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1. Coupled Sensor Configuration and Path-Planning in a Multimodal Threat Field

   St. Laurent, Chase L.; Cowlagi, Raghvendra V. (October 2022, Dynamic Data Driven Application Systems Conference DDDAS2022)

   Blasch, Erik; Ravela, Sai (Ed.)

   A coupled path-planning and sensor configuration method is proposed. The path-planning objective is to minimize exposure to an unknown, spatially-varying, and temporally static scalar field called the threat field. The threat field is modeled as a weighted sum of several scalar fields, each representing a mode of threat. A heterogeneous sensor network takes noisy measurements of the threat field. Each sensor in the network observes one or more threat modes within a circular field of view (FoV). The sensors are configurable, i.e., parameters such as location and size of field of view can be changed. The measurement noise is assumed to be normally distributed with zero mean and a variance that monotonically increases with the size of the FoV, emulating the FoV v/s resolution trade-off in most sensors. Gaussian Process regression is used to estimate the threat field from these measurements. The main innovation of this work is that sensor configuration is performed by maximizing a so-called task-driven information gain (TDIG) metric, which quantifies uncertainty reduction in the cost of the planned path. Because the TDIG does not have any convenient structural properties, a surrogate function called the self-adaptive mutual information (SAMI) is considered. Sensor configuration based on the TDIG or SAMI introduces coupling with path-planning in accordance with the dynamic data-driven application systems paradigm. The benefit of this approach is that near-optimal plans are found with a relatively small number of measurements. In comparison to decoupled path-planning and sensor configuration based on traditional information-driven metrics, the proposed CSCP method results in near-optimal plans with fewer measurements. 

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2. Coupled Sensor Configuration and Path-Planning in Unknown Environments with Adaptive Cluster Analysis

   https://doi.org/10.23919/ACC53348.2022.9867482  

   Laurent, Chase St.; Cowlagi, Raghvendra V. (June 2022, 2022 American Control Conference (ACC))

   We present an adaptive fast-approximation for sensor configuration which finds near-optimal placements and sensor field of views (FoV). The fast-approximation, either via partition-based or density-based cluster analysis, adapts based on the relation between statistical uncertainty of the path plan and environmental uncertainty. The sensor configurations are performed over regions of interest which most directly influence the path-planning efforts. These regions of interest can include exploratory paths by sampling the probabilistic environment model. The path-planning efforts aim to decide upon a path which minimizes an agent’s exposure to threats in an unknown static environment. The noisy sensor network observations are used to construct a threat field estimate using Gaussian Process Regression each iteration with a stationary kernel and heteroscedastic gaussian likelihood. The optimization of a task-driven information gain determines optimal sensor configurations when maximized. The numerical performance of the direct optimization and the adaptive cluster analysis method is presented. Finally, we show that the cluster centers can be utilized as a dimensionality reduction technique for FoV optimization whereby we only optimize FoV radial coverage. 

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3. Geometric Reinforcement Learning Based Path Planning for Mobile Sensor Networks in Advection-Diffusion Field Reconstruction

   https://doi.org/10.1109/CDC.2018.8619486  

   You, Jie; Wu, Wencen (December 2018, Proceeding of 2018 IEEE Conference on Decision and Control)

   We propose a geometric reinforcement learning algorithm for real-time path planning for mobile sensor networks (MSNs) in the problem of reconstructing a spatial-temporal varying field described by the advection-diffusion partial differential equation. A Luenberger state estimator is provided to reconstruct the concentration field, which uses the collected measurements from a MSN along its trajectory. Since the path of the MSN is critical in reconstructing the field, a novel geometric reinforcement learning (GRL) algorithm is developed for real-time path planning. The basic idea of GRL is to divide the whole area into a series of lattice to employ a specific time-varying reward matrix, which contains the information of the length of the path and the mapping error. Thus, the proposed GRL can balance the performance of the field reconstruction and the efficiency of the path. By updating the reward matrix, the real-time path planning problem can be converted to the shortest path problem in a weighted graph, which can be solved efficiently using dynamic programming. The convergence of calculating the reward matrix is theoretically proven. Simulation results serve to demonstrate the effectiveness and feasibility of the proposed GRL for an MSN. 

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4. Spatially temporally distributed informative path planning for multi-robot systems

   Nguyen, Binh; Nguyen, Linh; Nghiem, Truong X; La, Hung; Baca, Jose; Rangel, Pablo; Montoya, Miguel_Cid; Nguyen, Thang (July 2025, IEEE)

   This paper investigates the problem of informative path planning for a mobile robotic sensor network in spatially temporally distributed mapping. The robots are able to gather noisy measurements from an area of interest during their movements to build a Gaussian process (GP) model of a spatio-temporal field. The model is then utilized to predict the spatio-temporal phenomenon at different points of interest. To spatially and temporally navigate the group of robots so that they can optimally acquire maximal information gains while their connectivity is preserved, we propose a novel multi-step prediction informative path planning optimization strategy employing our newly defined local cost functions. By using the dual decomposition method, it is feasible and practical to effectively solve the optimization problem in a distributed manner. The proposed method was validated through synthetic experiments utilizing real-world data sets. 

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5. A new open‐path eddy covariance method for nitrous oxide and other trace gases that minimizes temperature corrections

   https://doi.org/10.1111/gcb.15986  

   Pan, Da; Gelfand, Ilya; Tao, Lei; Abraha, Michael; Sun, Kang; Guo, Xuehui; Chen, Jiquan; Robertson, G. Philip; Zondlo, Mark A. (December 2021, Global Change Biology)

   Abstract Low‐power, open‐path gas sensors enable eddy covariance (EC) flux measurements in remote areas without line power. However, open‐path flux measurements are sensitive to fluctuations in air temperature, pressure, and humidity. Laser‐based, open‐path sensors with the needed sensitivity for trace gases like methane (CH₄) and nitrous oxide (N₂O) are impacted by additional spectroscopic effects. Corrections for these effects, especially those related to temperature fluctuations, often exceed the flux of gases, leading to large uncertainties in the associated fluxes. For example, the density and spectroscopic corrections arising from temperature fluctuations can be one or two orders of magnitude greater than background N₂O fluxes. Consequently, measuring background fluxes with laser‐based, open‐path sensors is extremely challenging, particularly for N₂O and gases with similar high‐precision requirements. We demonstrate a new laser‐based, open‐path N₂O sensor and a general approach applicable to other gases that minimizes temperature‐related corrections for EC flux measurements. The method identifies absorption lines with spectroscopic effects in the opposite direction of density effects from temperature and, thus, density and spectroscopic effects nearly cancel one another. The new open‐path N₂O sensor was tested at a corn (Zea maysL.) field in Southwestern Michigan, United States. The sensor had an optimal precision of 0.1 ppbv at 10 Hz and power consumption of 50 W. Field trials showed that temperature‐related corrections were 6% of density corrections, reducing EC random errors by 20‐fold compared to previously examined lines. Measured open‐path N₂O EC fluxes showed excellent agreement with those made with static chambers (m = 1.0 ± 0.3;r² = .96). More generally, we identified absorption lines for CO₂and CH₄ flux measurements that can reduce the temperature‐related corrections by 10–100 times compared to existing open‐path sensors. The proposed method provides a new direction for future open‐path sensors, facilitating the expansion of accurate EC flux measurements. 

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