (2009) pp. 4543–4548.Google Scholar
Graham, R. and Cortes, J., “Cooperative Adaptive Sampling via Approximate Entropy Maximization,” Proceedings of the IEEE Conference on Decision and Control, Shanghai, China (2009) pp. 7055–7060.Google Scholar
Cortés, J., “Distributed Kriged Kalman filter for spatial estimation,” IEEE Trans. Autom. Control 54(12), 2816–2827 (2009).Google Scholar
Cortes, J., Martínez, S., Karatas, T. and Bullo, F., “Coverage control for mobile sensing networks,” IEEE Trans. Robot. Autom. 20(2), 243–254 (2004).CrossRefGoogle Scholar
Martínez, S., “Distributed interpolation schemes for field estimation by mobile sensor networks,” IEEE Trans. Syst, Control. Tech. 18(2), 491–500 (2010).Google Scholar
Binney, J., Krause, A. and Sukhatme, G. S., “Optimizing waypoints for monitoring spatiotemporal phenomena,” Int. Robot. Res. 32(8), 873–888 (2013).CrossRefGoogle Scholar
Cressie, N. A., Statistics for Spatial Data (Wiley, New York, USA, 1991).Google Scholar
Rasmussen, C. E. and Williams, C. K. I., Gaussian Processes for Machine Learning (The MIT Press, Cambridge, Massachusetts, London, UK, 2006).Google Scholar
Xu, Y. and Choi, J., “Adaptive sampling for learning Gaussian processes using mobile sensor networks,” Sensors 11(3), 3051–3066 (2011).CrossRefGoogle ScholarPubMed
Xu, Y., Choi, J., Dass, S. and Maiti, T., “Sequential Bayesian prediction and adaptive sampling algorithms for mobile sensor networks,” IEEE Trans. Autom. Control 57(8), 2078–2084 (2012).Google Scholar
Xu, Y., Choi, J. and Oh, S., “Mobile sensor network navigation using Gaussian processes with truncated observations,” IEEE Trans. Robot. 27(6), 1118–1131 (2011).CrossRefGoogle Scholar
Huang, S. and Tan, J., “Adaptive Sampling Using Mobile Sensor Networks,” Proceedings of the IEEE International Conference on Robotics and Automation, Minnesota, USA, May 2012, pp. 657–662.CrossRefGoogle Scholar
Marchant, R. and Ramos, F., “Bayesian Optimization for Intelligent Environmental Monitoring,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Algarve, Portugal, October 2012, pp. 2242–2249.CrossRefGoogle Scholar
Nguyen, L. V., Kodagoda, S., Ranasinghe, R. and Dissanayake, G., “Locational Optimization Based Sensor Placement for Monitoring Gaussian Processes Modeled Spatial Phenomena,” Proceedings of the 8th IEEE International Conference on Industrial Electronics and Applications, Melbourne, Australia, June 2013, pp. 1706–1711.Google Scholar
Nguyen, L. V., Kodagoda, S., Ranasinghe, R. and Dissanayake, G., “Spatially-Distributed Prediction with Mobile Robotic Wireless Sensor Networks,” Proceedings of the 2014 13th IEEE International Conference on Control, Automation, Robotics and Vision, Marina Bay Sands, Singapore, December 2014, pp. 1153–1158.Google Scholar
Nguyen, L. V., Kodagoda, S., Ranasinghe, R. and Dissanayake, G., “Information-driven adaptive sampling strategy for mobile robotic wireless sensor network,” IEEE Trans. Syst, Control. Tech. 24(1), 372–379 (2016).Google Scholar
Nguyen, L. V., Kodagoda, S., Ranasinghe, R. and Dissanayake, G., “Adaptive placement for mobile sensors in spatial prediction under locational errors,” IEEE Sens. J. 17(3), 794–802 (2017).CrossRefGoogle Scholar
Williams, C. K. I and Seeger, M., “Using the Nyström Method to Speed Up Kernel Machines,” Advances in Neural Information Processing Systems, vol. 13 (2001).Google Scholar
Smola, A. J. and Bartlett, P., “Sparse Greedy Gaussian Process Regression,” Advances in Neural Information Processing Systems, vol. 13 (2001).Google Scholar
Lawrence, N., Seeger, M. and Herbrich, R., “Fast Sparse Gaussian Process Methods: The Informative Vector Machine,” Proceedings of the 16th Annual Conference on Neural Information Processing Systems, Vancouver, BC, USA (2003) pp. 609–616.Google Scholar
Rue, H. and Held, L., Gaussian Markov Random Field: Theory and Applications (Chapman and Hall - CRC Press, London, UK, 2005).CrossRefGoogle Scholar
Rue, H. and Tjelmeland, H., “Fitting Gaussian Markov random fields to Gaussian fields,” Scand. J. Stat. 29(1), 31–49 (2002).CrossRefGoogle Scholar
Cressie, N. and Verzelen, N., “Conditional-mean least-squares fitting of Gaussian Markov random fields to Guassian fields,” Comput. Stat. Data Anal. 52(5), 2794–2807 (2008).CrossRefGoogle Scholar
Hartman, L. and Hössjer, O., “Fast kriging of large data sets with Gaussian Markov random fields,” Comput. Stat. Data Anal. 52(5), 2331–2349 (2008).CrossRefGoogle Scholar
Lindgren, F., Rue, H. and Lindström, J., “An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach,” J. R. Stat. Soc. (Ser. B) 73(4), 423–498 (2011).CrossRefGoogle Scholar
Ny, J. L. and Pappas, G. J., “On Trajectory Optimization for Active Sensing in Gaussian Process Models,” Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China (2009) pp. 6286–6292.Google Scholar
Nguyen, L. V., Kodagoda, S., Ranasinghe, R. and Dissanayake, G., “Mobile Robotic Wireless Sensor Networks for Efficient Spatial Prediction,” Proceedings of the 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, Chicago, IL, USA, September 2014, pp. 1176–1181.CrossRefGoogle Scholar
Nguyen, L. V., Kodagoda, S. and Ranasinghe, R., “Spatial sensor selection via Gaussian Markov random fields,” IEEE Trans. Syst. Man Cybernetics Syst. 46(9), 1226–1239 (2016).Google Scholar
Xu, Y., Choi, J., Dass, S. and Maiti, R., “Efficient Bayesian spatial prediction with mobile sensor networks using Gaussian Markov random fields,” Automatica 49(12), 3520–3530 (2013).CrossRefGoogle Scholar
Jadaliha, M. and Choi, J., “Fully Bayesian Simultaneous Localization and Spatial Prediction Using Gaussian Markov Random Fields,” Proceedings of the American Control Conference, Washington DC, USA, June 2013, pp. 4599–4604.CrossRefGoogle Scholar
Jadaliha, M., Xu, Y. and Choi, J., “Efficient Spatial Prediction Using Gaussian Markov Random Fields Under Uncertain Localization,” Proceedings of the ASME Dynamic Systems and Control Conference, Florida, USA, October 2012.Google Scholar
Xu, Y. and Choi, J., “Spatial prediction with mobile sensor networks using Gaussian processes with built-in Gaussian Markov random fields,” Automatica, 48(8), 1735–1740 (2012).CrossRefGoogle Scholar
Singh, A., Krause, A., Guestrin, C. and Kaiser, W. J., “Efficient informative sensing using multiple robots,” J. Artif. Intell. Res. 34(2009), 707–755 (2009).CrossRefGoogle Scholar
Bishop, C. M., Pattern Recognition and Machine Learning (Springer, New York, USA, 2006).Google Scholar
Bernstein, D. S., Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (Princeton University Press, Princeton, New Jersey, USA, 2005).Google Scholar
Rue, H., Martino, S. and Chopin, N., “Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations,” J. R. Stat. Soc. (Ser. B) 71(2), 319–392 (2009).CrossRefGoogle Scholar
Banerjee, S., Carlin, B. and Gelfand, A., Hierarchical Modeling and Analysis for Spatial Data (Chapman and Hall, New York, 2004).Google Scholar
Olfati-Saber, R., Fax, J. A. and Murray, R. M., “Consensus and cooperation in networked multi-agent systems,” Proc. IEEE 95(1), 215–233 (2007).CrossRefGoogle Scholar
Diggle, P. J. and Ribeiro, P. J., Model-Based Geostatistics (Springer, New York, USA, 2007).CrossRefGoogle Scholar
West, M. and Harrison, J., Bayesian Forecasting and Dynamic Models (Springer, New York, 1999).Google Scholar
Cover, T. M. and Thomas, J. A., Elements of Information Theory (John Wiley and Sons, Inc., Hoboken, New Jersey, 2006).Google Scholar
Ko, C., Lee, J. and Queyranne, M., “An exact algorithm for maximum entropy sampling,” Oper. Res. 43(4), 684–691 (1995).CrossRefGoogle Scholar
Nguyen, L., Hu, G. and Spanos, C. J., “Efficient sensor deployments for spatio-temporal environmental monitoring,” IEEE Trans. Syst. Man Cybern. Syst. Early Access, 1–11 (2018).Google Scholar
Stein, M. L., Chi, Z. and Welty, L. J., “Approximating likelihood for large spatial data sets,” J. R. Stat. Soc. (Ser. B) 66(2), 275–296 (2004).CrossRefGoogle Scholar
Mulla, D., Beatty, M. and Sekely, A., “Evaluation of Remote Sensing and Targeted Soil Sampling for Variable Rate Application of Nitrogen,” Proceedings of the 5th International Conference on Precision Agriculture, America (2001).Google Scholar
Tokekar, P., Hook, J. V., Mulla, D. and Isler, V., “Sensor planning for a symbiotic UAV and UGV system for precision agriculture,” IEEE Trans. Robot. 32(6), 1498–1511 (2016).CrossRefGoogle Scholar