Transformation Matrix Research Articles

A Matrix-Based Approach to Unified Synthesis of Planar Four-Bar Mechanisms for Motion Generation With Position, Velocity, and Acceleration Constraints

Abstract This paper introduces a novel matrix-based approach for the simultaneous type and dimensional synthesis of planar four-bar linkage mechanisms, accommodating various practical constraints, including position, velocity, acceleration, and joint placements. Traditional design processes segregate type synthesis, the determination of joint and link configurations, from dimensional synthesis, which involves specifying link sizes and pivot locations. This segregation often leads to complexities in addressing the complete design challenge. The novel methodology proposed in this paper departs from the conventional sequential design approach by concurrently evaluating type and dimensional parameters using a data-driven matrix formulation. The crux of the paper’s methodology involves formulating a singular design equation through a transformation matrix, parameterized by the Cartesian parameters of the mechanism’s dyads. This formulation linearly expresses a broad range of constraints, facilitating the identification of viable solutions through singular value decomposition and null space analysis. This integrated approach not only simplifies the synthesis process but also provides direct insights into the mechanism’s parameters, encompassing both type and dimensions, thereby obviating the need for further interpretative steps common to the use of quaternions and kinematic mapping. In essence, the paper presents two main contributions: the development of a unified design equation capable of encompassing a wide array of constraints within the mechanism synthesis process, and the introduction of an algorithm that effectively identifies all potential planar four-bar linkage mechanisms by accurately satisfying up to five constraints. This approach promises to enhance the design and optimization of mechanical systems by offering a more holistic and efficient pathway to mechanism synthesis.

A New Encryption Algorithm Utilizing DNA Subsequence Operations for Color Images

The computer network has fundamentally transformed modern interactions, enabling the effortless transmission of multimedia data. However, the openness of these networks necessitates heightened attention to the security and confidentiality of multimedia content. Digital images, being a crucial component of multimedia communications, require robust protection measures, as their security has become a global concern. Traditional color image encryption/decryption algorithms, such as DES, IDEA, and AES, are unsuitable for image encryption due to the diverse storage formats of images, highlighting the urgent need for innovative encryption techniques. Chaos-based cryptosystems have emerged as a prominent research focus due to their properties of randomness, high sensitivity to initial conditions, and unpredictability. These algorithms typically operate in two phases: shuffling and replacement. During the shuffling phase, the positions of the pixels are altered using chaotic sequences or matrix transformations, which are simple to implement and enhance encryption. However, since only the pixel positions are modified and not the pixel values, the encrypted image’s histogram remains identical to the original, making it vulnerable to statistical attacks. In the replacement phase, chaotic sequences alter the pixel values. This research introduces a novel encryption technique for color images (RGB type) based on DNA subsequence operations to secure these images, which often contain critical information, from potential cyber-attacks. The suggested method includes two main components: a high-speed permutation process and adaptive diffusion. When implemented in the MATLAB software environment, the approach yielded promising results, such as NPCR values exceeding 98.9% and UACI values at around 32.9%, demonstrating its effectiveness in key cryptographic parameters. Security analyses, including histograms and Chi-square tests, were initially conducted, with passing Chi-square test outcomes for all channels; the correlation coefficient between adjacent pixels was also calculated. Additionally, entropy values were computed, achieving a minimum entropy of 7.0, indicating a high level of randomness. The method was tested on specific images, such as all-black and all-white images, and evaluated for resistance to noise and occlusion attacks. Finally, a comparison of the proposed algorithm’s NPCR and UAC values with those of existing methods demonstrated its superior performance and suitability.

Research on High Power Density Flyback Converter With a New Passive Lossless Snubber

ABSTRACTThis paper proposes a flyback converter with a new passive lossless snubber. It eliminates the power dissipation of the traditional RCD snubber, while providing protection against MOS breakdown from energy stored in the power‐transformer leakage. This energy is used to power the power chip, which simplifies the design of the transformer. Meanwhile, an optimal design method for high power density planar transformers is presented. Applying the principle of flux cancellation, a matrix transformer that originally needed an independent magnetic core was integrated into a single magnetic core to reduce the volume of the core. This method effectively reduces the printed circuit board (PCB) layer number of the planar transformer and increases the possibility of the application of the planar transformer in the flyback converter. The detailed operation principle and design considerations are presented. Finally, a multi‐output flyback converter with a frequency of 100 kHz is designed to verify the practical performance of the structure.

New sequence spaces derived from the Catalan–Motzkin matrix and related matrix transformations

UDC 512.6 We consider the domain of a conservative matrix involving Catalan and Motzkin numbers in the sequence spaces c and c 0 . Moreover, the α -, β -, and γ -duals are given and some matrix mappings are presented on the resulting spaces.

Scene Measurement Method Based on Fusion of Image Sequence and Improved LiDAR SLAM

To address the issue that sparse point cloud maps constructed by SLAM cannot provide detailed information about measured objects, and image sequence-based measurement methods have problems with large data volume and cumulative errors, this paper proposes a scene measurement method that integrates image sequences with an improved LiDAR SLAM. By introducing plane features, the positioning accuracy of LiDAR SLAM is enhanced, and real-time odometry poses are generated. Simultaneously, the system captures image sequences of the measured object using synchronized cameras, and NeRF is used for 3D reconstruction. Time synchronization and data registration between the LiDAR and camera data frames with identical timestamps are achieved. Finally, the least squares method and ICP algorithm are employed to compute the scale factor s and transformation matrices R and t between different point clouds from LiDAR and NeRF reconstruction. Then, the precise measurement of the objects could be implemented. Experimental results demonstrate that this method significantly improves measurement accuracy, with an average error within 10 mm and 1°, providing a robust and reliable solution for scene measurement.

Ray Tracing Animated Displaced Micro‐Meshes

AbstractWe present a new method that allows efficient ray tracing of virtually artefact‐free animated displaced micro‐meshes (DMMs) [MMT23] and preserves their low memory footprint and low BVH build and update cost. DMMs allow for compact representation of micro‐triangle geometry through hierarchical encoding of displacements. Displacements are computed with respect to a coarse base mesh and are used to displace new vertices introduced during 1 : 4 subdivision of the base mesh. Applying non‐rigid transformation to the base mesh can result in silhouette and normal artefacts (see Figure 1) during animation. We propose an approach which prevents these artefacts by interpolating transformation matrices before applying them to the DMM representation. Our interpolation‐based algorithm does not change DMM data structures and it allows for efficient bounding of animated micro‐triangle geometry which is essential for fast tessellation‐free ray tracing of animated DMMs.

Mueller matrix analysis of a biologically sourced engineered tissue construct as polarimetric phantom.

The polarimetric properties of biological tissues are often difficult to ascertain independent of their complex structural and organizational features. Conventional polarimetric tissue phantoms have well-characterized optical properties but are overly simplified. We demonstrate that an innovative, biologically sourced, engineered tissue construct better recapitulates the desired structural and polarimetric properties of native collagenous tissues, with the added benefit of potential tunability of the polarimetric response. We bridge the gap between non-biological polarimetric phantoms and native tissues. We aim to evaluate a synthesized tissue construct for its effectiveness as a phantom that mimics the polarimetric properties in typical collagenous tissues. We use a fibroblast-derived, ring-shaped engineered tissue construct as an innovative tissue phantom for polarimetric imaging. We perform polarimetry measurements and subsequent analysis using the Mueller matrix decomposition and Mueller matrix transformation methods. Scalar polarimetric parameters of the engineered tissue are analyzed at different time points for both a control group and for those treated with the transforming growth factor . Second-harmonic generation (SHG) imaging and three-dimensional collagen fiber organization analysis are also applied. We identify linear retardance and circular depolarization as the parameters that are most sensitive to the tissue culture time and the addition of . Aside from a statistically significant increase over time, the behavior of linear retardance and circular depolarization indicates that the addition of accelerates the growth of the engineered tissue, which is consistent with expectations. We also find through SHG images that collagen fiber organization becomes more aligned over time but is not susceptible to the addition of . The engineered tissue construct exhibits changes in polarimetric properties, especially linear retardance and circular depolarization, over culture time and under treatments. This tissue construct has the potential to act as a controlled modular optical phantom for polarimetric-based methods.

Prognostic value of synthetized right-side precordial leads in arrhythmogenic right ventricular cardiomyopathy: data from nordic, dutch, and canadian ARVC registers

Abstract Background T-wave inversion (TWI) in standard ECG leads is a proven risk marker for life-threatening ventricular arrhythmias (VA) in arrhythmogenic right ventricular cardiomyopathy (ARVC). Right-sided precordial leads (RSPL), which may be more sensitive for detection of the arrhythmogenic substrate, are rarely recorded and understudied in this context. Computerized ECG signal-processing allows synthesis of right-sided precordial ECG leads derived from standard 12-lead ECG. Objective We aimed to assess the value of TWI in RSPL, synthetized from the standard 12-lead ECG, for prediction of VA risk in ARVC patients with subtle ECG phenotypes. Methods Patients with definite ARVC by TFC2010 and no history of sustained VA prior to diagnosis from the Nordic, Canadian and Dutch ARVC registries were included. Patients with major repolarization criterion or complete right bundle branch block (RBBB) were excluded. RSPL (V3R-V6R) were derived from digitally recorded eight linearly independent leads (I, II and precordial V1 to V6) of the standard ECG using a linear ECG transformation matrix. The matrix was previously developed based on a library of body surface potential maps from a mixed group of healthy subjects and patients with cardiac diseases using multivariate linear regression and QRS-T data obtained from averaged beats of the right-sided-precordial leads and the basis leads. TWI exceeding 0.1 mV in any of the synthetized leads was tested for its ability to predict sustained VA, defined as either sustained ventricular tachycardia, appropriate ICD shock, aborted cardiac arrest, or sudden cardiac death. In a similar manner, the value of TWI in any of the inferior leads III, aVF or II was assessed. Hazard ratio was calculated using Cox regression analysis adjusted for age, sex, and proband status. Results In total, 144 patients without prior VA history were identified. After exclusion of patients with major repolarization criterion (n=37) and RBBB (n=11), 96 patients comprised the study group (mean age 40±16, 42% female, 41% probands, 48% ICD carriers). Fifty-nine patients (62%) had TWI in one or more synthetized RSPL and 33 patients (34%) had TWI in any of the inferior leads. During 10 years of follow-up, 11 patients (12%) developed VA. Kaplan-Meier curve analysis showed significant association between the presence of TWI in at least one of the RSPL and the risk of VA, which remained an independent predictor in the adjusted Cox regression analysis (HR 10.6, 95%CI 1.3-84.4, p=0.026). TWI in any of the inferior leads was not associated with the risk of VA in this cohort (HR 1.2 95%CI 0.26-5.42). Conclusions Synthetized right-sided precordial leads appear to contain information potentially useful for refining risk stratification of primary prevention ARVC patients with a subtle ECG phenotype, in whom traditional repolarization markers, such as major repolarization criterion or TWI in inferior leads, are not informative.

Approximation of Doublewalsh–Fourier Series by Means of the Matrix Transform

Approximation of Doublewalsh–Fourier Series by Means of the Matrix Transform

Dynamics of a knuckle crane carrying a load subjected to wind pressure

AbstractThe paper presents the authors’ model of a knuckle crane offshore type that takes into account the flexibility of boom and drives, which is used to analyze the effect of constant wind pressure or cyclical gusts on the dynamics of the crane and the load. The mathematical model of the crane is derived using a formalism of joint coordinates, homogeneous transformation matrices, and Lagrange equations. Using this model, the influence of wind pressure on the torques and forces in the crane drives and on the accuracy of load positioning is investigated. The results show that the influence of wind on the accuracy of load positioning should not be assessed by limiting the observation to the movement of its gravity center but by observing the movement of characteristic points, the corners of the load. Root mean squared (RMS) indicators are used to quantitatively assess this impact on the driving torque and forces, and appropriate indicators are proposed to assess the accuracy of load positioning.

MAGIC SQUARES OF PERFECT SQUARES AND PELL NUMBERS

Order three magic squares of distinct squared integers are studied. We show that such a magic square is not possible if the smallest entry is the square of a prime number, or unity. A method for generating all arithmetic progressions of three squared integers whose smallest term is the square of a prime or unity is presented via a set of linear transformation matrices involving the Pell numbers.

CRTF-MoeICP: A robust coarse-to-fine reflector-based LiDAR indoor positioning algorithm

The reflector-based Light Detection and Ranging (LiDAR) positioning method is susceptible to environmental interferences, resulting in instability. This instability not only reduces movement accuracy but also poses safety hazards. To solve the above problems in the application of LiDAR sensors in the field of indoor positioning, we propose a Coarse Registration algorithm based on the Triangular Feature (CRTF) and a fine registration algorithm based on Multi-level outlier elimination and Iterative Closest Point (MoeICP) for the reflector-based LiDAR positioning. The proposed coarse-to-fine positioning algorithm CRTF-MoeICP addresses the issue of reflector-based LiDAR positioning failure arising from the improper selection of the initial transformation matrix and outlier interference in indoor structured industrial environments. The experiment results show that the CRTF-MoeICP algorithm can ensure the stable registration of the LiDAR point cloud and the reflector map by completely removing all outliers, greatly improving the indoor positioning stability of LiDAR sensors. Besides, the proposed algorithm can be realized by LiDARs with different performance, and improve the static positioning repeatability to ±3 mm. The high precision and stable positioning results improve the motion accuracy, ensuring that the Automatic Guided Vehicle (AGV) can accurately and stably complete the handling task.

Complex system fault diagnosis based on interpretive structural model

To realize the fault diagnosis of complex systems, a fault diagnosis method for complex systems based on the explanatory structural model is proposed. According to the fault mechanism analysis, the fault association matrix of system elements is established. The explanatory structural model is applied to transform the fault association relationship of complex systems into an intuitive hierarchical structural model through matrix transformation, so as to realize the structuring and hierarchical propagation of system faults. The PageRank algorithm is introduced to evaluate the influence and impact of system element faults. According to the influence and impact of the same-layer components and the fault transmission logic, the main cause of system fault transmission is clarified, which provides a basis for fault diagnosis. Finally, a specific application is carried out with a certain device as an example to verify the effectiveness of the method.

Atomic force microscopy wide-field scanning imaging using homography matrix optimization

During the offline combination of multiple atomic force microscopy (AFM) images, changes in probe displacement can be affected by dynamic noise, leading to dislocation and tearing in the stitching. To overcome this, we designed a homography matrix optimization method to describe the relative positional relationship between images by constructing the original image matrix and applying singular value decomposition to denoise the homography matrix. Additionally, we implemented a scale-invariant feature transform (SIFT) to extract feature points. To verify the effectiveness of this method, the SIFT + RANSAC (R), SIFT + affine transformation (AT), and oriented FAST and rotated BRIEF (ORB) algorithms were compared with the proposed algorithm. The experimental results demonstrate that the proposed method precisely computes the transformation matrix, thereby guaranteeing the geometric consistency of mosaic imaging. The proposed method preserves the intricate details of the original image and enhances the stitching quality of wide-field images.

GNSS-assisted optimal alignment method for low-cost SINS motion of vehicle

Abstract To improve the alignment accuracy and environmental applicability of the micro-electromechanical system (MEMS)-based strapdown inertial navigation system (SINS), this study proposes a global navigation satellite system (GNSS)-assisted multi-vector determination of the attitude optimal indirect coarse alignment. Using the inertial information output from the inertial measurement unit and the velocity information from the GNSS, a simplified velocity observation vector is constructed and the velocity lever arm stemming from the mounting position inconsistencies of the GNSS and SINS is fed back into the velocity of the carrier system. When constructing the observation vectors, the integration interval is shortened by reconstructing the two-vector integration formula for reducing the cumulative error of the inertial device. The attitude matrix problem is defined as the Wahba problem, which is solved using the singular value decomposition method. Based on the relationship between gyro zero bias and misalignment angle, the corresponding state and measurement equations are designed. Furthermore, owing to the measurement noise uncertainty, the adaptive traceless Kalman filtering algorithm is introduced to realize the effective adaptation processing of the measurement noise. More accurate attitude matrix estimates are obtained by continuously correcting the carrier system transformation matrix. The running car experiment results show that the proposed method exhibits higher alignment accuracy and environmental applicability than the current MEMS strapdown inertial navigation coarse alignment method and the traditional optimization-based alignment method.

Industrial robot calibration optimization method based on R-optimal criterion and improved IOOPS algorithm

Abstract In this paper, a novel kinematic parameter calibration method based on the R-optimal criterion and the improved iterative one-by-one pose search (IOOPS) algorithm is proposed to improve the end-effector positioning accuracy of industrial robots. First, a novel industrial robot error calibration model based on the product of exponential model and generalized error model is established, and the ideal pose transformation matrix from the robot base coordinate system to the laser tracker measurement coordinate system is obtained using the least-squares method, thereby obtaining the initial parameter vector of the robot calibration system. Second, various joint angle values at different positions within the robot’s workspace and the corresponding end-effector coordinate data, namely calibration sampling point data, are collected. Subsequently, the improved IOOPS algorithm combined with the observability index O R proposed by the R-optimal criterion is used to select the optimized calibration sampling points. Finally, the optimized sampling point data are combined with the Levenberg–Marquardt algorithm to optimize the parameters and obtain the optimal kinematic parameters. The experimental results show that the average end-effector error of the robot decreases from 0.5822 to 0.2492 mm after calibration using this method, demonstrating the effectiveness of the optimized sampling points in the calibration process achieved through the improved algorithm and the new observability index.

Other fundamental systems of solutions of the differential equation (D 2 – 2αD + α 2 + β 2) n y = 0, β ≠ 0

Abstract This paper generalizes the results of the first part of the paper [Fecenko, J.—Diekema, E.: On the linear (in)dependence of sequences of derivatives of the functions xn sin x and xn cos x, http://arxiv.org/abs/2305.11184]. The main goal is to prove that the sequence of functions f(x), Df(x), …, D 2n–1 f(x), where f(x) is x n−1e αx sin βx or x n−1 e αx cos βx for β ≠ 0, forms a fundamental system of solutions of the differential equation (D 2 – 2αD + α 2 + β 2) n y = 0. Or more generally, that the sequence of functions Dkf(x), D k+1 f(x), …, D 2n+k–1 f(x), k ∈ ℕ also forms a fundamental system of solutions of the aforementioned differential equation. The problem is solved using a suitable transformation of the Wronskian matrix, by solving a nonlinear differential equation and then calculating the determinant of the modified Wronskian matrix by applying Laplace’s generalized expansion.

Quasi-Diabatization Based on Minimizing Derivative Couplings in a Limited Configuration Space: Elimination of Boundary Condition Dependence.

Due to the cuspidal ridges of adiabatic potential energy surfaces (PESs) and singularities of nonadiabatic couplings (NACs), obtaining an analytical expression for the adiabatic Hamiltonian is difficult. Thereby, nonadiabatic dynamics simulations are often carried out on-the-fly, which is time-consuming. This motivates us to construct quasi-diabatic representations, which have smooth PESs and diabatic couplings. In this study, we propose a new quasi-diabatization method based on minimizing derivative couplings (MDC) in a limited configuration space. The boundary conditions are first considered and finally released to obtain the adiabatic-to-diabatic rotation angles and transformation matrices. As demonstrated in representative one- and two-dimensional models and the widely studied linear H3 molecule, MDC performs significantly better than the direct integration quasi-diabatization approach. In particular, accurate diabatic potential energy matrices have been successfully obtained even when the NACs of all configurations in the considered space are nonnegligible.

A precise registration method for large-scale urban point clouds based on phased and spatial geometric features

Abstract The dense high-rise buildings and multipath effects in urban areas significantly reduce the positioning signal accuracy of laser scanning systems, leading to layering and offset issues in the collected point cloud data on the same road. In order to acquire comprehensive and consistent three-dimensional information on the objects, thereby providing field inspection data for large-scale road traffic network scenarios, in this paper, an improved point cloud registration method is proposed to divide the registration process into two stages: elevation registration and plane registration. Elevation registration takes the ground point cloud as the registration primitive, reduces the number of point clouds through curvature down-sampling, and constrains the feature point sequence with a fixed range to provide a good initial pose for fine registration. The plane registration first inherits the elevation registration parameters, combining the dynamic distance parameters of spherical region step based on the median, using robust multi-scale loss functions to address residual points, effective adjacent point pairs are selected to obtain the spatial transformation matrix, and realizes accurate registration. Experimental results with multiple sets of urban point cloud data show that the root mean square error of point cloud registration can be controlled within 0.06 m, achieving a relatively superior registration accuracy, it can provide detailed prior data for measurement information analysis.

Information fusion in order-2 fuzzy environments: A matrix transformation perspective

Order-2 information granules, as a representation of multi-layer structured information, have recently rekindled discussions. It is usually generated by abstracting order-1 information granules. When the dependence relationship and corresponding membership function of the order-1 information granules (reference information granules) are known, Pedrycz et al. used a method based on gradient optimization to complete the aggregation of the order-2 information granules. In this paper, we discuss a more specific scenario: not only the dependencies between reference information granules are captured, but also the order-1 information granules can be expressed as specific fuzzy information distributions. For this, we propose a fusion scheme of order-2 fuzzy sets based on matrix transformation called CQRP. To our knowledge, it is the first method that completely integrates the structural information of the order-2 environment into the fusion of order-2 fuzzy sets. In the process, we also creatively proposed the attraction and exclusion of structural information, deepening the understanding of structural information. Through sufficient comparison and analysis, we prove that it makes fuller use of information in the order-2 environment and is more reasonable and effective in tasks such as classification and identification.