Structurally Aware 3D Gas Distribution Mapping Using Belief Propagation: A Real-Time Algorithm for Robotic Deployment

<p>Location awareness has been widely used for cooperative localization of target in wireless sensor networks (WSN). But as the number of agent node increases, cooperative localization based on nonparametric belief propagation (BP) causes high communication and computation burden. In addition, high localization accuracy is also the goal of this paper. To this end, this paper based on parameterized BP strategy proposed a distributed cubature Kalman filter (DCKF) algorithm named BP-DCKF. Firstly, basing on joint posterior probability density function of all nodes, this paper constructs a factor graph (FG) model, then the edge posterior distribution of the nodes is obtained by BP strategy. Secondly, considering Gaussian parameterized BP which reconstruct the parameterized message of agents transmitting, this paper proposed the improved DCKF method, moreover, obtaining the locating model of agent node related to posterior distribution of each node in the FG. Finally, based on the localization model, the location estimation of mobile agent node can be obtained utilizing DCKF method to iteratively solve the edge posterior distribution of agent node. Simulation results show that comparing with traditional algorithm, the proposed algorithm is higher on localization accuracy, lower on communication burden.</p> <p> </p>

Robot motion planning via probabilistic inference renders a unique viewpoint on the trajectory optimization problem, in which the joint distribution of motion objectives is represented as a factor graph. Thus, the objectives are solved by obtaining the Maximum a Posteriori of the factor graph. While this distinctly improves the computational efficiency by applying least square optimization, the approach is incapable of handling hard constraints directly. In this work, we put forth an alternate perspective and argue that a message passing framework, such as Belief Propagation, offers greater utility as a solution method for robot planning problems. We present the theoretical formulation of Gaussian Belief Propagation (GaBP) as a generic message passing framework that exploits the structure of the factor graph to solve multiple planning scenarios such as batch planning, incremental planning and re-planning. In addition, the GaBP algorithm has been extended to handle hard state constraints by adopting the Difference Map strategy. We benchmark our framework in a simulation environment. The results show that our algorithms outperform the state-of-the-art with respect to collision avoidance and constraint handling ability within our benchmark. We close this article with the outline of a real-world robotic application within industrial disassembly.

We investigate the deployment of a submersible platform with stereovision imaging capability for three-dimensional (3D) mapping of benthic habitats and other sea-floor structures over local areas. A complete framework is studied, comprising: 1) suitable trajectories to be executed for data collection; 2) data processing for positioning and trajectory followed by online frame-to-frame and frame-to-mosaic registration of images, as well as recursive global realignment of positions along the path; and 3) 3D mapping by the fusion of various visual cues, including motion and stereo within a Kalman filter. The computational requirements of the system are evaluated, formalizing how processing may be achieved in real time. The proposed scenario is simulated for testing with known ground truth to assess the system performance, to quantify various errors, and to identify how performance may be improved. Experiments with underwater images are also presented to verify the performance of various components and the overall scheme.

Belief propagation (BP) has been applied in a variety of inference problems as an approximation tool. BP does not necessarily converge in loopy graphs, and even if it does, is not guaranteed to provide exact inference. Even so, BP is useful in many applications due to its computational tractability. In this article, we investigate a regularized BP scheme by focusing on loopy Markov graphs (MGs) induced by a multivariate Gaussian distribution in canonical form. There is a rich literature surrounding BP on Gaussian MGs (labelled Gaussian belief propagation or GaBP), and this is known to experience the same problems as general BP on graphs. GaBP is known to provide the correct marginal means if it converges (this is not guaranteed), but it does not provide the exact marginal precisions. We show that our adjusted BP will always converge, with sufficient tuning, while maintaining the exact marginal means. As a further contribution we show, in an empirical study, that our GaBP variant can accelerate GaBP and compares well with other GaBP-type competitors in terms of convergence speed and accuracy of approximate marginal precisions. These improvements suggest that the principle of regularized BP should be investigated in other inference problems. The selection of the degree of regularization is addressed through the use of two heuristics. A by-product of GaBP is that it can be used to solve linear systems of equations; the same is true for our variant and we make an empirical comparison with the conjugate gradient method.

We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the problem of interest is not unique. It depends on the state variables and their mutual interdependencies. Many short loops in factor graphs may impede the accuracy of BP. We propose a systematic way to cluster loops of naively assigned factor graphs such that the resulting transformed factor graphs have no additional loops as compared to the original network. They guarantee an accurate performance of BP with only slightly increased computational effort, as we demonstrate by a concrete and realistic implementation for power grids. The method outperforms existing alternatives to handle the loops. We point to other applications to supply networks such as gas-pipeline or other flow networks that share the structure of constraints in the form of analogues to Kirchhoff’s laws. Whenever small and abundant loops in factor graphs are systematically generated by constraints between variables in the original network, our factor-graph assignment in BP complements other approaches. It provides a fast and reliable algorithm to perform marginalization in tasks like state determination, estimation, or optimization issues in supply networks.Graphical abstract

This paper explores a belief propagation algorithm approach, for state estimation of thermal states of aggregated populations of thermostatically controlled loads to provide balancing services in power systems. Balancing services such as frequency control require high accuracy and thus estimation is crucial, especially when sensing and communication in real time is not available or partially. We use Markov chain models to describe the thermal states of aggregated thermostatically controlled loads populations and belief propagation for state estimation. Kalman filter, which has been used in similar studies, is known to be an instance of belief propagation framework. This fact motivates us to introduce belief propagation in this framework, and demonstrate that it provides the same results as Kalman filter. Moreover, belief propagation algorithm is fully decentralized, offering higher flexibility of system modeling using factor graphs. Besides demand response, belief propagation can be applied for different purposes in power systems, either in fully distributed or in mixed systems, and is easily integrated with Kalman filter or similar probabilistic frameworks.

With the development of novel RGB-D visual sensors, data association has been a basic problem in 3D Visual Simultaneous Localization and Mapping (VSLAM). To solve the problem, a VSLAM algorithm based on Multiple Iterative Closest Point (MICP) is presented. By using both RGB and depth information obtained from RGB-D camera, 3D models of indoor environment can be reconstructed, which provide extensive knowledge for mobile robots to accomplish tasks such as VSLAM and Human-Robot Interaction. Due to the limited views of RGB-D camera, additional information about the camera pose is needed. In this paper, the motion of the RGB-D camera is estimated by a motion capture system after a calibration process. Based on the estimated pose, the MICP algorithm is used to improve the alignment. A Kinect mobile robot which is running Robot Operating System and the motion capture system has been used for experiments. Experiment results show that not only the proposed VSLAM algorithm achieved good accuracy and reliability, but also the 3D map can be generated in real time.

An autonomous vehicle requires the technology of generating maps by recognizing the surrounding environment. The recognition of the vehicle's environment can be achieved by using distance information from a 2D laser scanner and color information from a camera. Such sensor information is used to generate 2D or 3D maps. A 2D map is used mostly for generating routs, because it contains information only about a section. In contrast, a 3D map involves height values also, and therefore can be used not only for generating routs but also for finding out vehicle accessible space. Nevertheless, an autonomous vehicle using 3D maps has difficulty in recognizing environment in real time. Accordingly, this paper proposes the technology for generating 2D maps that guarantee real-time recognition. The proposed technology uses only the color information obtained by removing height values from 3D maps generated based on the fusion of 2D laser scanner and camera data.

Gaussian belief propagation (BP) is a computationally efficient method to approximate the marginal distribution and has been widely used for inference with high dimensional data as well as distributed estimation in large-scale networks. However, the convergence of Gaussian BP is still an open issue. Though sufficient convergence conditions have been studied in the literature, verifying these conditions requires gathering all the information over the whole network, which defeats the main advantage of distributed computing by using Gaussian BP. In this paper, we propose a novel sufficient convergence condition for Gaussian BP that applies to both the pairwise linear Gaussian model and to Gaussian Markov random fields. We show analytically that this sufficient convergence condition can be easily verified in a distributed way that satisfies the network topology constraint.

To introduce and investigate a method for free-breathing three-dimensional (3D) mapping of the human body at ultrahigh field (UHF), which can be used to generate homogenous flip angle (FA) distributions in the human body at UHF. A 3D relative mapping sequence with a radial phase-encoding (RPE) k-space trajectory was developed and applied in 11 healthy subjects at 7T. An RPE-based actual flip angle mapping method was applied with a dedicated shim setting to calibrate the relative maps yielding absolute maps of the individual transmit channels. The method was evaluated in a motion phantom and by multidimensional in vivo measurements. Additionally, 3D gradient echo scans with and without static phase-only shims were used to qualitatively validate shim predictions. The phantom validation revealed good agreement for maps between dynamic measurement and static reference acquisition. The proposed 3D method was successfully validated in vivo by comparing magnitude and phase distributions with a 2D Cartesian reference. 3D maps free from visible motion artifacts were successfully acquired for 11 subjects with body mass indexes ranging from 19 kg/m2 to 34 kg/m2 . 3D respiration-resolved absolute maps indicated FA differences between inhalation and exhalation up to 15% for one channel and up to 24% for combined channels for shallow breathing. The proposed method provides respiration-resolved absolute 3D maps of the human body at UHF, which enables the investigation and development of 3D shimming and parallel transmission methods to further enhance body imaging at UHF.

The ability to detect changes occurring on the Earth's surface is essential for comprehensively monitoring and understanding evolving landscapes and environments.To achieve a comprehensive understanding, it is imperative to employ methodologies capable of efficiently capturing and analyzing both two-dimensional (2D) and three-dimensional (3D) changes across various periods.Artificial Intelligence (AI)  stands out as a primary resource for investigating these alterations, and when combined with Remote sensing (RS) data, it has demonstrated superior performance compared to conventional Change Detection (CD) algorithms.The recent introduction of the MultiTask Bitemporal Images Transformer [1] (MTBIT) network has made it possible to simultaneously solve 2D and 3D CD tasks leveraging bi-temporal optical images.However, this network presents certain limitations that necessitate being considered. These constraints encompass a tendency to overfit the training distribution and challenges in inferring extreme values [1]. To address these shortcomings, this work introduces a series of custom augmentations, including strategies like Random Crop, Crop or Resize, Mix up, Gaussian Noise on the 3D CD maps, and Radiometric Transformation. Applied individually or in specific combinations, these augmentations aim to bolster MTBIT's ability to discern intricate geometries and subtle structures that are otherwise difficult to detect.Furthermore, the evaluation metrics used to assess MTBIT, such as Root Mean Squared Error (RMSE) and the change RMSE (cRMSE), have their limitations. As a response, the introduction of the true positive RMSE (tpRMSE) offers a more comprehensive evaluation, specifically focusing on MTBIT's efficacy in the 3D CD task by considering only the pixels affected by actual elevation changes.The implementation of custom augmentations particularly when applied in synergy, like Crop or Resize with Gaussian Noise on the 3D map, yielded substantial improvements. These interventions led – through the best augmentation configuration – to the reduction of the cRMSE to 5.88 meters and the tpRMSE to 5.34 meters, compared to the baseline (standard MTBIT) values of 6.33 meters and 5.60 meters, respectively.The proposed augmentations significantly bolster the practical usability and reliability of MTBIT in real-world applications, effectively addressing critical challenges within the realm of Remote Sensing CD. REFERENCES: [1] Marsocci, V., Coletta, V., Ravanelli, R., Scardapane, S., Crespi, M., 2023. Inferring 3D change detection from bitemporal optical images. ISPRS Journal of Photogrammetry and Remote Sensing, 196, 325-339

We consider channel equalization with Gaussian Belief Propagation (GaBP) in a SISO polar coded single carrier transmission. GaBP requires soft values on reliability information for coded bits when the channel decoder is concatenated and iteratively decoded with GaBP. However, it is not so easy to generate the soft values of coded bits in general polar decoders. In this paper, we use soft successive cancellation list (SSCL) decoding for generating log-likelihood ratio (LLR) values of coded bits. In addition, we propose simpler methods to generate LLR values based on Log-domain SSCL decoding. The simulation results show that the SSCL decoding and its modified versions work well with GaBP and that the proposed method provides the same or better performance with less complex algorithm than that of SSCL decoding.

UWB Multi-robot Localization with Gaussian Belief Propagation on Factor Graph

Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise naturally when working with factor graphs. Belief propagation is a widely deployed iterative method for solving these problems. However, despite its significant empirical success, not much is known about the correctness and efficiency of belief propagation. Bethe approximation is an optimization-based framework for approximating partition functions. While it is known that the stationary points of the Bethe approximation coincide with the fixed points of belief propagation, in general, the relation between the Bethe approximation and the partition function is not well understood. It has been observed that for a few classes of factor graphs, the Bethe approximation always gives a lower bound to the partition function, which distinguishes them from the general case, where neither a lower bound, nor an upper bound holds universally. This has been rigorously proved for permanents and for attractive graphical models. Here we consider bipartite normal factor graphs and show that if the local constraints satisfy a certain analytic property, the Bethe approximation is a lower bound to the partition function. We arrive at this result by viewing factor graphs through the lens of polynomials. In this process, we reformulate the Bethe approximation as a polynomial optimization problem. Our sufficient condition for the lower bound property to hold is inspired by recent developments in the theory of real stable polynomials. We believe that this way of viewing factor graphs and its connection to real stability might lead to a better understanding of belief propagation and factor graphs in general.

Advancing research into autonomous micro aerial vehicle navigation requires data structures capable of representing indoor and outdoor 3D environments. The vehicle must be able to update the map structure in real time using readings from range-finding sensors when mapping unknown areas; it must also be able to look up occupancy information from the map for the purposes of localization and path-planning. Mapping models that have been used for these tasks include voxel grids, multi-level surface maps, and octrees. In this paper, we suggest a new approach to 3D mapping using a multi-volume occupancy grid, or MVOG. MVOGs explicitly store information about both obstacles and free space. This allows us to correct previous potentially erroneous sensor readings by incrementally fusing in new positive or negative sensor information. In turn, this enables extracting more reliable probabilistic information about the occupancy of 3D space. MVOGs outperform existing probabilistic 3D mapping methods in terms of memory usage, due to the fact that observations are grouped together into continuous vertical volumes to save space. We describe the techniques required for mapping using MVOGs, and analyze their performance using indoor and outdoor experimental data.