Adaptive Sampling to Estimate Quantiles for Guiding Physical Sampling

Scientists interested in studying natural phenomena often take physical samples for later analysis at locations specified by expert heuristics. Instead, we propose to guide scientists’ physical sampling by using a robot to perform an adaptive sampling survey to find locations to suggest that correspond to the quantile values of pre-specified quantiles of interest. We develop a robot planner using novel objective functions to improve the estimates of the quantile values over time and an approach to find locations which correspond to the quantile values. We demonstrate our approach on two different sampling tasks in simulation using previously collected aquatic data and validate it in a field trial. Our approach outperforms objectives that maximize spatial coverage or find extrema in planning and is able to localize the quantile spatial locations.

[1]  Geoffrey A. Hollinger,et al.  Topological Hotspot Identification for Informative Path Planning with a Marine Robot , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[2]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[3]  Marc Toussaint,et al.  The Bayesian Search Game , 2014, Theory and Principled Methods for the Design of Metaheuristics.

[4]  J. S. Maritz,et al.  A Note on Estimating the Variance of the Sample Median , 1978 .

[5]  Geoffrey A. Hollinger,et al.  Sampling-based robotic information gathering algorithms , 2014, Int. J. Robotics Res..

[6]  Gaurav S. Sukhatme,et al.  Adaptive Sampling using POMDPs with Domain-Specific Considerations , 2021, 2021 IEEE International Conference on Robotics and Automation (ICRA).

[7]  Howie Choset,et al.  Trajectory-Optimized Sensing for Active Search of Tissue Abnormalities in Robotic Surgery , 2017, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[8]  Dan Cornford,et al.  Gaussian Process Quantile Regression using Expectation Propagation , 2012, ICML.

[9]  Gaurav S. Sukhatme,et al.  Data-driven robotic sampling for marine ecosystem monitoring , 2015, Int. J. Robotics Res..

[10]  Shie Mannor,et al.  A Tutorial on the Cross-Entropy Method , 2005, Ann. Oper. Res..

[11]  R. Wilcox.  Introduction to Robust Estimation and Hypothesis Testing , 1997 .

[12]  Julia Kastner,et al.  Introduction to Robust Estimation and Hypothesis Testing , 2005 .

[13]  Gaurav S. Sukhatme,et al.  Pilot Surveys for Adaptive Informative Sampling , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[14]  Rob J Hyndman,et al.  Sample Quantiles in Statistical Packages , 1996 .

[15]  Joel Veness,et al.  Monte-Carlo Planning in Large POMDPs , 2010, NIPS.

[16]  Martin Ludvigsen,et al.  Information‐driven robotic sampling in the coastal ocean , 2018, J. Field Robotics.

[17]  Scott Sanner,et al.  Sequential Bayesian Optimisation for Spatial-Temporal Monitoring , 2014, UAI.

[18]  Diego Klabjan,et al.  Improving the Expected Improvement Algorithm , 2017, NIPS.

[19]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[20]  Andreas Krause,et al.  Near-optimal sensor placements in Gaussian processes , 2005, ICML.

[21]  B. Reich.  Spatiotemporal quantile regression for detecting distributional changes in environmental processes , 2012, Journal of the Royal Statistical Society. Series C, Applied statistics.

[22]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[23]  Fabio Tozeto Ramos,et al.  Bayesian optimisation for active perception and smooth navigation , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[24]  G. Sukhatme,et al.  Comparison of Path Planning Approaches for Harmful Algal Bloom Monitoring , 2019, OCEANS 2019 MTS/IEEE SEATTLE.