Geometric Mapping Research Articles

Feasible minimum distance feedback-based-navigation for a differential drive robot in an environment with obstacles

Consider a differential drive robot (DDR) equipped with an omnidirectional sensor that provides the distances from the robot to corners and walls in a simply connected polygonal environment. Furthermore, the robot does not know a global geometric representation of the world and does not know its position in a global reference frame either. This paper addresses the problem of executing the DDR motion with closed-loop controllers to make the center of the robot travel the smallest distance in the environment to attain a goal configuration modeled as a landmark. As a result, the principal contribution of this article is a closed-loop optimal navigation strategy that does not require the availability of a global geometric map. A formal analysis on the optimality of the task is provided and experiments in a physical DDR are also given. These experiments show the practical viability of the proposed theoretical modeling.

A Geometric Significance-Aware Deep Mutual Learning Network for Building Extraction from Aerial Images

Knowledge-driven building extraction method exhibits a restricted adaptability scope and is vulnerable to external factors that affect its extraction accuracy. On the other hand, data-driven building extraction method lacks interpretability, heavily relies on extensive training data, and may result in extraction outcomes with building boundary blur issues. The integration of pre-existing knowledge with data-driven learning is essential for the intelligent identification and extraction of buildings from high-resolution aerial images. To overcome the limitations of current deep learning building extraction networks in effectively leveraging prior knowledge of aerial images, a geometric significance-aware deep mutual learning network (GSDMLNet) is proposed. Firstly, the GeoSay algorithm is utilized to derive building geometric significance feature maps as prior knowledge and integrate them into the deep learning network to enhance the targeted extraction of building features. Secondly, a bi-directional guidance attention module (BGAM) is developed to facilitate deep mutual learning between the building feature map and the building geometric significance feature map within the dual-branch network. Furthermore, the deployment of an enhanced flow alignment module (FAM++) is utilized to produce high-resolution, robust semantic feature maps with strong interpretability. Ultimately, a multi-objective loss function is crafted to refine the network’s performance. Experimental results demonstrate that the GSDMLNet excels in building extraction tasks within densely populated and diverse urban areas, reducing misidentification of shadow-obscured regions and color-similar terrains lacking building structural features. This approach effectively ensures the precise acquisition of urban building information in aerial images.

Rectifying Discrepancies Between GB-SAR Images and Terrain Model Caused by Measurement Deviations in Open-Pit Mines

Ground-based Interferometric Synthetic Aperture Radar (GB-InSAR) is a valuable technique for monitoring deformation of landslides. GB-InSAR can construct high-resolution 2D images in a range-doppler plane. However, it is difficult for geo-engineers who are unfamiliar with radar monitoring geometry to interpret the results. Geometric mapping method has been applied to the co-registration of terrain models and radar images for the deformation zonation, but the mismatching correction with GB-InSAR and terrain model is not fully investigated by existing researches. To address this issue, this paper proposes a method exploiting an optimum linear transformation based on ground control points (GCPs). The proposed method was evaluated on simulated data and a field campaign in an open pit mine. The deformation mapping result of the method was verified by a collapse event. The method proposed in this paper has an RMSE value ranging from 0.502 to 0.720[Formula: see text]m (@700[Formula: see text]m average monitoring range) when the average density of the terrain point cloud is 0.5[Formula: see text]m. Although this method cannot accurately evaluate the antenna footprint vector deflection parameters, it can meet the needs of coarse matching calibration in relatively flat slope sub-target areas of open-pit mines for engineering applications.

Temporal geometric mapping defines morphoelastic growth model of Type B aortic dissection evolution

The human aorta undergoes complex morphologic changes that mirror the evolution of disease. Finite element analysis (FEA) enables the prediction of aortic pathologic states, but the absence of a biomechanical understanding hinders the applicability of this computational tool. We incorporate geometric information from computed tomography angiography (CTA) imaging scans into FEA to predict a trajectory of future geometries for four aortic disease patients. Through defining a geometric correspondence between two patient scans separated in time, a patient-specific FEA model can recreate the deformation of the aorta between the two time points, showing that pathologic growth drives morphologic heterogeneity. FEA-derived trajectories in a shape-size geometric feature space, which plots the variance of the shape index versus the inverse square root of aortic surface area (δS vs. AT−1), quantitatively demonstrate an increase in δS. This represents a deviation from physiologic shape changes and parallels the true geometric progression of aortic disease patients.

Vision-Based Situational Graphs Exploiting Fiducial Markers for the Integration of Semantic Entities

Situational Graphs (S-Graphs) merge geometric models of the environment generated by Simultaneous Localization and Mapping (SLAM) approaches with 3D scene graphs into a multi-layered jointly optimizable factor graph. As an advantage, S-Graphs not only offer a more comprehensive robotic situational awareness by combining geometric maps with diverse, hierarchically organized semantic entities and their topological relationships within one graph, but they also lead to improved performance of localization and mapping on the SLAM level by exploiting semantic information. In this paper, we introduce a vision-based version of S-Graphs where a conventional Visual SLAM (VSLAM) system is used for low-level feature tracking and mapping. In addition, the framework exploits the potential of fiducial markers (both visible and our recently introduced transparent or fully invisible markers) to encode comprehensive information about environments and the objects within them. The markers aid in identifying and mapping structural-level semantic entities, including walls and doors in the environment, with reliable poses in the global reference, subsequently establishing meaningful associations with higher-level entities, including corridors and rooms. However, in addition to including semantic entities, the semantic and geometric constraints imposed by the fiducial markers are also utilized to improve the reconstructed map’s quality and reduce localization errors. Experimental results on a real-world dataset collected using legged robots show that our framework excels in crafting a richer, multi-layered hierarchical map and enhances robot pose accuracy at the same time.

Evaluating Learning-based Tie Point Matching for Geometric Processing of Off-Track Satellite Stereo

Abstract. Tie-point matching of off-track stereo images is a very challenging task, which can impact bias compensation and digital surface model (DSM) generation. Compared to in-track stereo images, off-track stereo images are more complex primarily due to the radiometric differences caused by sun illumination, sensor responses, atmospheric conditions, and seasonal land cover variations, and secondly due to the longer baseline and larger intersection angle. These challenges significantly limit the use of the vast number of images in satellite archives for automated geometric processing and mapping. Recent advances in deep learning (DL) based matching show promising results against images with diverse illuminations, viewing angles and scales through learning examples. This paper evaluates the potentials of addressing the tie point matching problems in off-track satellite stereo images. Specifically, we focus on stereo pairs that failed or underperformed in classic matching algorithms (i.e., SIFT (scale invariant feature transform)), and evaluate the DL-based tie points matchers by its resulting geometric accuracy in relative orientation, and the generated DSM. The experiments are carried out using 40 off-track satellite stereo pairs from four different regions around the world. We conclude that DL-based methods provide a significant higher success rate in matching challenging multi-temporal stereo pairs, even if their matching accuracy is slightly lower than classic algorithms.

Wireless Communication-aware Path Planning and Multiple Robot Navigation Strategies for Assisted Inspections

Among the many challenges robots encounter in the mining industry, exploring confined environments receives significant attention. This work tackles problems associated with robot communication in hazardous and confined environments, where its cluttered and extensive nature frequently precludes traditional cable-based and wireless solutions. Our methods resort to off-the-shelf long-range radio frequencies to profile the signal propagation behaviour over the geometrical map to assist navigation algorithms that seek to preserve the connection. We consider mathematical models to predict signal power behaviour and serve as input to path planning. We also propose a semi-autonomous leader-follower scheme, with signal repeater units forming a mobile wireless network to enable inspection in hard-to-reach locations. Finally, we present a multi-robot connection-aware system, combining path planning based on radio signal power with multiple robot navigation. Results show the applicability of the proposed solutions, generating single and multi-robot paths for optimal signal reception based on power estimation, thus enabling operations in remote and isolated areas with no line-of-sight between the command base and the robotic inspection device. Experiments conducted in long corridors and in a representative mining environment using the EspeleoRobô and Pioneer platforms demonstrate significant improvements over the traditional communication methods for robotic operation regarding communication quality and inspection range limits.

Crater Triangle Matching Algorithm Based on Fused Geometric and Regional Features

Craters are regarded as significant navigation landmarks during the descent and landing process in small body exploration missions for their universality. Recognizing and matching craters is a crucial prerequisite for visual and LIDAR-based navigation tasks. Compared to traditional algorithms, deep learning-based crater detection algorithms can achieve a higher recognition rate. However, matching crater detection results under various image transformations still poses challenges. To address the problem, a composite feature-matching algorithm that combines geometric descriptors and region descriptors (extracting normalized region pixel gradient features as feature vectors) is proposed. First, the geometric configuration map is constructed based on the crater detection results. Then, geometric descriptors and region descriptors are established within each feature primitive of the map. Subsequently, taking the salience of geometric features into consideration, composite feature descriptors with scale, rotation, and illumination invariance are generated through fusion geometric and region descriptors. Finally, descriptor matching is accomplished by computing the relative distances between descriptors and adhering to the nearest neighbor principle. Experimental results show that the composite feature descriptor proposed in this paper has better matching performance than only using shape descriptors or region descriptors, and can achieve a more than 90% correct matching rate, which can provide technical support for the small body visual navigation task.

In-situ rapid nondestructive characterization of multiple irregular three-dimensional grain boundary structures and electrical properties by nanorobot with SEM in ZnO

To address the problem of spatial quantification of irregular grain boundaries, a unique approach for the nondestructive characterization of multiple irregular three-dimensional grain boundaries is proposed using nanorobots with scanning electron microscopy (SEM) to accomplish in-situ rapid synchronized quantification of structures and electrical properties. By constructing a three-dimensional trigonometric geometric mapping relationship, multiple irregular three-dimensional grain boundary structures and electrical properties can be rapidly quantified. Experimental results demonstrate that it is feasible to accomplish in-situ rapid nondestructive characterizations. The two-dimensional profile shapes of the targeted grain boundaries at each layer exhibit irregular and non-uniform features in the Y-Z plane. The hypotenuse length between the virtual space tilting lines presents a three-dimensional characteristic in the X-Z plane. The spatial tilt angle of the virtual space tilting line can be calculated using the right-triangle relation. The unequal numbers of grains along the same tilted hypotenuse direction with equal lengths directly illustrate the existence of irregular and nonlinear grain boundaries in bulk ZnO ceramics. The relatively uniform spatial sizes of the grain boundary illustrate the coupled spatial characteristics existing in the irregular micro-structures. The relatively uniform equivalent circuit fitting parameters confirm the existence of relatively uniform doping components in bulk ZnO ceramics. Furthermore, this method provides a unique approach for the rapid nondestructive quantitative analysis of multiple three-dimensional irregular grain boundaries in bulk polycrystalline materials.

RNAscape: geometric mapping and customizable visualization of RNA structure.

Analyzing and visualizing the tertiary structure and complex interactions of RNA is essential for being able to mechanistically decipher their molecular functions in vivo. Secondary structure visualization software can portray many aspects of RNA; however, these layouts are often unable to preserve topological correspondence since they do not consider tertiary interactions between different regions of an RNA molecule. Likewise, quaternary interactions between two or more interacting RNA molecules are not considered in secondary structure visualization tools. The RNAscape webserver produces visualizations that can preserve topological correspondence while remaining both visually intuitive and structurally insightful. RNAscape achieves this by designing a mathematical structural mapping algorithm which prioritizes the helical segments, reflecting their tertiary organization. Non-helical segments are mapped in a way that minimizes structural clutter. RNAscape runs a plotting script that is designed to generate publication-quality images. RNAscape natively supports non-standard nucleotides, multiple base-pairing annotation stylesand requires no programming experience. RNAscape can also be used to analyze RNA/DNA hybrid structures and DNA topologies, including G-quadruplexes. Users can upload their own three-dimensional structures or enter a Protein Data Bank (PDB) ID of an existing structure. The RNAscape webserver allows users to customize visualizations through various settings as desired. URL: https://rnascape.usc.edu/.

Contribution to advancing aquifer geometric mapping using machine learning and deep learning techniques: a case study of the AL Haouz-Mejjate aquifer, Marrakech, Morocco

Groundwater resources in Morocco often face sustainability challenges due to increased exploitation and climate change. Specifically, the Al-Haouz-Mejjate groundwater in the Marrakesh region is faced with overexploitation and insufficient recharge. However, the complex subsurface geometries hamper hydrogeological modeling, characterization, and effective management. Reliably estimating aquifer substrate topography is critical for groundwater models but is challenged by limited direct measurements. This study develops nonlinear machine learning models to infer substrate depths by fusing sparse borehole logs with regional geospatial data. A Gaussian process regression approach provided robust holistic mapping, leveraging flexibility, and uncertainty quantification. Supplementary neural network architectures focus on isolating specific variable relationships, like surface elevation–substrate. Model accuracy exceeded 0.8 R-squared against validation boreholes. Spatial visualizations confirmed consistency across landscape transects. Elevation and piezometric data proved most predictive, though multivariate inputs were required for the lowest errors. The results highlight the power of statistical learning to extract meaningful patterns from disparate hydrological data. However, model opacity and the need for broader training datasets remain barriers. Overall, the work demonstrates advanced machine learning as a promising avenue for illuminating complex aquifer geometries essential for sustainability. Hybrid approaches that use both data-driven and physics-based methods can help solve long-standing problems with hydrogeological characterization.

UAV-Borne Mapping Algorithms for Low-Altitude and High-Speed Drone Applications.

This article presents an analysis of current state-of-the-art sensors and how these sensors work with several mapping algorithms for UAV (Unmanned Aerial Vehicle) applications, focusing on low-altitude and high-speed scenarios. A new experimental construct is created using highly realistic environments made possible by integrating the AirSim simulator with Google 3D maps models using the Cesium Tiles plugin. Experiments are conducted in this high-realism simulated environment to evaluate the performance of three distinct mapping algorithms: (1) Direct Sparse Odometry (DSO), (2) Stereo DSO (SDSO), and (3) DSO Lite (DSOL). Experimental results evaluate algorithms based on their measured geometric accuracy and computational speed. The results provide valuable insights into the strengths and limitations of each algorithm. Findings quantify compromises in UAV algorithm selection, allowing researchers to find the mapping solution best suited to their application, which often requires a compromise between computational performance and the density and accuracy of geometric map estimates. Results indicate that for UAVs with restrictive computing resources, DSOL is the best option. For systems with payload capacity and modest compute resources, SDSO is the best option. If only one camera is available, DSO is the option to choose for applications that require dense mapping results.

A semantic SLAM-based method for navigation and landing of UAVs in indoor environments

Autonomous navigation and landing of Unmanned aerial vehicles (UAVs) are critical functions towards full intelligence in unknown environments. However, current methods heavily rely on positioning devices or geometric maps, leading to two limitations: (1) UAVs fail to work normally indoors when signals are blocked, and (2) Navigation systems are not capable of achieving high-level decision-making missions. In this paper, we propose a novel and complete framework to realize the autonomous landing of UAVs in unknown indoor scenes based on visual SLAM, semantic segmentation, terrain estimation, and a decision-making model. Firstly, our 3D map is built on top of the visual SLAM system with semantic features, and then multiple types of maps (e.g., texture map, octo-map, grid-map, and semantic topology) are created for different function requirements. To achieve high-level scene understanding, we design a data association rule to fuse semantic features extracted by a deep learning model into the mapping process of topology structure. Next, a terrain estimation strategy is performed in the lightweight grid-map, which is modeled only via low-level elevation representation. Through multiple terrain constraints factor, a few optimized landing sites are selected in safe regions via clustering algorithm. Finally, based on the guidance of semantic topology, we construct a decision-making model for UAV landing that effectively integrates terrain safety, environment perception, and path planning. We perform extensive autonomous landing experiments on multiple indoor scenes from the TUM RGB-D dataset, and the full unknown environment maps are created simultaneously. The experiment proves that the proposed framework can select an optimal landing site for the advanced mission of UAVs effectively.

Foundations of spatial perception for robotics: Hierarchical representations and real-time systems

3D spatial perception is the problem of building and maintaining an actionable and persistent representation of the environment in real-time using sensor data and prior knowledge. Despite the fast-paced progress in robot perception, most existing methods either build purely geometric maps (as in traditional SLAM) or “flat” metric-semantic maps that do not scale to large environments or large dictionaries of semantic labels. The first part of this paper is concerned with representations: we show that scalable representations for spatial perception need to be hierarchical in nature. Hierarchical representations are efficient to store, and lead to layered graphs with small treewidth, which enable provably efficient inference. We then introduce an example of hierarchical representation for indoor environments, namely a 3D scene graph, and discuss its structure and properties. The second part of the paper focuses on algorithms to incrementally construct a 3D scene graph as the robot explores the environment. Our algorithms combine 3D geometry (e.g., to cluster the free space into a graph of places), topology (to cluster the places into rooms), and geometric deep learning (e.g., to classify the type of rooms the robot is moving across). The third part of the paper focuses on algorithms to maintain and correct 3D scene graphs during long-term operation. We propose hierarchical descriptors for loop closure detection and describe how to correct a scene graph in response to loop closures, by solving a 3D scene graph optimization problem. We conclude the paper by combining the proposed perception algorithms into Hydra, a real-time spatial perception system that builds a 3D scene graph from visual-inertial data in real-time. We showcase Hydra’s performance in photo-realistic simulations and real data collected by a Clearpath Jackal robots and a Unitree A1 robot. We release an open-source implementation of Hydra at https://github.com/MIT-SPARK/Hydra.

Comparative Analysis of Metaheuristic Optimization Methods for Trajectory Generation of Automated Guided Vehicles

This paper presents a comparative analysis of several metaheuristic optimization methods for generating trajectories of automated guided vehicles, which commonly operate in industrial environments. The goal is to address the challenge of efficient path planning for mobile robots, taking into account the specific capabilities and mobility limitations inherent to automated guided vehicles. To do this, three optimization techniques are compared: genetic algorithms, particle swarm optimization and pattern search. The findings of this study reveal the different efficiency of these trajectory optimization approaches. This comprehensive research shows the strengths and weaknesses of various optimization methods and offers valuable information for optimizing the trajectories of industrial vehicles using geometric occupancy maps.

Exploring new geometric contraction mappings and their applications in fractional metric spaces

<abstract><p>This article delves deeply into some mathematical basic theorems and their diverse applications in a variety of domains. The major issue of interest is the Banach Fixed Point Theorem (BFPT), which states the existence of a unique fixed point in fractional metric spaces. The significance of this theorem stems from its utility in a variety of mathematical situations for approximating solutions and resolving iterative problems. On this foundational basis, the study expands by introducing the concept of fractional geometric contraction mappings, which provide a new perspective on how convergence develops in fractional metric spaces.</p></abstract>

Geometric mapping from rectilinear material orthotropy to isotropy: Insights into plates and shells.

Orthotropic shell structures are ubiquitous in biology and engineering, from bacterial cell walls to reinforced domes. We present a rescaling transformation that maps an orthotropic shallow shell to an isotropic one with a different local geometry. The mapping is applicable to any shell sectionfor which the material orthotropy directions match the principal curvature directions, assuming the commonly used Huber form for the orthotropic shear modulus. Using the rescaling transformation, we derive exact expressions for the buckling pressure as well as the linear indentation response of orthotropic cylinders and general ellipsoids of revolution, which we verify against numerical simulations. Our analysis disentangles the separate contributions of geometric and material anisotropy to shell rigidity. In particular, we identify the geometric mean of orthotropic elastic constants as the key quantifier of material stiffness, playing a role akin to the Gaussian curvature which captures the geometric stiffness contribution. Besides providing insights into the mechanical response of orthotropic shells, our work rigorously establishes the validity of isotropic approximations to orthotropic shells and also identifies situations in which these approximations might fail.

IGDM: An Information Geometric Difference Mapping Method for Signal Detection in Non-Gaussian Alpha-Stable Distributed Noise

IGDM: An Information Geometric Difference Mapping Method for Signal Detection in Non-Gaussian Alpha-Stable Distributed Noise

LSMCL: Long-term Static Mapping and Cloning Localization for autonomous robot navigation using 3D LiDAR in dynamic environments

One of the challenges in autonomous robot navigation applications is recognizing the exact location in a dynamic environment in which the location of surrounding objects changes frequently. This study proposes a long-term static mapping and cloning localization (LSMCL) method for estimating real-time accurate location using only natural landmarks even in a dynamic environment using a 3D LiDAR sensor. LSMCL comprises long-term static mapping (LSM) and cloning localization (CL). A LSM creates a 2D grid map and a 3D geometric feature map for objects whose positions do not change in space. A CL uses the generated 2D grid map and particle filter to estimate the 2D global position at the initial stage. After cloning the 2D global location to 3D space, the location is tracked through a 3D feature map and map matching. To verify the LSMCL’s usability in a real dynamic environment, a robot navigation experiment was conducted in a highly dynamic parking lot. The experimental results, analyzed in terms of initial localization success rate, location estimation accuracy and precision, processing time, and congested space application confirmed the LSMCL’s real-world applicability.

Terracini Loci: Dimension and Description of Its Components

We study the Terracini loci of an irreducible variety X embedded in a projective space: non-emptiness, dimensions and the geometry of their maximal dimension’s irreducible components. These loci were studied because they describe where the differential of an important geometric map drops rank. Our best results are if X is either a Veronese embedding of a projective space of arbitrary dimension (the set-up for the additive decomposition of homogeneous polynomials) or a Segre–Veronese embedding of a multiprojective space (the set-up for partially symmetric tensors). For an arbitrary X, we give several examples in which all Terracini loci are empty, several criteria for non-emptiness and examples with the maximal defect possible a priori of an element of a minimal Terracini locus. We raise a few open questions.