Coordinate System Transformation Research Articles

Modelling and parameter design of a 3-DOF compliant platform driven by magnetostrictive actuators

Precision platforms composed of smart-material-based actuators and compliant mechanisms show advantages of high accuracy and fast response. This research focuses on a 3-degree-of-freedom compliant platform driven by magnetostrictive actuators. A parameterized physical model is established for the platform with consideration of three kinds of coupling effects. The magneto-mechanical coupling of the magnetostrictive actuator is described by a modified Jiles-Atherton model. The structural coupling of the platform is characterized in the process of stiffness matrix modelling and coordinate system transformation of the compliant components. The coupling between the magnetostrictive actuator and the compliant structure is considered in the overall actuation model. Parameter design is performed based on the numerical simulation of the proposed model. Due to the coupling effect, the dimensions of the compliant amplifier affect both the amplification ratio and the actuation stroke of the actuator. Thus, a combined optimization is essential to obtain the optimal design. The influences of the key dimensions on platform stiffness and actuation performances are demonstrated. With optimized key dimensions, the parasitic displacements can be effectively reduced at very little cost of the moving strokes. Open-loop experiments are taken to verify the accuracy of the proposed physical model, and closed-loop experiments are performed to demonstrate the platform performance on precision positioning. The main errors are caused by the friction in a sliding pair and the inertia of the loads.

A method to generate AWJ cutting path for a large-size part without well-defined location characteristics

Machining composite parts is a challenging manufacturing process. Many of these composite parts are not only with very large sizes but also lack of well-defined location characteristics. And usually, these composite parts are with burrs distributed on the periphery that require trimming. An industrial robot equipped with an abrasive water jet (AWJ) has been proved to be an effective method for trimming composite parts. This article proposed a method to solve the problem of trimming large-size composite parts without well-defined location characteristics with an AWJ robot. A standard block is bound on the end effector of the AWJ robot, as a locating reference. Then, by moving the AWJ robot so that this standard block is at the proximity of selected regions, the selected regions, along with this standard block, are scanned with a portable laser scanner. With the help of the standard block, a local coordinate system is established for the point cloud generated at each region. And further, the point clouds of these several regions are constructed into an integrated point cloud system through coordinate system transformation. Therefore, without using a large batch of magnetic stickers, a point cloud system of the large-size part is obtained. Finally, by matching the point cloud system with the 3D model of the expected final product, the 3D model of the expected final product is used to generate the tool cutting path with a special 3D CAM program. With this method, trimming large-size composite parts without well-defined location characteristics becomes realistic.

Planetary Sensor Models Interoperability Using the Community Sensor Model Specification

AbstractThis paper presents the photogrammetric foundations upon which the Community Sensor Model specification depends, describes common coordinate system and reference frame transformations that support conversion between image sensor (charge‐coupled device) coordinates to some arbitrary body coordinate, and describes the U.S. Geological Survey Astrogeology Community Sensor Model implementation (https://github.com/USGS-Astrogeology/usgscsm). We present a new image support data specification that provides the position, pointing, timing, and metadata information necessary to properly locate a pixel or observations location on a body and describe a system architecture designed to explicitly identify the responsibilities of software components within a larger pipeline or analytical environment. This paper concludes with a set of experiments that illustrate positional and pointing error in the sensor location and the impact on the computed surface location.

Simulation Research on Operation of Union Purchase System in Navigation Simulator

Navigation is the only way to develop and utilize marine resources, while the promotion of seafarers’ quality is the basic force of navigation, so navigation simulator plays an important role in modern navigation education. The simulation research on the operation of the union purchase is important to improve the special operation training of the actual cargo handling of the union purchase. On the basis of the Cartesian coordinate system transformation algorithm, the algorithm model of the union purchase operation is constructed. On the basis of three-dimensional (3D) rendering engine technology of open scene graph (OSG), the algorithm model of finding the space coordinates of the cargo point is established. The model of catenary equation is used to optimize the scene appearance of the cargo wire. By combination of QT channel signal mechanism and OSG, the simulation interaction of the union purchase operating system is realized. By acquiring the 3D coordinate values of each point, we fit the trajectories of each point in the operation and compare the trajectories. The results show that the model has high interactivity and small error. The comparison of the states of the cargo wire before and after optimization shows that the optimized wire is more realistic and the high fidelity meets the needs of operational training and simulation systems.

Determining Worm-Mill Profiles

The proposed mathematical model permits shaping of worm mills for the machining of parts with helical surfaces. The model includes a module generating matrices for the spatial transformation of coordinate systems. An algorithm is presented for formulating a model of the worm-mill surface. Shaping is completed in one stage, without determining the profile of the conjugate helical rack.

Study on the Method of Conversion from Beidou Coordinate System to Local Coordinate System

The coordinate system involved in surveying and mapping is rather complicated. The combination transformation of coordinate systems can solve many problems in real life and work. At the same time, the transformation between coordinate systems is also a difficult problem to be solved urgently. Aiming at the parameters and characteristics of Beidou coordinate system and the projection parameters of local city coordinate system, a set of transformation methods suitable for Beidou coordinate and local city coordinate system are developed by combining parameter transformation algorithm, the feasibility of the algorithm is verified by transforming the known control points.

Model Predictive Control of a Vehicle using Koopman Operator

Abstract This paper continues in the work from Cibulka et al. (2019) where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher order, namely the Koopman operator. The vehicle system typically features a lot of nonlinearities such as rigid-body dynamics, coordinate system transformations and most importantly the tire. These nonlinearities are approximated in a predefined subset of the state-space by the linear Koopman operator and used for a linear Model Predictive Control (MPC) design in the high-dimension state space where the nonlinear system dynamics evolve linearly. The result is a nonlinear MPC designed by linear methodologies. It is demonstrated that the Koopman-based controller is able to recover from a very unusual state of the vehicle where all the aforementioned nonlinearities are dominant. The controller is compared with a controller based on a classic local linearization and shortcomings of this approach are discussed.

Correction to “Nonlinear Model Identification Method for Crane Damage Detection Without Baseline Data”

Unfortunately, we did not consider transformation of the local coordinate system as we calculated the relative errors between the identified and the actual crack tips for each damage case. We made some mistakes in Table 8 , Table 10 , Figure 13 and Figure 22 . In addition, some symbols were mistaken using in Equation 9 and Equation 38 . They had no influence on the discussion and conclusions in the paper. The correct results are given here.

Heliostat field aiming strategies for solar central receivers

This thesis deals with the development of optical models for solar power tower technology. Specifically, this work is focused on modeling flux mapping and aiming strategies for central receiver systems (CRS). The resulting codes are applicable to CRS design and operation. This dissertation essentially presents four computational models. The first model, on which the rest of the models are built up, computes the flux density distribution incident on any kind of central receiver which is caused by a single heliostat. The procedure relies on the oblique projection of the receiver mesh onto the image plane, where an accurate analytic function, e.g. UNIZAR, is evaluated. Oblique projection is accomplished by transformation of coordinate systems. The 4-step projection method remarkably reproduces the distorted spot found for large incidence angles on the heliostat and the receiver. This basic model was validated against flux measurements on a flat receiver and Monte Carlo Ray Tracing simulations on a cylindrical receiver. Compared to SolTrace, the model takes 50 times less computation time and higher level of resolution. The second model was developed to determine canting errors in the facets of real heliostats. Based on a deterministic optimization algorithm, a procedure was set up to minimize the difference between computed flux maps and captured images on a lambertian target. Experimental images from THEMIS plant were employed to find out canting errors in selected CETHEL heliostats. From results of the model, one of the heliostats was successfully readjusted, significantly improving its optical quality, and validating the proposed methodology. The third model extends the basic model to superpose single heliostat flux maps in a whole field of heliostats. Shading and blocking losses are computed by parallel projection of neighbor heliostats. An aiming strategy, symmetric about the receiver equator, was developed on the basis of only one parameter: k, aiming factor. Nearly single equatorial aiming is achieved with k>3, while k=0 results in pointing to either upper or lower receiver edges. For the Gemasolar case study, an aiming factor equal to 2 yielded the most uniform flux maps, i.e. flat profile in the central region, and negligible increase in spillage losses compared to equatorial aiming. An optimal aiming strategy for molten salt receivers was implemented in the fourth model. An algorithm was developed to maximize receiver thermal output, while meeting at the same time corrosion and thermal stress limits; which were translated into allowable flux densities, AFD. Compared to unreliable single aiming, the optimized aiming strategy ensures receiver integrity and spillage losses only increase up to 4 percentage points. It was found that optimal aim points are, on average, slightly shifted towards the panel entrance. Despite the conflicting demand between adjacent panels in multi-panel receivers with serpentine flow pattern, the fit algorithm performs noticeable matching to the AFD profile. The resulting code takes around 2 minutes in a standard PC to compute the optimal aim points for a field made up of 2650 heliostats.

Nondestructive Determination of Nitrogen, Phosphorus and Potassium Contents in Greenhouse Tomato Plants Based on Multispectral Three-Dimensional Imaging.

Measurement of plant nitrogen (N), phosphorus (P), and potassium (K) levels are important for determining precise fertilization management approaches for crops cultivated in greenhouses. To accurately, rapidly, stably, and nondestructively measure the NPK levels in tomato plants, a nondestructive determination method based on multispectral three-dimensional (3D) imaging was proposed. Multiview RGB-D images and multispectral images were synchronously collected, and the plant multispectral reflectance was registered to the depth coordinates according to Fourier transform principles. Based on the Kinect sensor pose estimation and self-calibration, the unified transformation of the multiview point cloud coordinate system was realized. Finally, the iterative closest point (ICP) algorithm was used for the precise registration of multiview point clouds and the reconstruction of plant multispectral 3D point cloud models. Using the normalized grayscale similarity coefficient, the degree of spectral overlap, and the Hausdorff distance set, the accuracy of the reconstructed multispectral 3D point clouds was quantitatively evaluated, the average value was 0.9116, 0.9343 and 0.41 cm, respectively. The results indicated that the multispectral reflectance could be registered to the Kinect depth coordinates accurately based on the Fourier transform principles, the reconstruction accuracy of the multispectral 3D point cloud model met the model reconstruction needs of tomato plants. Using back-propagation artificial neural network (BPANN), support vector machine regression (SVMR), and gaussian process regression (GPR) methods, determination models for the NPK contents in tomato plants based on the reflectance characteristics of plant multispectral 3D point cloud models were separately constructed. The relative error (RE) of the N content by BPANN, SVMR and GPR prediction models were 2.27%, 7.46% and 4.03%, respectively. The RE of the P content by BPANN, SVMR and GPR prediction models were 3.32%, 8.92% and 8.41%, respectively. The RE of the K content by BPANN, SVMR and GPR prediction models were 3.27%, 5.73% and 3.32%, respectively. These models provided highly efficient and accurate measurements of the NPK contents in tomato plants. The NPK contents determination performance of these models were more stable than those of single-view models.

On the transformation of the coordinates of points from the SK-42 system to WGS-84

The significant and effective use of global positioning satellite systems for solution of important theoretical and applied problems of Earth sciences means the preserving of the possibility to use a huge quantity of geodetic, cartographic, gravimetric and other data created on the basis of traditional methods and in different referencing coordinate systems. It is impossible without the correct coordinate transformation at the transition from one system to another. The determination of the coordinates of points using the satellite radio navigation system NAVSTAR GPS is closely related to the world geodetic coordinate system WGS-84. At the same time, data on gravity observations within the Pulkovo 1942 coordinate system have been accumulated in large volumes. It is obvious the need for recalculation of coordinates given in different systems. Information is given on the coordinate systems, geodetic coordinates, units of measurement, display formats for latitude and longitude values. The reference coordinate system of Pulkovo 1942 and the modern world geodetic system WGS-84 are described in sufficient detail. Formulas are given for calculating the normal gravity in these systems. Historical background and classification of coordinate transformation methods are considered. Significant role is given to the high-precision method of Molodensky and the modified Helmert method of coordinate transformation. The standard method of Molodensky is described at the level it is described in official open reports of US government agencies. Programs are considered that automate the solution of the problem of recalculating the coordinates of objects, as well as the issues of transformation of coordinate systems in geographical information systems. The attention is focused on the rash use of the software that might lead to some very strange and inexplicable results.

Solving the problem transform of size images on series base points found on frames in the problem of stitching images

Stitching several images into a single content is an important task for many areas, including video analytics, machine vision, security, etc. The operation of combining is based on the solution of a number of operations related to the allocation of local features, the selection of transformation matrices of objects, changing the scale and saturation of the image. The process fixing frames is he’s with a number of difficulties, includes the appearance of a noise component in the image, blurring, various non-linear effects of the optical system, as well as problems associated with incorrect operation of data preprocessing software. To select the key points used as alignment points is a complex problem, the solution of which is the subject of many works. However, the transformation of coordinate systems of images with combination frames is a difficult problem, since the system is nonlinear.The article discusses the solution to the problem of changing the position of points in clusters, under conditions of their nonlinearity. The method and algorithm that implements the procedure of nonlinear transformations size over the entire image is presented. Operations include vector analysis, as well as the results of changing the scale of a group of pixels. The set of test data shows the possibility of applying these approaches to change one of the images according to the specified combination points by the operators.

Autonomous trajectory planning for launch vehicle under thrust drop failure

An online autonomous rescue strategy and the algorithm for launch vehicle are studied in the case of a thrust drop during ascending flight. First, an iterative guidance method and numerical integration are used to evaluate the remaining carrying capacity. When the target orbit is unreachable, but the lowest safe orbit could be met, an optimal rescue orbit (ORO) needs to be solved. Using the geocentric angle estimation, orbit coordinate system transformation, and convexification, the maximum-height circular orbit in the orbit plane determined by states at failure time, is found under the constraint of geocentric angle. Then, an optimal circular orbit (OCO) relaxing the above constraint is solved by the adaptive collocation method (ACM) using the former solution as initial values. Finally, a decision whether to adjust other orbital elements by comparing the height between OCO and target orbit is made. The algorithm gives priority to the orbit height, optimizes the ORO based on the objective function weights, and makes full use of the advantages of geocentric angle estimation: simplifying the terminal constraints, making the convex optimization achieve good convergence, and improving the effectiveness of the ACM under reasonable initial guess. The simulation results show that the proposed strategy and algorithm are adaptable and, convergent for onboard application.

Theoretical and Experimental Study of Transient Behavior of Spiral-Groove Thrust Bearings during Start-Up

In this study, a transient mixed lubrication model that considers mass-conserving cavitation and deterministic asperity contacts is established to study the evolution of the tribological behavior of spiral-groove thrust bearings during start-up. To overcome oil film thickness discontinuity at the edges and the complicated boundary shape of spiral grooves, a boundary-fitted coordinate system transformation is adopted. The evolution of the tribological behavior, including the asperity contact force, load-carrying capacity, minimum oil film thickness, and friction torque during start-up, is presented using the current model. To illustrate more clearly, the evolution of hydrodynamic pressure and cavitation fraction is also displayed. Experiments are performed to verify the proposed theoretical model. The results demonstrate that this model is able to capture the evolution of the tribological behavior of spiral-groove thrust bearings during start-up. To improve start-up performance, a parametric analysis is conducted to identify the effects of the main design parameters (groove depth, groove width ratio, and spiral angle) on the lift-off speed.

Research on Optimization of Working Mode of Long-range Early Warning Radar Guided by Space-based Information

The long-range early warning radar is the key equipment in the early defense process of ballistic missile. For the problem of low working efficiency of long-range early warning radar without guidance information, this paper studies the working process of long-range early warning radar with space-based guidance information, and proposed a new long-range warning radar working mode. Firstly, the coordinate system transformation and guidance information extraction of space-based guidance information are given. Then the concept of coherent accumulation of radar signals is introduced and a new radar operation mode is proposed. Finally, the radar signal coherent accumulation process is established. A mathematical model of radar search distance and intercept probability. The typical scene is built and simulated. The results show that the proposed radar working mode will effectively reduce the search airspace of the long-range early warning radar and improve the radar detection range.

Single XNAV integrated navigation based on series filtering

Celestial navigation system (CNS) and inertial navigation system (INS) are traditional autonomous integrated navigation methods. CNS is generally used to correct the cumulative error of the gyroscope in INS. The cumulative error of the accelerometer in INS cannot be corrected. As a new type of autonomous navigation method, the X-ray pulsar navigation system (XNAV) can correct the cumulative error of the accelerometer.This study proposes an integrated navigation method based on a combination of single x-ray pulsar navigation (SXPN), INS, and CNS. The method constructs a virtual accelerometer (VA) by coordinate system transformation, then compensates the error of the virtual accelerometer by using single X-ray pulsar navigation method, and then estimates the position, velocity, and angle errors by Kalman filtering method. The proposed method is an improvement of the SXPN navigation method of Q. Xu et al. in 2018. These improvements are twofold, that is, the positioning has high accuracy and is stable. A method was proposed to correct the error of the accelerometer and then analysis and simulation to support our guess is provided. This navigation method not only can correct the zero-order error of the accelerometer but also the first-order error that few scholars have studied.Simulations show that the proposed method reduces the total position error in three directions. In comparison with the method of adding the pulsar arrival time directly to the observation equation, our proposed method not only has higher precision, but it can also alleviate the jitter of the velocity position and attitude curve.

ANALYSIS OF COMMON QUALITY PROBLEMS IN COORDINATE TRANSFORMATION BETWEEN REFERENCE COORDINATE SYSTEM AND GEOCENTRIC COORDINATE SYSTEM

Abstract. In the working of the existing reference coordinate system transformed into the coordinate system of the geocentric coordinate system, many experts and scholars have in-depth research on the transformation methods such as geodetic control point results (including GNSS base station coordinates, GNSS control point coordinates, triangle point coordinates), basic geographic information data results (including DLG, DOM, DEM, DRG, DSM, etc.) and other spatial information data. On the basis of these studies, many provinces and cities have completed the coordinate system transformation of surveying and mapping results in China. This paper expounds the method of transforming the existing reference coordinate system into the geocentric coordinate system, summarizes and sorts out the common quality problems in the process of different data and different methods, and analyses the causes of the problems and the impact on the transforming results. Based on the above work, The paper provides reference and suggestions for the transforming work, which is aimed to improve the transformation quality in the future.

Estimation of Doppler Curve for LEO Satellites

Doppler frequency shift which is defined as “the observed changes in frequency of transmitted waves when relative motion exists between the source of waves and an observer”, has wide applications in science, technology and different industries including communications, medicine, aerospace, electronics and etc. One of its common applications in aerospace is its use in tracking satellites and orbit determination. In low earth orbiting satellites, because of their low altitude to earth and their high rotation period around it, Doppler shift is appropriate to be used for tracking. In this paper, satellite distance and its derivative in time which is parameter in obtaining Doppler shift is derived. Position of the satellite is firstly derived using equations governing on them and TLE which contains orbital elements and essential information in different coordinate systems such as ECI, ECEF and topocentric. Then satellite distance to ground station and its changes in time is calculated via transformations of coordinate systems to each other. Having the distance, its derivative and beacon signal frequency, Doppler curve can be estimated in each pass of the satellite. Doppler shift can be used in an appropriate and precise satellite tracking technique.

Fully Local Amplification Factor Transport Equation for Stationary Crossflow Instabilities

The traditional linear stability analysis for transition prediction includes the following steps: solving velocity profiles using boundary-layer equations or a computational fluid dynamics solver, guessing and searching operations for the eigenvalues, computing the linear perturbation equations, and integrating the amplification factor . It is difficult to implement into modern computational fluid dynamics solvers with parallel computations because it requires many nonlocal variables and coordinate system transformations. In this Paper, an amplification factor transport equation, which can be coupled with a modern computational fluid dynamics parallel solver, is established based on the analysis results through linear stability theory for stationary crossflow instabilities. According to the analysis results of Falkner–Skan–Cooke similarity velocity profiles using linear stability theory analysis, the source term of the present transport equation is formulated locally to describe the growth of stationary crossflow waves in the laminar boundary layer. This new equation is added to the equation proposed by Coder and Maughmer for Tollmien–Schlichting instabilities. Finally, coupling of these two amplification factor transport equations and Menter’s shear stress transport turbulence model completes an effective transition turbulence model. Comparisons between the present predictions, wind tunnel experiments and the standard linear stability theory analysis on an NLF(2)-0415 infinite swept wing, Petzold’s sickle-shaped wing and 6:1 inclined prolate spheroid validate the reasonable establishment of the present amplification factor transport equation for stationary crossflow instabilities.

Prediction of cutting force for ball end mill in sculptured surface based on analytic model of CWE and ICCE

The force prediction is the precondition of improving equipment utilization ratio and optimizing process for CNC machining. Cutter-workpiece engagement (CWE) and in-cut cutting edge (ICCE) are the keys. In this article, a new analytic method of CWE and ICCE is proposed for ball end milling of sculptured surface and the prediction model of milling force is established. The sculptured surface is discretized into a series of infinitesimal inclined planes corresponding to cutter location points. The geometry relationships of cutter axis, feed direction and inclined plane are defined parametrically. The boundary curves and the boundary inflection points of the CWE are obtained by intersecting spatial standard curved surfaces with rotation transformation of coordinate system. The effective intersection points of the CWE and the cutter edge curve in Xc-Yctwo-dimensional plane are the upper and lower boundary points of ICCE. Based on the instantaneous chip thickness considering arbitrary feed direction, the force prediction model for ball end mill of three-axis surface milling is established. Simulation and experiment show that CWE and ICCE calculated by analytic method are well consistent with those of solid method. The predicted cutting forces match well with the measurements both in magnitude and variation trend.