Sensors are routinely mounted on robots to acquire various forms of measurements in spatiotemporal fields. Locating features within these fields and reconstruction (mapping) of the dense fields can be challenging in resource-constrained situations, such as when trying to locate the source of a gas leak from a small number of measurements. In such cases, a model of the underlying complex dynamics can be exploited to discover informative paths within the field. We use a fluid simulator as a model to guide inference for the location of a gas leak. We perform localization via minimization of the discrepancy between observed measurements and gas concentrations predicted by the simulator. Our method is able to account for dynamically varying parameters of wind flow (e.g., direction and strength) and its effects on the observed distribution of gas. We develop algorithms for offline inference as well as for online path discovery via active sensing. We demonstrate the efficiency, accuracy, and versatility of our algorithm using experiments with a physical robot conducted in outdoor environments. We deploy an unmanned air vehicle mounted with a CO @math sensor to automatically seek out a gas cylinder emitting CO @math via a nozzle. We evaluate the accuracy of our algorithm by measuring the error in the inferred location of the nozzle, based on which we show that our proposed approach is competitive with respect to state-of-the-art baselines.
Another aspect of active sensing is the method for collecting samples so as to maximise a notion of information gain. While the underlying exploration-exploitation tradeoffs can be posed formally in decision theoretic terms, most practical techniques tend to be myopic in their operation. Gaussian processes le2009trajectory,ouyang2014multi and the Kernel DM+V W algorithm @cite_14 address this question. One could also formulate this as optimal design of sequential experiments @cite_13 . However, this requires access to analytically defined dynamics models which may be hard to construct for the specific scenario at hand. Notably, source term estimation was recently addressed with Bayesian estimation implemented using sequential Monte Carlo @cite_38 . By using parameterized Gaussian plume dispersion model recursive Bayesian updates can be performed accounting for uncertainty in wind, dispersion, etc. This was additionally implemented on a UAV @cite_41 , performing outdoor localization of gas leaks using predefined flying pattern and ground station for performing computations. We formulate active sensing with a fluid simulation in the loop and devise an efficient algorithm for simulation alignment.
@cite_41 @cite_38 @cite_14 @cite_13
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We develop a computationally efficient control policy for active perception that incorporates explicit models of sensing and mobility to build 3D maps with ground and aerial robots. Like previous work, our policy maximizes an information-theoretic objective function between the discrete occupancy belief distribution (e.g., voxel grid) and future measurements that can be made by mobile sensors. However, our work is unique in three ways. First, we show that by using Cauchy-Schwarz Quadratic Mutual Information (CSQMI), we get significant gains in efficiency. Second, while most previous methods adopt a myopic, gradient-following approach that yields poor convergence properties, our algorithm searches over a set of paths and is less susceptible to local minima. In doing so, we explicitly incorporate models of sensors, and model the dependence (and independence) of measurements over multiple time steps in a path. Third, because we consider models of sensing and mobility, our method naturally applies to both ground and aerial vehicles. The paper describes the basic models, the problem formulation and the algorithm, and demonstrates applications via simulation and experimentation. Gaining information about an unknown gas source is a task of great importance with applications in several areas including: responding to gas leaks or suspicious smells, quantifying sources of emissions, or in an emergency response to an industrial accident or act of terrorism. In this paper, a method to estimate the source term of a gaseous release using measurements of concentration obtained from an unmanned aerial vehicle (UAV) is described. The source term parameters estimated include the three dimensional location of the release, its emission rate, and other important variables needed to forecast the spread of the gas using an atmospheric transport and dispersion model. The parameters of the source are estimated by fusing concentration observations from a gas detector on-board the aircraft, with meteorological data and an appropriate model of dispersion. Two models are compared in this paper, both derived from analytical solutions to the advection diffusion equation. Bayes’ theorem, implemented using a sequential Monte Carlo algorithm, is used to estimate the source parameters in order to take into account the large uncertainties in the observations and formulated models. The system is verified with novel, outdoor, fully automated experiments, where observations from the UAV are used to estimate the parameters of a diffusive source. The estimation performance of the algorithm is assessed subject to various flight path configurations and wind speeds. Observations and lessons learned during these unique experiments are discussed and areas for future research are identified. Received 28 May 2002; revised 18 September 2002; accepted 24 September 2002; published 14 February 2003. [1] When an inverse problem is solved to estimate an unknown function such as the hydraulic conductivity in an aquifer or the contamination history at a site, one constraint is that the unknown function is known to be everywhere nonnegative. In this work, we develop a statistically rigorous method for enforcing function nonnegativity in Bayesian inverse problems. The proposed method behaves similarly to a Gaussian process with a linear variogram (i.e., unrestricted Brownian motion) for parameter values significantly greater than zero. The method uses the method of images to define a prior probability density function based on reflected Brownian motion that implicitly enforces nonnegativity. This work focuses on problems where the unknown is a function of a single variable (e.g., time). A Markov chain Monte Carlo (MCMC) method, specifically, a highly efficient Gibbs sampler, is implemented to generate conditional realizations of the unknown function. The new method is applied to the estimation of the trichloroethylene (TCE) and perchloroethylene (PCE) contamination history in an aquifer at Dover Air Force Base, Delaware, based on concentration profiles obtained from an underlying aquitard. INDEX TERMS: 1831 Hydrology: Groundwater quality; 1869 Hydrology: Stochastic processes; 3260 Mathematical Geophysics: Inverse theory; KEYWORDS: stochastic inverse modeling, contaminant source identification, inference under constraints, Markov chain Monte Carlo (MCMC), Gibbs sampling, Bayesian inference A key problem of robotic environmental sensing and monitoring is that of active sensing: How can a team of robots plan the most informative observation paths to minimize the uncertainty in modeling and predicting an environmental phenomenon? This paper presents two principled approaches to efficient information-theoretic path planning based on entropy and mutual information criteria for in situ active sensing of an important broad class of widely-occurring environmental phenomena called anisotropic fields. Our proposed algorithms are novel in addressing a trade-off between active sensing performance and time efficiency. An important practical consequence is that our algorithms can exploit the spatial correlation structure of Gaussian process-based anisotropic fields to improve time efficiency while preserving near-optimal active sensing performance. We analyze the time complexity of our algorithms and prove analytically that they scale better than state-of-the-art algorithms with increasing planning horizon length. We provide theoretical guarantees on the active sensing performance of our algorithms for a class of exploration tasks called transect sampling, which, in particular, can be improved with longer planning time and or lower spatial correlation along the transect. Empirical evaluation on real-world anisotropic field data shows that our algorithms can perform better or at least as well as the state-of-the-art algorithms while often incurring a few orders of magnitude less computational time, even when the field conditions are less favorable.