Coordinate Transformation Method Research Articles

Chiral Optical Properties of Möbius Graphene Nanostrips.

The advancement of optical technology demands the development of chiral nanostructures with a strong dissymmetry of optical response. Here, we comprehensively analyze the chiral optical properties of circular twisted graphene nanostrips, with a particular emphasis on the case of a Möbius graphene nanostrip. We use the method of coordinate transformation to analytically model the electronic structure and optical spectra of the nanostrips, while employing the cyclic boundary conditions to account for their topology. It is found that the dissymmetry factors of twisted graphene nanostrips can reach 0.01, exceeding the typical dissymmetry factors of small chiral molecules by 1-2 orders of magnitude. The results of this work thus demonstrate that twisted graphene nanostrips of Möbius and similar geometries are highly promising nanostructures for chiral optical applications.

Design of Distributed Interval Observers for Multiple Euler–Lagrange Systems

This paper investigates the problem of distributed interval estimation for multiple Euler–Lagrange systems. An interconnection topology is supposed to be strongly connected. To design distributed interval observers, the coordinate transformation method is employed. The construction of the distributed interval observer is given by the monotone system theory, and the stability is analyzed by the Lyapunov stability theory. Unlike the current works, each sub-interval observer has its own gain; in addition to this, additional observer gains are used to reduce the conservatism of design. The gains of all sub-interval observers are determined by both the monotone system theory and the Lyapunov stability theory. Finally, a simulation example verifies the feasibility of the presented distributed interval observers.

Sound transmission characteristics of a plate backed by an irregular cavity

The study of the coupling cavity provides an effective theoretical reference for the acoustic design. However, most of the previous studies are based on idealized models and there is little research on the sound radiation power about the irregular shapes. The work in this paper achieves the generalization of the model and explores the impact of irregular back cavities on the sound radiation of the plate structures. The influence on the results of the sound insulation performance testing of the plate is also investigated when irregular cavities involved. The displacement of the plate and the sound pressure inside the cavities are expressed as multidimensional Fourier series with additional terms, which will contribute to maintaining the continuity of pressure and velocity at the boundaries. The sound field of the irregular cavity is considered as a unit cubic one in a new coordinate system by coordinate transformation method. The arbitrary boundary of the cavities is realized by adding the energy terms of impedance into the Lagrange equation. The Hamilton’s principle is employed to realize the complete coupling between the plate and the sound fields on both sides. The sound radiation power of the plate can be obtained by using the Rayleigh integral. By using Fast Cosine Transform, the quadruple integrals of the radiation power are simplified to improve accuracy and efficiency of the calculation. Numerical results from the analytical approach are compared with those given by Finite Element Analysis (FEM) to guarantee the rightness and validity of the models. Moreover, experimental results are also given to discuss the reasons of the bias between theory and practice.

Sparsity-based efficient simulation of cluster targets electromagnetic scattering

An efficient and real-time simulation method is proposed for the dynamic electromagnetic characteristics of cluster targets to meet the requirements of engineering practical applications. First, the coordinate transformation method is used to establish a geometric model of the observation scene, which is described by the azimuth angles and elevation angles of the radar in the target reference frame and the attitude angles of the target in the radar reference frame. Then, an approach for dynamic electromagnetic scattering simulation is proposed. Finally, a fast-computing method based on sparsity in the time domain, space domain, and frequency domain is proposed. The method analyzes the sparsity-based dynamic scattering characteristic of the typical cluster targets. The error between the sparsity-based method and the benchmark is small, proving the effectiveness of the proposed method.

Scattering of SH waves by cavity with arbitrary shapes and crack at arbitrary positions in anisotropic elastic half-space media

In this paper, the complex function method, Green's function method and coordinate transformation method are used to solve the scattering problem of cavity with arbitrary shape and crack at arbitrary position in the orthotropic elastic half-space under the incidence of SH waves. Firstly, the displacement field and stress field caused by cavity scattering in the orthotropic elastic half-space under the action of incident SH wave are obtained. Secondly, the solution of Green's function is derived when the plane line source load acts on the orthotropic elastic half-space with cavity. Then, the crack is constructed based on the method of crack ‘cutting.’ The total displacement field and stress field can be further obtained. Then, the analytical solutions of the dynamic stress concentration factor (DSCF) around the cavity, the surface displacement amplitude |W| and the dynamic stress intensity factor (DSIF) at the crack tip are obtained. Finally, taking the existence of elliptical cavity and crack in the orthotropic elastic half-space as an example, a large number of numerical calculations were carried out. Numerous numerical examples show that different parameters have a great influence on the DSCF around the cavity, the surface displacement amplitude |W| and the DSIF at the crack tip.

Robot 3D spatial motion measurement via vision-based method

Measuring the motion of a robot accurately is an important and integral part of evaluating the dynamic and static performance of the robot. The performance index of a robot, such as kinematic accuracy, bearing capacity, deformation, vibration, stability, and structural mode can all be calculated according to the motion displacement of the robot. Therefore, improving the robot motion measurement method, promoting the measurement accuracy, and enriching the measurement content have received considerable scholarly attention worldwide. In this paper, an approach based on binocular vision was proposed to measure the 3D spatial motion of a robot. In the process of reconstructing robot movement, a mathematical model that can facilitate the solving process and improve the accuracy of results was derived to build 3D coordinates information. A novel coordinate transformation method that is based on the singular value decomposition was drawn up to realize the transformation from camera coordinates to robot coordinates. Several experiments were carried out on the self-built three-degree-of-freedom rectangular coordinate robot platform. The marker was designed specially and glued to the end of robot, and a new train of thought was adopted to extract the marker’s feature point. The vision-based measurement results were compared with the actual coordinate value. Results of experiments demonstrated that the proposed method can successfully reconstruct the 3D spatial motion of a robot more exactly, which can meet the requirements of high-precision motion control, motion performance evaluation, and operation state evaluation.

Vision and Inertial Navigation Combined-Based Pose Measurement Method of Cantilever Roadheader

Pose measurement of coal mine excavation equipment is an important part of roadway excavation. However, in the underground mining roadway of coal mine, there are some influencing factors such as low illumination, high dust and interference from multiple equipment, which lead to the difficulty in the position and pose measurement of roadheader with low measurement accuracy and poor stability. A combination positioning method based on machine vision and optical fiber inertial navigation is proposed to realize the position and pose measurement of roadheader and improve the accuracy and stability of the position and pose measurement. The visual measurement model of arm roadheader is established, and the optical fiber inertial navigation technology and the spatial coordinate transformation method are used. Finally, the Kalman filter fusion algorithm is used to fuse the two kinds of data to get the accurate roadheader pose data, and the inertia is compensated and corrected. Underground coal mine experiments are designed to verify the performance of the proposed method. The results show that the positioning error of the roadheader body using this method is within 40 mm, which meets the positioning accuracy requirements of roadway construction. This method compensates for the shortcomings of low accuracy and poor reliability of single vision measurement, single inertial navigation measurement and single odometer measurement.

Disturbance-observer-based fixed-time control for 6-DOF spacecraft rendezvous and docking operations under full-state constraints

The problem of fixed-time control is addressed for the autonomous proximity of non-cooperative targets with full-state constraints, input saturation, parameter uncertainties, and matched and unmatched disturbances. A six degrees of freedom (6-DOF) relative motion model for non-cooperative targets is constructed. Combining with a radial basis function neural network (RBF-NN), a fixed-time disturbance observer is proposed to estimate system disturbances. Model items and assumptions for the boundedness of the derivatives of the disturbances are not required in the proposed disturbance observer. The back-stepping technique provides an adaptive fixed-time controller to stabilize the full-state constrained relative error system and a unified framework for dealing with constrained and unconstrained cases is proposed by designing a coordinate transformation method. The fixed-time stability of the relative error system is guaranteed by the proposed controller regardless of the constraints. Finally, two simulation scenarios validate the effectiveness and robustness of the developed controller design.

The modulation instability of shallow wake flows based on the higher-order generalized cubic-quintic complex Ginzburg–Landau equation

In the context of the parallel flow hypothesis, we derive a higher-order generalized cubic-quintic complex Ginzburg–Landau (GCQ-CGL) equation to describe the amplitude evolution of shallow wake flow from the dimensionless shallow water equations by using multi-scale analysis, perturbation expansion, and weak nonlinear theory. The evolution model includes not only the slowly changing envelope approximation but also the influence of higher-order dissipation, dispersion, and cubic and quintic nonlinear effects. We give the analytical solution of the higher-order GCQ-CGL equation based on the ansatz and coordinate transformation methods, and we discuss the influence of the higher-order dissipation coefficient on the amplitude and frequency of the wake flow by means of three-dimensional diagrams, contour maps, and plane graphs. The subsequent linear stability analysis gives a theoretical basis for the modulation instability (MI) of plane waves, and the linear theory predicts the instability of any amplitude of the main waves. Finally, we focus on the MI of shallow wake flows. Results show that the MI gain function is internally related to the background wave number, disturbance wave number, background amplitude, disturbance expansion parameter, and dissipation coefficient. The area of the MI decreases as the higher-order dissipation coefficient decreases.

A Trajectory Compensation Method Considering the Car-Following Behavior for Data Missing of Millimeter-Wave Radar in Roadside Detection Applications.

Concerning roadside traffic detection applications, and to address the millimeter-wave radar's missing data problem caused by target occlusion or the absence of features in low-speed conditions, this paper proposes a trajectory compensation method regarding car-following behavior. Referring to the installation scheme of the detector, a coordinate transformation method is presented to unify the radar spatial coordinates with the road coordinates. Considering the driver's car-following behavior, the optimal velocity model (OV), full velocity difference model (FVD), and the full velocity difference and acceleration (FVDA) model are applied for tracking the vehicle's trajectory related to the movement of the vehicle ahead. Finally, a data compensation scheme is presented. Taking actual trajectory data as samples, the proposed methods are verifiably useful for compensating for missing data and reconstructing target trajectories. Statistical results of different missing data trajectories demonstrate the rationality of the application of car-following models for the missing data compensation, and the FVDA model performs well compared with the OV and FVD models.

Subsection and superposition method for reservoir formation damage evaluation of complex-structure wells

Kinds of complex-structure wells can effectively improve production, which are widely used. However, in the process of drilling and completion, complex-structure wells with long drilling cycle and large exposed area of reservoir can lead to the fact that reservoir near wellbore is more vulnerable to the working fluid invasion, resulting in more serious formation damage. In order to quantitatively describe the reservoir formation damage in the construction of complex-structure well, taking the inclined well section as the research object, the coordinate transformation method and conformal transformation method are given according to the flow characteristics of reservoir near wellbore in anisotropic reservoir. Then the local skin factor in orthogonal plane of wellbore is deduced. Considering the uneven distribution of local skin factor along the wellbore, the oscillation decreasing model and empirical equation model of damage zone radius distribution along the wellbore direction are established and then the total skin factor model of the whole well is superimposed to realize the reservoir damage evaluation of complex-structure wells. Combining the skin factor model with the production model, the production of complex-structure wells can be predicted more accurately. The two field application cases show that the accuracy of the model can be more than 90%, which can also fully reflect the invasion characteristics of drilling and completion fluid in any well section of complex-structure wells in anisotropic reservoir, so as to further provide guidance for the scientific establishment of reservoir production system.

A Cooperative Relative Localization System for Distributed Multi-Agent Networks

While absolute position information is inaccessible for multi-agent networks due to the lack of global reference in GNSS-challenged or infrastructure-free scenarios, relative pose information among the agents can be obtained via agent cooperation. In this paper, we develop a cooperative relative localization system for distributed multi-agent networks. In particular, we propose a node activation strategy to select the backbone agents that minimize the information loss caused by malformed topology, and then the listener agents localize themselves based on the backbone topology. The scheme also incorporates a back calibration step that utilizes the position estimates of the listener agents to further improve the localization accuracy of the backbone topology. Moreover, a multi-sensory information fusion scheme is developed for dynamic scenes, where a coordinate transformation method is proposed to reduce the accumulated error caused by the coordinate misalignment. Finally, the system is implemented on a low-cost hardware platform with the ultra-wideband radios, and extensive simulations and experiments demonstrate that the proposed system can achieve decimeter-level relative localization accuracy.

Research on the Cloud Platform for Urban Rail Transit based on Track Inspection Vehicle

The aim of this paper was to improve the automation of track inspection, data utilization rate, informationization of maintenance dispatch. We designed a track inspection vehicle based on multi-sensor information fusion, then gave the method of coordinate transformation and data fusion. And then researched the service of data displaying, data management and data analysis, proposed the system architecture and network topology, realized the system deployment on the cloud. And then demonstrated stability by comparing the results of two machine tests, and proved accuracy by comparing the results of machine tests with manual tests. The result shows that it had a high accuracy and stability. At last, designed the reserve of cloud platform function extension, discussed the method of data analysis. Research shows that, the track inspection vehicle can measure the track geometric parameter. The application of cloud platform technology can reduce the cost of operation, simplify the function extension. The research result has a positive impact on solving the current problem of track inspection, improving passenger comfort and ensuring safe operation.

Coordinates transformation method for pointer gauge reading by machine vision

In this report we present a machine vision algorithm for pointer gauge reading based on coordinates transformation. Since a pointer gauge is a polar representation of a linear scale, it is possible to transform its polar reading to the original linear counterpart. Once the picture of a pointer gauge is captured digitally, we can assign the polar positions to each pixel of the image. Those polar coordinates can be plotted on a rectangular frame to form a transformed image. The scale lines and the pointer are transformed to point vertically (or horizontally). Locations of the scale lines and pointer can be obtained from their pixel histograms maxima. The main advantage of our algorithm is its simplicity. We can read the pointer orientation and scale lines position of a pointer gauge directly from its geometrical structure. The complication of feature extraction process from the conventional algorithm, e.g., Hough transformation, can be avoided. We have tested the algorithm with the ideal and real image of pointer gauges. In the latter case, even though there are some noises on the transformed image, the locations of pointer and scale lines can still be easily found. Due to its simplicity, our algorithm is fast. We expect that our method can be useful in practice as an alternative machine vision algorithm when the real time pointer gauge reading system, e.g., the automatic dial gauge tester, is needed.

Computer-vision-guided semi-autonomous concrete crack repair for infrastructure maintenance using a robotic arm

Engineering inspection and maintenance technologies play an important role in safety, operation, maintenance and management of buildings. In project construction control, supervision of engineering quality is a difficult task. To address such inspection and maintenance issues, this study presents a computer-vision-guided semi-autonomous robotic system for identification and repair of concrete cracks, and humans can make repair plans for this system. Concrete cracks are characterized through computer vision, and a crack feature database is established. Furthermore, a trajectory generation and coordinate transformation method is designed to determine the robotic execution coordinates. In addition, a knowledge base repair method is examined to make appropriate decisions on repair technology for concrete cracks, and a robotic arm is designed for crack repair. Finally, simulations and experiments are conducted, proving the feasibility of the repair method proposed. The result of this study can potentially improve the performance of on-site automatic concrete crack repair, while addressing such issues as high accident rate, low efficiency, and big loss of skilled workers.

Spatially discretised compensation method for coordinate transformation in large-scale metrology under nonuniform temperature field

Temperature-variation-induced error compensation plays a pivotal role in large-scale metrology, in which the nonuniform temperature field would greatly influence the coordinate transformation process between different systems. This paper proposes a novel analytical thermal deformation compensation method with spatial discretisation modelling among 2D distributed enhanced reference system points to reduce the thermal influence on the coordinate transformation process. First, the analytical thermal deformation model based on the spatial discretisation is established with the plane thermal elastic mechanics and the Finite Difference Method. Then the nonuniform temperature field model is developed based on Ordinary Kriging spatial interpolation. Finally, a compensation method for the coordinate transformation process is proposed based on the actual measurement data and the proposed thermal deformation model. The experimental results illustrate the existence and significance of the nonuniform feature of the temperature field. By the proposed compensation method, the coordinate transformation error is reduced by 47.13% and 76.67% in the x and y directions, respectively. The method is applicable to diminish the influence of thermal deformation under a nonuniform temperature field on the coordinate transformation of large-scale metrology.

Illuminator scheduling method for passive radar sea surface target detection based on RCS characteristic

ABSTRACT In order to improve the signal-to-clutter-noise ratio (SCNR) of received signal, this letter studies the illuminator scheduling problem in the detection process with the aim of maximizing SCNR time series. In order to use the illuminator with long detection time as much as possible and get high SCNR in the detection process, we propose a neighbourhood search illuminator scheduling method. Firstly, we study the characteristics of radar cross-sections (RCS) of target and sea surface under different incident directions and polarizations, and analyse the regions of high target RCS and low sea surface RCS. Then the coordinate transformation method is used to get the scheduling sequence within the detection range. Based on the global scheduling sequence, the neighbouring frames are searched to obtain the illuminator sequence of the randomly appearing target. Simulation results show that the proposed method can effectively improve the received signal SCNR 15 dB on average.

Coupled Analysis of Acoustic Space and Thin-Plate Vibrations by a Lumped-Mass Model Using Raviart–Thomas Elements

Suppression of noise and vibration in machine products is an important problem, and many methods have been studied. In particular, structural–acoustic coupled effects due to the weight reduction of machines cannot be ignored. In structural–acoustic coupled analysis, the finite-element method in which the acoustic space is described by sound pressure and the structure is described by displacement is often used. However, the eigenvalue analysis in that method takes a great deal of computational time because the mass and stiffness matrices are asymmetric. Instead, in this paper, we propose an efficient coupled analysis method for a three-dimensional acoustic space and a two-dimensional thin plate using a lumped-mass model. The proposed modeling method is derived systematically using Raviart–Thomas elements. In addition, we propose a coordinate transformation method that accelerates the calculations by reducing the number of degrees of freedom (DOF). In this way, a symmetric eigenvalue problem with no extra DOF is derived. The effectiveness of the proposed method is confirmed by numerical calculations. This analysis method is particularly effective for systems in which the acoustic space contributes to the majority of the DOF, since the acoustic space is sparse owing to the adoption of edge elements.

A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation

Acoustic cloaking is an important application of acoustic metamaterials. This article proposes a novel design scheme for acoustic cloaking based on the region partitioning and multi-origin coordinate transformation. The cloaked region is partitioned into multiple narrow strips. For each strip, a local coordinate system is established with the local origin located at the strip center, and a coordinate transformation in the local coordinate system is conducted to squeeze the material along the strip length direction to form the cloaked region. To facilitate the implementation of the acoustic cloak, the multilayer effective medium is used to approximate the non-uniform anisotropic material parameters. The effectiveness of the proposed coordinate transformation method is verified by comparing the results from our method with those in the literature. Firstly, the results of a circular acoustic cloak in the literature are reproduced by using our finite element (FE) simulations for validation. Then, a comparison is made between the traditional coordinate transformation scheme and our new scheme for simulating an elliptical acoustic cloak. The results indicate that the proposed multi-origin coordinate transformation method has a better cloaking effect on the incident wave along the ellipse minor axis direction than the traditional method. This means that for the same object, an appropriate transformation scheme can be selected for different incident wave directions to achieve the optimal control effect. The validated scheme is further used to design an arch-shaped cloak composed of an upper semicircular area and a lower rectangular area, by combining the traditional single-centered coordinate transformation method for the semicircular area and the proposed multi-origin method for the rectangular area. The results show that the designed cloak can effectively control the wave propagation with significantly reduced acoustic pressure level. This work provides a flexible acoustic cloak design method applicable for arbitrary shapes and different wave incident directions, enriching the theory of acoustic cloaking based on coordinate transformation.

Design and Kinematics Model of Autonomous Wheel-Claw Reconfigurable Amphibious Robot

In order to improve the adaptability of traditional wheeled robots to complex environments, a passive wheel-claw reconfigurable amphibious robot is proposed in this paper. This robot has strong mobility when moving on the ground. In complex scenes, if there are obstacles, it will automatically switch to claw mode. By studying the motion mechanism of the wheel-claw reconstruction process, the kinematics model of the robot under multiple working conditions is established by using the coordinate transformation method, and the wheel-claw transformation process is analysed in detail. Based on the virtual prototype of Adams, the dynamic simulation under the conditions of flat ground and obstacle crossing is carried out, the established dynamic mathematical model is verified. The simulation results provide theoretical data basis for the actual design of the robot. The experimental results of the prototype platform show that the designed passive wheel claw robot has the ability to work in complex scenes.