Cartesian Coordinate Space Research Articles

Robot Manipulator Minimum Jerk Trajectory Planning Based on the Improved Dung Beetle Optimizer Algorithm

Trajectory planning of robotic manipulators in complex environments involves generating smooth and collision-free paths, and key aspects to consider include dynamic environment perception, path planning, trajectory smoothing and optimization, and obstacle avoidance. This paper discusses different algorithms and finally proposes a fusion of the improved Dung Beetle Optimizer (IDBO) algorithm using chaotic mapping, sinusoidal random mutation, and nonlinear convergence strategies with the bidirectional Rapidly exploring Random Tree (RRT) algorithm to achieve manipulator trajectory planning and minimum jerk optimization trajectory. In the experiment, the IDBO algorithm was compared with other heuristic algorithms. The path obtained was shortened by 9.18% on average, and the calculation time was shortened by 33.81% on average. Then, the paper explored Cartesian coordinate space trajectory planning and joint space trajectory planning when the robot was working in 3D space, and verified the superiority of the latter. In controlling the movement of the robot, by combining the minimum angle jerk planning and the bidirectional RRT obstacle avoidance algorithm to drive the joint angle parameters obtained by the spatial trajectory planning, the trajectory of the robot manipulator can be smoother, more efficient, and avoid obstacles in complex 3D space. This research helps improve the performance, safety, and technical support of robots, and is of great research significance.

Transitioning Low-Temperature GDC Socs: Lab to Commercialization Scale

Solid oxide fuel cells (SOFCs) electrochemically convert hydrogen and oxygen into electricity, heat, and water with high efficiency (~55%) [1], while in reverse operation, water and electricity are converted to hydrogen and oxygen in solid oxide electrolysis cells (SOECs). Appropriately designed solid oxide cells (SOCs) can operate in both SOFC and SOEC mode.Conventional SOCs typically demand elevated operating temperatures (800-1000°C), resulting in higher cost and accelerated degradation issues. Lowering operating temperatures below 600°C reduces thermal stresses, shortens start-up times, and broadens applications [2].Ce1-xGdxO2-δ (GDC), due to its superior oxygen ion conductivity at reduced temperatures, has lower ohmic losses than competing electrolyte materials. Thus, our 1.2 cm diameter circular anode supported GDC cell with 0.31 cm2 active area exhibits exceptional power densities, reaching approximately 3 watt per square centimeter at 650°C. Through optimal design, these cells exhibit exceptional performances in fuel cell mode, significantly enhancing efficiency and effectiveness when operating as an electrolyzer for fuel generation. This advance in performance is a result of mitigating the leakage current issues typical of ceria-based electrolytes through precise engineering of the cathodic microstructure and surface chemistry modification [3].The transition from lab-scale to large-scale commercialization (with active areas of 16 cm² &; 81 cm²) presents significant challenges such as tailoring material properties for large-cell versus button-cell synthesis while maintaining high performance levels.In this work we explore the challenges encountered during the scaling-up process. We report on fabrication strategies employed to achieve cell flatness, maintain high efficiency, ensure cost-effectiveness, and achieve long-term stability. Specifically, we have fabricated graded anode-supported cells [4] by developing an innovative lamination strategy involving tapes oriented perpendicular to each other. This approach notably contributed to achieving superior electrolyte densification and resulted in significantly flatter (low curvature values) with respect to both horizontal and vertical axes in cartesian coordinate space. When compared to the flatness values of 10x10 cm2 commercially available cells, our cells demonstrated remarkably flatter curvatures as shown in figure 1. This characteristic has proven highly beneficial for stack assembly, minimizing issues such as cell cracking and reducing sealing-related problems. By optimizing the cathode scaffold and infiltration process on larger area cells through a spray-coating machine, scaling up challenges are effectively mitigated compared to the button cell approach, where scaffold preparation and infiltration were performed using blade coating and a hand pipette, respectively. This approach effectively tackles electronic conduction issues in ceria-based electrolytes, leading to higher Open Circuit Voltages (OCVs) in fuel cell mode and increased efficiencies in reversible mode.

Multilevel superposition for deciphering the conformational variability of protein ensembles.

The dynamics and variability of protein conformations are directly linked to their functions. Many comparative studies of X-ray protein structures have been conducted to elucidate the relevant conformational changes, dynamics and heterogeneity. The rapid increase in the number of experimentally determined structures has made comparison an effective tool for investigating protein structures. For example, it is now possible to compare structural ensembles formed by enzyme species, variants or the type of ligands bound to them. In this study, the author developed a multilevel model for estimating two covariance matrices that represent inter- and intra-ensemble variability in the Cartesian coordinate space. Principal component analysis using the two estimated covariance matrices identified the inter-/intra-enzyme variabilities, which seemed to be important for the enzyme functions, with the illustrative examples of cytochrome P450 family 2 enzymes and class A $\beta$-lactamases. In P450, in which each enzyme has its own active site of a distinct size, an active-site motion shared universally between the enzymes was captured as the first principal mode of the intra-enzyme covariance matrix. In this case, the method was useful for understanding the conformational variability after adjusting for the differences between enzyme sizes. The developed method is advantageous in small ensemble-size problems and hence promising for use in comparative studies on experimentally determined structures where ensemble sizes are smaller than those generated, for example, by molecular dynamics simulations.

A Vlasov-Fokker-Planck-Landau code for the simulation of colliding supersonic dense plasma flows

A Vlasov-Fokker-Planck-Landau (VFPL) code is developed for the study of colliding supersonic dense plasma flows, in which the VFPL equations for both electrons and ions are solved by the time splitting strategy in the two-dimensional Cartesian coordinate space and the two-dimensional velocity space (2D2V). To accurately handle two colliding supersonic plasma flows with their velocities even much higher than the thermal velocities of ions, the full Fokker-Planck-Landau operator is employed for the collision terms. Using advanced numerical methods such as the fast spectral method and the asymptotic-preserving scheme, the ion-ion and electron-electron collision terms can be properly solved with a relatively large time step so that both high accuracy and efficiency of the developed code can be achieved. Further, the quantum degeneracy effect due to the high density and relatively low initial temperature of the electrons is included in the model. In addition, both the energy and momentum conservation are well satisfied. The developed code provides a unique numerical tool to study the interactions between high-velocity high-density plasma flows, which may be encountered in some advanced schemes of inertial confinement fusion and laser-driven laboratory astrophysics experiments.

The uniformly continuous theorem of fractal interpolation surface function and its proof

<abstract> <p>In order to research uniform continuity of fractal interpolation surface function on a closed rectangular area, the accumulation principle was applied to prove uniform continuity of fractal interpolation surface function on a closed rectangular area. First, fractal interpolation surface function was constructed by affine mapping. Second, the continuous concept of fractal interpolation surface function at a planar point in a three-dimensional cartesian coordinate space system and uniform continuity of fractal interpolation surface function on a closed rectangular area were defined in the paper. Finally, the uniformly continuous theorem of fractal interpolation surface function was proven through accumulation principle in the paper. The conclusion showed that fractal interpolation surface was uniformly continuous function on a closed rectangular area.</p> </abstract>

Quaternion fractional-order weighted generalized Laguerre–Fourier moments and moment invariants for color image analysis

Orthogonal moments based on Laguerre polynomials, especially the quaternion representation of fractional-order orthogonal moments have attracted interest in the imaging field. However, most of the existing quaternion fractional-order color orthogonal moments (QFr-COMs) based on Laguerre polynomials are constructed on Cartesian coordinate space and do not have direct rotation geometric invariance. Inspired by the idea of polynomial transformation, we present a weighted radial normalized fractional-order generalized Laguerre polynomials (WRNFr-GLPs) in polar coordinate space. On the basis, a new set of quaternion fractional-order weighted generalized Laguerre–Fourier moments (QFr-WGLFMs) is proposed and a fast and reliable computing method for geometric invariance of QFr-WGLFMs also is introduced in this paper. Theoretical analyses and experimental results showed that the proposed QFr-WGLFMs and moment invariants offer enhanced image reconstruction and pattern recognition compared with the existing quaternion fractional-order-based orthogonal moments and deep learning-based​ methods, especially under the conditions of image processing with noise and smooth filtering.

Investigation of Ionization Potential in Quantum Dots Using the Stratified Stochastic Enumeration of Molecular Orbitals Method.

The overarching goal of this work is to investigate the size-dependent characteristics of the ionization potential of PbS and CdS quantum dots. The ionization potentials of quantum dots provide critical information about the energies of occupied states, which can then be used to quantify the electron-removal characteristics of quantum dots. The energy of the highest-occupied molecular orbital is used to understand electron-transfer processes when invesigating the energy-level alignment between quantum dots and electron-accepting ligands. Ionization potential is also important for investigating and interpreting electron-detachment processes induced by light (photoelectron spectra), external voltage (chemiresistance), and collision with other electrons (impact ionization). Accurate first-principles calculations of ionization potential continue to be challenging because of the computational cost associated with the construction of the frequency-dependent self-energy operator and the numerical solution of the associated Dyson equation. The computational cost becomes prohibitive as the system size increases because of the large number of 2particle-1hole (2p1h) and 1particle-2hole (1p2h) terms needed for the calculation. In this work, we present the Stratified Stochastic Enumeration of Molecular Orbitals (SSE-MO) method for efficient construction of the self-energy operator. The SSE-MO method is a real-space method and the central strategy of this method is to use stochastically enumerated sampling of molecular orbitals and molecular-orbital indices for the construction of the 2p1h and 1p2h terms. This is achieved by first constructing a composite MO-index Cartesian coordinate space followed by transformation of the frequency-dependent self-energy operator to this composite space. The evaluation of both the real and imaginary components of the self-energy operator is performed using a stratified Monte Carlo technique. The SSE-MO method was used to calculate the ionization potentials and the frequency-dependent spectral functions for a series of PbS and CdS quantum dots by solving the Dyson equation using both single-shot and iterative procedures. The ionization potentials for both PbS and CdS quantum dots were found to decrease with increasing dot size. Analysis of the frequency-dependent spectral functions revealed that for PbS quantum dots the intermediate dot size exhibited a longer relative lifetime whereas in CdS the smallest dot size had the longest relative lifetime. The results from these calculations demonstrate the efficacy of the SSE-MO method for calculating accurate ionization potentials and spectral functions of chemical systems.

Kinemaitcs in spatially flat FLRW spacetimes

The kinematics on spatially flat FLRW spacetimes is presented for the first time in local charts with physical coordinates, i.e., the cosmic time and proper Cartesian space coordinates of Painlevé-type. It is shown that there exists a conserved momentum that determines the form of the covariant four-momentum on geodesics in terms of physical coordinates. Moreover, with the help of this conserved momentum, the peculiar momentum can be defined, thus separating the peculiar and recessional motions without ambiguity. It is shown that the energy and peculiar momentum satisfy the mass-shell condition of special relativity while the recessional momentum does not produce energy. In this framework, the measurements of the kinetic quantities along geodesics performed by different observers are analyzed, pointing out an energy loss of the massive particles similar to that producing the photon redshift. The examples of the kinematics on the de Sitter expanding universe and a new Milne-type spacetime are extensively analyzed.

Quaternion fractional-order color orthogonal moment-based image representation and recognition

Inspired by quaternion algebra and the idea of fractional-order transformation, we propose a new set of quaternion fractional-order generalized Laguerre orthogonal moments (QFr-GLMs) based on fractional-order generalized Laguerre polynomials. Firstly, the proposed QFr-GLMs are directly constructed in Cartesian coordinate space, avoiding the need for conversion between Cartesian and polar coordinates; therefore, they are better image descriptors than circularly orthogonal moments constructed in polar coordinates. Moreover, unlike the latest Zernike moments based on quaternion and fractional-order transformations, which extract only the global features from color images, our proposed QFr-GLMs can extract both the global and local color features. This paper also derives a new set of invariant color-image descriptors by QFr-GLMs, enabling geometric-invariant pattern recognition in color images. Finally, the performances of our proposed QFr-GLMs and moment invariants were evaluated in simulation experiments of correlated color images. Both theoretical analysis and experimental results demonstrate the value of the proposed QFr-GLMs and their geometric invariants in the representation and recognition of color images.

리 군에서의 이동 로봇 위치와 자세 추정

In this paper, the Lie group theory is used to estimate the position and attitude of a mobile robot. In the proposed method, a Kalman filter (KF) is implemented in a Lie group, specifically in a two-dimensional special Euclidean group SE(2). Position and attitude are represented as variables in SE(2). State transition is modeled using the exponential of the Lie algebra se(2) , which corresponds to SE(2) . Covariance of the estimates and correction of the predicted state are calculated using Lie algebra se(2). The performance of the proposed method is tested by conducting a simulation and is compared with the conventional extended KF, where Cartesian space coordinates and heading angle are used as state variables. The test results verify that the proposed method provides estimates that have smaller errors than those provided by the conventional extended KF. The Kalman gain and measurement innovation of the proposed method have superior convergence performance than the usual extended KF.

Adaptive Washout Filter Based on Fuzzy Logic for a Motion Simulation Platform With Consideration of Joints’ Limitations

Motion simulation platforms (MSPs) are widely used to generate driving/flying motion sensations for the users. The MSPs have a restricted workspace area due to the dynamical and physical restrictions of the Motion Platforms active joints as well as the physical limitations of its passive joints. The motion cueing algorithm (MCA) is the reproduction of the motion signal including linear accelerations and angular velocities. It aims to simultaneously respect the MSP's workspace limitations and make the same motion feeling for the user as a real vehicle. The Classical washout filter (WF) is a well-known type of MCA. The classical WF is easy to set-up, offers a low computational burden and high functionality but has some major drawbacks such as fixed WF parameters tuned according to worst-case scenarios and no consideration of the human vestibular system. As a result, adaptive WFs were developed to consider the human vestibular system and enhance the efficiency of the method using time-varying filters. The existing adaptive WFs only cogitate the boundaries of the end-effector in the Cartesian coordinate space as a substitute for the active and passive joints limitations, which is MSP's main limiting factor. This conservative assumption reduces the available workspace area of the MSP and increases the motion sensation error for the MSPs user. In this study, a fuzzy logic-based WF is developed, to consider the dynamical and physical boundaries of the active joints as well as the physical boundaries of the passive joints. A genetic algorithm is used to select the membership functions' values of the active and passive joints' boundaries. The model is designed using MATLAB /Simulink and the outcomes demonstrate the efficiency of the proposed method versus existing adaptive WFs.

Bistatic-Range-Doppler-Aperture Wavenumber Algorithm for Forward-Looking Spotlight SAR With Stationary Transmitter and Maneuvering Receiver

Bistatic forward-looking spotlight synthetic aperture radar with stationary transmitter and maneuvering receiver (STMR-BFSSAR) is a promising sensor for various applications, such as the automatic navigation and landing of maneuvering vehicles. Because of the bistatic forward-looking configuration and the receiver’s maneuvers, conventional image formation algorithms suffer from high computational complexity or small size of a well-focused scene if applied to STMR-BFSSAR. In this article, we propose a wavenumber-domain algorithm for STMR-BFSSAR image formation, which is termed the bistatic-range-Doppler-aperture wavenumber algorithm (BDWA). First, a novel range model in bistatic-range and Doppler-aperture coordinate space instead of conventional Cartesian coordinate space is established by employing the elliptic polar coordinate system and the method of series reversion. The novel range model not only makes the echo’s samples to be regular along the direction of the bistatic-range wavenumber axis but also constructs a curved wavefront close to the true wavefront. Second, an operation termed wavenumber-domain gridding is conceived to regularize the echo’s samples along the Doppler-aperture wavenumber axis, which can be implemented by 1-D interpolation. The proposed algorithm significantly outperforms the conventional algorithms in terms of computational complexity and scene size limits. Both point and distributed targets are simulated for two STMR-BFSSAR systems with different parameters. The simulation results verify the validity and superiority of the proposed BDWA.

Trajectory coordination for a cooperative multi-manipulator system and dynamic simulation error analysis

To achieve temporal and spatial correspondence between multiple robotic manipulators, the system must correctly analyze the coordinated path required for a specific task. Based on manipulator kinematics analysis, we first studied the kinematic constraints between the end-effectors of cooperative manipulators, and deduced the multi-manipulator cooperative kinematics constraint equations in the Cartesian coordinate system space under different motion modes. Then, we created two MD-6 manipulator models to simulate the trajectory simulation of the synchronous and relative motion of the manipulator. This allowed us to verify the correctness of the proposed trajectory coordination method, and analyze the influence of external loads on the position and posture of the end-effector of the manipulator, to effectively predict the cooperative motion error of the manipulator system. Finally, in order to verify the effectiveness of the proposed trajectory coordination method, we established a robotic experimental platform and conducted experimental research. The results show that the multi-manipulator trajectory coordination method studied in this paper can make multi-manipulators effectively achieve the target requirements of tasks such as time and space cooperative handling and circular drawing operations.

A Linear Time-Varying Model Predictive Control-Based Motion Cueing Algorithm for Hexapod Simulation-Based Motion Platform

The hexapod manipulator is the most common motion platform, which is widely used as a simulation-based motion platform (SBMP). As the hexapod manipulator has a limited workspace, it is not physically possible to regenerate the real vehicle motion signals using the SBMP. The motion cueing algorithm (MCA) is responsible for regenerating a realistic vehicle motion sensation for the user when the SBMP operates within its physical and dynamical limitations. Recently, model predictive control (MPC) has been introduced to extract the optimal input motion signals while considering the SBMP limitations in the Cartesian coordinate space, which leads to a linear time-invariant (LTI) MPC-based MCA methods. Unfortunately, the existing LTI MPC-based MCA methods are still not able to consider the parameters of the SBMP's hexapod mechanisms inside their models. In general, the current studies only consider the constraints in the Cartesian coordinate system of the hexapod mechanism, instead of its design parameters. This consideration results in a poor usage of the hexapod workspace due to the conservative assumptions; consequently, the SBMP users do not experience realistic motions. The main contribution of this article is to take the SBMP's physical limitations into account in the MPC model such that more precise motion cues can be extracted for the users. A linear time-varying (LTV) MPC-based MCA method is designed for the first time in this article to consider the parameters of the hexapod mechanism in the MPC model. The proposed model (LTV MPC-based MCA) is validated using the MATLAB software, and the results depict better motion sensation with more accurate motion signals as compared with those from the existing LTI MPC-based MCA methods.

A generalization of the Minkowski distance and new definitions of thecentral conics

In this paper, we give a generalization of the well-known Minkowski distance family in the n-dimensional Cartesian coordinate space. Then we consider three special cases of this family, which are also generalizations of the taxicab, Euclidean, and maximum metrics, respectively, and we determine some circle properties of them in the real plane. While we determine some properties of circles of these generalized distances, we discover a new definition of ellipses, and then we also determine a similar definition of hyperbolas, which will be new members among different metrical definitions of central conics in the Euclidean plane.

CartesianToPolar and PolarToCartesian Image Filters

In this paper, we describe a set of filters, implemented in the Insight Toolkit www.itk.org, for converting an image from Cartesian co-ordinate space to Polar co-ordinate space and vice-versa. Cartesian to Polar conversion of an image is a useful operation in preprocessing stage of certain image-processing algorithm where feature of interest has simplified representation in the polar space. This paper is accompanied with the source code, input data, parameters and output data that the authors used for validating the algorithm described in this paper. This adheres to the fundamental principle that scientific publications must facilitate reproducibility of the reported results.

АЛГОРИТМИ ВИДІЛЕННЯ ТЕКСТУРНИХ ОЗНАК РАЙДУЖНОЇ ОБОЛОНКИ ОКА

Undoubtedly, human authentication is an urgent task, a practical solution that employs thousands and millions of people around the world. The tasks of authentication and human identification are now solved with the help of automatic biometric systems, constituting one of the new fields of applied mathematics, biometric identification. From the point of view of reliability, the most effective methods of identification and authentication today are biometrics, which allow to solve the problems of losing passwords and personal identifiers. Among biometric technologies, one of the most promising is biometrics with the use of the iris, which has a specific structure and contains a lot of textural information. Spatial structures observed in the iris are unique to each individual, and individual differences appear in the process of anatomical development. The limiting factor for the proliferation of Iris systems has always been their high cost, but ongoing research and development will reduce costs, and expanding the scope will allow authentication technology for Iris to occupy a prominent segment in the access control market. The paper analyzes the disadvantages of iris processing using the Gabor mathematical apparatus used by Dr. John Daugman and offers an alternative method of extracting informative features from the image of the iris, based on the use of a DoG filter. A feature of the DoG filter is that its response changes the mark in areas of the image where there is a difference in brightness. In homogeneous areas of the image, the response of the filter is zero, but there are almost no such areas in the image of the iris. The advantage of using a DoG filter is that only the Cartesian coordinate space, which is natural for image processing, is used to calculate it, and the features obtained provide better class separation than features based on Gabor filters.

Energy transport pathway in proteins: Insights from non-equilibrium molecular dynamics with elastic network model

Intra-molecular energy transport between distant functional sites plays important roles in allosterically regulating the biochemical activity of proteins. How to identify the specific intra-molecular signaling pathway from protein tertiary structure remains a challenging problem. In the present work, a non-equilibrium dynamics method based on the elastic network model (ENM) was proposed to simulate the energy propagation process and identify the specific signaling pathways within proteins. In this method, a given residue was perturbed and the propagation of energy was simulated by non-equilibrium dynamics in the normal modes space of ENM. After that, the simulation results were transformed from the normal modes space to the Cartesian coordinate space to identify the intra-protein energy transduction pathways. The proposed method was applied to myosin and the third PDZ domain (PDZ3) of PSD-95 as case studies. For myosin, two signaling pathways were identified, which mediate the energy transductions form the nucleotide binding site to the 50 kDa cleft and the converter subdomain, respectively. For PDZ3, one specific signaling pathway was identified, through which the intra-protein energy was transduced from ligand binding site to the distant opposite side of the protein. It is also found that comparing with the commonly used cross-correlation analysis method, the proposed method can identify the anisotropic energy transduction pathways more effectively.

De Sitter geodesics

The geodesics on the (1 + 3)-dimensional de Sitter (dS) spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann–Lemaître–Robertson–Walker, de Sitter–Painlevé and static local charts with Cartesian space coordinates. Moreover, it is shown that there exists a special static chart in which the geodesics are genuine hyperbolas whose asymptotes are given by the conserved momentum and the associated dual momentum.

Intergenerational effects of nutrition on immunity: a systematic review and meta-analysis.

Diet and immunity are both highly complex processes through which organisms interact with their environment and adapt to variable conditions. Parents that are able to transmit information to their offspring about prevailing environmental conditions have a selective advantage by 'priming' the physiology of their offspring. We used a meta-analytic approach to test the effect of parental diet on offspring immune responses. Using the geometric framework for nutrition (a method for analysing diet compositions wherein food nutrient components are expressed as axes in a Cartesian coordinate space) to define dietary manipulations in terms of their energy and macronutrient compositions, we compiled the results of 226 experiments from 38 published papers on the intergenerational effects of diet on immunity, across a range of study species and immunological responses. We observed intergenerational impacts of parental nutrition on a number of offspring immunological processes, including expression of pro-inflammatory biomarkers as well as decreases in anti-inflammatory markers in response to certain parental diets. For example, across our data set as a whole (encompassing several types of dietary manipulation), dietary stress in parents was seen to significantly increase pro-inflammatory cytokine levels measured in offspring (overall d=0.575). All studies included in our analysis were from experiments in which the offspring were raised on a normal or control diet, so our findings suggest that a nutrition-dependent immune state can be inherited, and that this immune state is maintained in the short term, despite offspring returning to an 'optimal' diet. We demonstrate how the geometric framework for nutrition can be used to disentangle the role that different forms of dietary manipulation can have on intergenerational immunity. For example, offspring B-cell responses were significantly decreased when parents were raised on a range of different diets. Similarly, our approach allowed us to show that a parental diet elevated in protein (regardless of energy composition and relative to a control diet) can increase expression of inflammatory markers while decreasing B-cell-associated markers. By conducting a systematic review of the literature, we have identified important gaps that impair our understanding of the intergenerational effects of diet, such as a paucity of experimental studies involving increased protein and decreased energy, and a lack of studies directed at the whole-organism consequences of these processes, such as immune resilience to infection. The results of our analyses inform our understanding of the effects of diet on physiological state across diverse biological fields, including biomedical sciences, maintenance of agricultural breed stock and conservation breeding programs, among others.