Multi-Robot Formation Control Based on CVT Algorithm and Health Optimization Management

In view of the low formation redundancy in the traditional rigid formation algorithm and its difficulty in dynamically adapting to the external environment, this study considers the use of the CVT (centroidal Voronoi tessellation) algorithm to control multiple robots to form the desired formation. This method significantly increases the complexity of the multi-robot system, its structural redundancy, and its internal carrying capacity. First, we used the CVT algorithm to complete the Voronoi division of the global map, and then changed the centroid position of the Voronoi cell by adjusting the density function. When the algorithm converged, it could ensure that the position of the generated point was the centroid of each Voronoi cell and control the robot to track the position of the generated point to form the desired formation. The use of traditional formations requires less consideration of the impact of the actual environment on the health of robots, the overall mission performance of the formation, and the future reliability. We propose a health optimization management algorithm based on minor changes to the original framework to minimize the health loss of robots and reduce the impact of environmental restrictions on formation sites, thereby improving the robustness of the formation system. Simulation and robot formation experiments proved that the CVT algorithm could control the robots to quickly generate formations, easily switch formations dynamically, and solve the formation maintenance problem in obstacle scenarios. Furthermore, the health optimization management algorithm could maximize the life of unhealthy robots, making the formation more robust when performing tasks in different scenarios.

Analysis of Mechanical Properties and Permeability of Trabecular-Like Porous Scaffold by Additive Manufacturing

Human bone cells live in a complex environment, and the biomimetic design of porous structures attached to implants is in high demand. Porous structures based on Voronoi tessellation with biomimetic potential are gradually used in bone repair scaffolds. In this study, the mechanical properties and permeability of trabecular-like porous scaffolds with different porosity levels and average apertures were analyzed. The mechanical properties of bone-implant scaffolds were evaluated using finite element analysis and a mechanical compression experiment, and the permeability was studied by computational fluid dynamics. Finally, the attachment of cells was observed by confocal fluorescence microscope. The results show that the performance of porous structures can be controlled by the initial design of the microstructure and tissue morphology. A good structural design can accurately match the performance of the natural bone. The study of mechanical properties and permeability of the porous structure can help address several problems, including stress shielding and bone ingrowth in existing biomimetic bone structures, and will also promotes cell adhesion, migration, and eventual new bone attachment.

Methodological foundation of a numerical taxonomy of urban form

Cities are complex products of human culture, characterised by a startling diversity of visible traits. Their form is constantly evolving, reflecting changing human needs and local contingencies, manifested in space by many urban patterns. Urban morphology laid the foundation for understanding many such patterns, largely relying on qualitative research methods to extract distinct spatial identities of urban areas. However, the manual, labour-intensive and subjective nature of such approaches represents an impediment to the development of a scalable, replicable and data-driven urban form characterisation. Recently, advances in geographic data science and the availability of digital mapping products open the opportunity to overcome such limitations. And yet, our current capacity to systematically capture the heterogeneity of spatial patterns remains limited in terms of spatial parameters included in the analysis and hardly scalable due to the highly labour-intensive nature of the task. In this paper, we present a method for numerical taxonomy of urban form derived from biological systematics, which allows the rigorous detection and classification of urban types. Initially, we produce a rich numerical characterisation of urban space from minimal data input, minimising limitations due to inconsistent data quality and availability. These are street network, building footprint and morphological tessellation, a spatial unit derivative of Voronoi tessellation, obtained from building footprints. Hence, we derive homogeneous urban tissue types and, by determining overall morphological similarity between them, generate a hierarchical classification of urban form. After framing and presenting the method, we test it on two cities – Prague and Amsterdam – and discuss potential applications and further developments. The proposed classification method represents a step towards the development of an extensive, scalable numerical taxonomy of urban form and opens the way to more rigorous comparative morphological studies and explorations into the relationship between urban space and phenomena as diverse as environmental performance, health and place attractiveness.

On the Potential of 3D Transdimensional Surface Wave Tomography for Geothermal Prospecting of the Reykjanes Peninsula

Seismic travel time tomography using surface waves is an effective tool for three-dimensional crustal imaging. Historically, these surface waves are the result of active seismic sources or earthquakes. More recently, however, surface waves retrieved through the application of seismic interferometry have also been exploited. Conventionally, two-step inversion algorithms are employed to solve the tomographic inverse problem. That is, a first inversion results in frequency-dependent, two-dimensional maps of phase velocity, which then serve as input for a series of independent, one-dimensional frequency-to-depth inversions. As such, a set of localized depth-dependent velocity profiles are obtained at the surface points. Stitching these separate profiles together subsequently yields a three-dimensional velocity model. Relatively recently, a one-step three-dimensional non-linear tomographic algorithm has been proposed. The algorithm is rooted in a Bayesian framework using Markov chains with reversible jumps, and is referred to as transdimensional tomography. Specifically, the three-dimensional velocity field is parameterized by means of a polyhedral Voronoi tessellation. In this study, we investigate the potential of this algorithm for the purpose of recovering the three-dimensional surface-wave-velocity structure from ambient noise recorded on and around the Reykjanes Peninsula, southwest Iceland. To that end, we design a number of synthetic tests that take into account the station configuration of the Reykjanes seismic network. We find that the algorithm is able to recover the 3D velocity structure at various scales in areas where station density is high. In addition, we find that the standard deviation of the recovered velocities is low in those regions. At the same time, the velocity structure is less well recovered in parts of the peninsula sampled by fewer stations. This implies that the algorithm successfully adapts model resolution to the density of rays. It also adapts model resolution to the amount of noise in the travel times. Because the algorithm is computationally demanding, we modify the algorithm such that computational costs are reduced while sufficiently preserving non-linearity. We conclude that the algorithm can now be applied adequately to travel times extracted from station–station cross correlations by the Reykjanes seismic network.

Porous Structure of Cylindrical Particle Compacts

The porous compacts of non-spherical particles are frequently used in energy storage devices and other advanced applications. In the present work, the microstructures of compacts of monodisperse cylindrical particles are investigated. The cylindrical particles with various aspect ratios are generated using superquadrics, and the discrete element method was adopted to simulate the compacts formed under gravity deposition of randomly oriented particles. The Voronoi tessellation is then used to quantify the porous microstructure of compacts. With one exception, the median reduced free volume of Voronoi cells increases, and the median local packing density decreases for compacts composed of cylinders with a high aspect ratio, indicating a loose packing of long cylinders due to their mechanical interlocking during compaction. The obtained data are needed for further optimization of compact porous microstructure to improve the transport properties of compacts of non-spherical particles.

Can Empirical Biplots Predict High Entropy Oxide Phases?

High entropy oxides are entropy-stabilised oxides that adopt specific disordered structures due to entropy stabilisation. They are a new class of materials that utilises the high-entropy concept first discovered in metallic alloys. They can have interesting properties due to the interactions at the electronic level and can be combined with other materials to make composite structures. The design of new meta-materials that utilise this concept to solve real-world problems may be a possibility but further understanding of how their phase stabilisation is required. In this work, biplots of the composition’s mean electronegativity are plotted against the electron-per-atom ratio of the compounds. The test dataset accuracy in the resulting biplots improves from 78% to 100% when using atomic-number-per-atom Z/a ratios as a biplot parameter. Phase stability maps were constructed using a Voronoi tessellation. This can be of use in determining stability at composite material interfaces.

Hybrid Composite Material Reinforced with Carbon Nanolaminates for Gradient Stiffness: Preparation and Characterization

Currently, the procurement of lightweight, tough, and impact resistant materials is garnering significant industrial interest. New hybrid materials can be developed on the basis of the numerous naturally found materials with gradient properties found in nature. However, previous studies on granular materials demonstrate the possibility of capturing the energy generated by an impact within the material itself, thus deconstructing the initial impulse into a series of weaker impulses, dissipating the energy through various mechanisms, and gradually releasing undissipated energy. This work focuses on two production methods: spin coating for creating a granular material with composition and property gradients (an acrylonitrile–butadiene–styrene (ABS) polymer matrix reinforced by carbon nanolaminates at 0.10%, 0.25%, and 0.50%) and 3D printing for generating viscoelastic layers. The aim of this research was to obtain a hybrid material from which better behaviour against shocks and impacts and increased energy dissipation capacity could be expected when the granular material and viscoelastic layers were combined. Nondestructive tests were employed for the morphological characterization of the nanoreinforcement and testing reinforcement homogeneity within the matrix. Furthermore, the Voronoï tessellation method was used as a mathematical method to supplement the results. Finally, mechanical compression tests were performed to reveal additional mechanical properties of the material that had not been specified by the manufacturer of the 3D printing filaments.

On point processes defined by angular conditions on Delaunay neighbors in the Poisson–Voronoi Tessellation

Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associated with the latter and depending on a parameter $\theta$ . The first is the set of points that belong to some one-dimensional facet of the Voronoi tessellation and such that the angle with which they see the two nuclei defining the facet is $\theta$ . The main question of interest on this first point process is its intensity. The second point process is that of the intersections of the said tessellation with a straight line having a random orientation. Its intensity is well known. The intersection points almost surely belong to one-dimensional facets. The main question here concerns the Palm distribution of the angle with which the points of this second point process see the two nuclei associated with the facet. We will give answers to these two questions and briefly discuss their practical motivations. We also discuss natural extensions to three dimensions.