Coordinate Transformation Relationship Research Articles

Three-dimensional simulation based on mesh modelling for warp-knitted fully-formed garments

PurposeThe warp-knitted fully-formed shorts are one kind of fully-formed garments knitted by a double-needle bar machine, which is widely used in the medical field. Because of its distinctive forming method, designers are unable to grasp the final effect of the product accurately during the design process. The purpose of this paper is to clarify a visible 3D simulation method in the design process along with the knitting method and structure characteristics, which is reflected in the final product effect.Design/methodology/approachThis study introduces a simulation process for warp-knitted fully-formed fabric from an input 3D surface model group. Stitch mesh models are established according to the garment structure and the triangle index of the garment model that swchape-controlling points belong to is calculated. The garment model group includes a 2D plate and a 3D model, between which there is a space coordinate transformation relationship. The study makes use of the 3D tubes to connect the coordinate points in order and render the tubes in real yarn colors. The effects of two parameters, radial segment and tubular segment, are analyzed and decided to obtain a fine surface within a reasonable rendering time.FindingsA stereoscopic simulation process from flat fabric to 3D product is realized using computer graphics technology. The warp-knitted fully-formed short is shown during the design process within a short time by setting the rendering parameters of tubular segments (ts = 125) and radial segments (rs = 6).Originality/valueVisual simulation for the shorts provides a time-saving and resource-saving method for structure design and parameter modification before knitting. There is no need to knit samples repeatedly to satisfy demand, which indicates that it is a saver of time and resources.

A novel 3D vision-based robotic welding path extraction method for complex intersection curves

With the rapid development of robot technology, robotic welding technology has gradually been applied in the complex co-main intersection pipeline welding field. However, due to the existence of clamping errors and processing dimensional errors in intersecting pipes of the same specification, the actual welding path deviates from the taught path and cannot meet the accuracy requirements of robot welding, which further hinders the development and application of robotic welding in this field. To solve these problems, we propose a 3D vision-based robotic welding path extraction method for complex intersecting curves without programming and teaching. We begin by selecting the complex co-main intersection pipeline as the research object and building a robotic welding system based on 3D vision. Through mathematical analysis of the complex intersecting pipe model and an analysis of the internal coordinate transformation relationship within the welding system, we establish a mathematical model of the complex intersection curves at any clamping position in the manipulator coordinate system. On this basis, We propose a multi-view point cloud stitching method using Eye-in-Hand calibration and the ICP algorithm to obtain a complete co-main intersection pipeline point cloud. Subsequently, we propose a mathematical model parameter-solving algorithm based on the co-main intersection pipeline point cloud. Finally, the obtained actual parameters of the workpiece are combined with the established mathematical model to extract the welding path of the robot’s current position. Experimental results demonstrate that the proposed method can automatically extract welding seams for complex intersection curves without the need for programming and teaching.

Grinding wheel profile design and temperature field analysis of the pinion for internal meshing gear with curve configuration

To further develop the performance testing and practical application of internal meshing gear with curve configuration, the grinding manufacturing method is proposed in this paper. Based on basic principle of internal meshing gear with curve configuration, Newton’s iterative method is used to derive the contact line condition equation during the process of form grinding. Then, the spatial coordinate transformation relationship of the pinion is established, and normal profile of the grinding wheel is derived. An improved transversal algorithm is proposed to analyze the tooth profile error after form grinding simulation, and the results verify the correctness of the designed grinding wheel. A meshing model with single tooth is established. The effects of different parameters on the grinding temperature field under dry and wet grinding conditions are simulated respectively, which will be helpful to the optimization and control of temperature in grinding process. The research results lay the essential theoretical foundation and engineering analysis for practical form grinding applications of the new internal gears. Further study on experimental analysis of grinding manufacturing process of the new tooth surfaces will be carried out.

Optical Trapping of Chiral Particles by Dual Laser Beams

In this paper, an analytical method for studying the radiation force (RF) of chiral spheres generated by dual laser beams is presented under the framework of generalized Lorenz–Mie theory (GLMT). According to the coordinate transformation relations, the arbitrarily incident laser beam is represented by vector spherical harmonic functions (VSHFs) in the sphere system. The entire induced field expression coefficients of dual laser beams can be obtained by superposition of each illuminated field. Based on the momentum conservation theory, the concrete expression of lateral and axial RF on chiral sphere is derived. The current theories are shown to be valid by comparison with the existing reference. To investigate the stable capture state of chiral sphere, the influences of the corresponding parameters of chiral particles and dual laser beams on the trapping and manipulation are investigated in detail. The analytical study on the RF of dual laser beams on chiral particles is an efficient method for improving optical tweezers technology and can become an encouraging approach to realize the high accuracy operation of chiral particles.

Research on guidance information extraction technology of strap-down seeker based on adaptive cubature Kalman filter

In comparison to the traditional platform seeker, strap-down seeker, which is firmly connected with rocket-propelled vehicle, has a lot of strength in a smaller size, a simpler structure, and a lower cost. However, because it is fixed on the rocket-propelled vehicle, inertial line-of-sight(LOS) angular velocity demanded by guidance system could not be directly obtained during the rocket-propelled vehicle flight. In this paper, according to the coordinate transformation relationship, the inertial LOS angular velocity decoupling model is established. Aiming at measurement error characteristics of a seeker, a guidance information extraction algorithm which is on basis of the adaptive cubature Kalman filter is studied, and the digital simulation experiment is carried out in combination with the engineering practice. The simulation data demonstrate that the suggested algorithm has a significant effect on improving the filtering estimation stability and accuracy of guidance information extraction and guaranteeing the accuracy of rocket-propelled vehicle hits.

A variational nodal formulation for multi-dimensional unstructured neutron diffusion problems

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations.Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (keff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2–3.

Three-dimensional reconstruction from a fringe projection system through a planar transparent medium.

A vision measurement system is placed in a protective cover made of a transparent medium to avoid environmental influences. Due to the deflection of light rays on the front and rear surfaces of the transparent medium, the imaging position of an object on the camera target plane is deviated, which makes the traditional vision detection methods based on the triangulation principle produce large measurement errors. This work introduces a three-dimensional (3D) reconstruction method by fringe projection system through a planar transparent medium. We derive the coordinate transformation relationship between a real-object point and a pseudo-object point caused by light refraction based on Snell's law of flat refraction. Based on the relationship, a modified fringe projection method is proposed for unbiased 3D reconstruction. Two experiments, including 3D shape measurement of a white plate with ring markers and 3D shape measurement of a regular spherical object are conducted. The results demonstrate the effectiveness of the proposed method in such measurement environment.

A new model of covariant electrodynamics of moving media based on an alternative coordinate transformation relation instead of the usual Lorentz transformation

A new model of covariant electrodynamics of moving media based on an alternative coordinate transformation relation instead of the usual Lorentz transformation

Research on joint calibration and compensation of the inclinometer installation and instrument errors in the celestial positioning system

AbstractThe application of celestial navigation based on inclinometer to aircraft in near‐earth space and planetary rovers is a significant development direction. Due to the installation and instrument errors of the inclinometer, it is difficult for tilted platforms to obtain high‐precision positioning results. But the installation error of the inclinometer is coupled with the error of the instrument itself, and there is no effective way to measure the two errors separately. To improve the positioning accuracy of the tilted platform, a joint calibration and compensation algorithm of the inclinometer's installation and instrument errors is proposed. First, based on the principle of celestial positioning, the influence analysis model of the inclinometer error on the positioning accuracy is built according to the definition of inclinometer installation error and instrument error, which indicates the traditional algorithms are not suitable for tilted platforms. Then, a joint calibration and compensation algorithm for the inclinometer installation and instrument errors is presented based on coordinate transformation relationship and error propagation characteristics. Finally, a ground test platform is built and the experimental verification of the joint calibration and compensation algorithm of inclinometer error is accomplished. Experiment results show the root mean square errors of the longitude and latitude are and , and the mean distance error is 397.46 m, which is far less than the mean distance error 3629.27 m of the traditional calibration algorithm. It indicates the joint calibration and compensation algorithm can effectively compensate for the errors caused by the inclinometer and obtain higher positioning accuracy.

Novel rotation scheme for dual-axis rotational inertial navigation system based on body diagonal rotation of inertial measurement unit

Traditional rotational inertial navigation systems are based on rotation around one or two sensitive axes of inertial sensors. However, as the rotation and sensitive axes of inertial sensors lie along the same direction, it is difficult to modulate the relative error of the inertial sensor in the axial direction. This paper proposes a dual-axis rotation scheme based on the diagonal rotation of the inertial measurement unit (IMU) body. The scheme selects the body diagonal of the three orthogonal inertial sensors of the IMU as the horizontal rotation axis, and sets the vertical rotation axis orthogonal to this axis. As the rotation axis and the inertial sensor are oriented in different directions, at any moment of rotation, the errors of the inertial sensor in the three axial directions can all be modulated, especially the installation error. First, a mathematical model based on the diagonal rotation of the IMU body is established. On this basis, the coordinate transformation relationship and the error equations are derived, and the error propagation characteristics are obtained. Finally, the comprehensive error of the system is tested. Under the same error conditions, the system latitude error is reduced from 0.1089 nautical miles/72 h in the traditional scheme to 0.0368 nautical miles/72 h, and the longitude error is reduced from 0.3587 nautical miles/72 h to 0.1332 nautical miles/72 h. These results verify the effectiveness of the proposed scheme. This method of rotating around the body diagonal of the IMU also exhibits certain advantages when applied to other rotational inertial navigation schemes.

ACCURACY ANALYSIS OF REAL-TIME OBJECT POSITIONING WITHOUT GCP FOR IMAGES FROM UAV OBLIQUE ULTRA-LONG FOCAL SMALL VIEW FIELD WHISKBROOM CAMERA SYSTEM

Abstract. Using images from UAV oblique ultra-long focal small view field whiskbroom camera (ULF-SVF-WC) system for object positioning and mapping is more difficult than conventional aerial photogrammetry, for the particularity of oblique ULF-SVF-WC imaging mode. Therefore, the precision and accuracy of its object positioning are also quite different from that of the conventional UAV photography. In this paper, we analysed the accuracy of real-time object positioning without ground control points (GCPs) for images from UAV oblique ULF-SVF-WC System. Firstly, we studied the imaging principles and characteristics of the oblique ULF-SVF-WC system. Then, we established the coordinate transformation relationship from the object point to the image point and constructed a strict imaging model for oblique ULF-SVF-WC image, which was used for real-time single-ray back-projection positioning assisted by DEM. Thirdly, we quantitatively analysed the distribution and variation of the oblique ULF-SVF-WC image single-ray back-projection errors in theory based on error propagation law and simulation data. Finally, we conducted the experiment of real oblique ULF-SVF-WC flight images for the actual positioning accuracy analysis. The experiment results showed that: the influence of system error on positioning generally conforms to the distribution and variation of theoretical precision, that is, the accuracy of scanning direction is much lower than that of the flight direction; while the accuracy of actual single-ray back-projection positioning is evidently lower than that of the theoretical analysis and there are obvious system errors in the positioning residuals. It indicates that the 6 external orientation elements calculated from POS data contains obvious system error whose influence is greater than random error and this should be eliminated in real-time single-ray back-projection for object positioning.

The jump and stagnation of mass with speed

In the general theory of relativity, the four-dimensional space-time of describing a mass body accelerated motion or in a gravitational field, although it is a curved Riemannian geometric space from the perspective of “integral geometry”, but for any instantaneous position of the moving mass body, there is a local Flat Space of Riemannian geometric space. The local Flat Space is a Mincowski space in which the inertial coordinate system can be used in the local small area. Between the proper coordinate systems of two interacting moving masses, or between a series of following proper coordinate systems experienced by a mass body moving in any way, there should be a coordinate transformation relationship similar to the traditional special theory of relativity. However, they have an important difference: in these instantaneous local inertial systems, the speed of light is no longer the constant c of vacuum, the effect of gravitational field or acceleration on the speed of light is the same as that of a medium with a dielectric constant of ε and a magnetic permeability of μ. Using the special theory of relativity with variable speed of light that the author has established can discuss relevant relativity physics issues in these instantaneous local inertial systems. This article uses the special theory of relativity with variable speed of light to derive the functional relationship between a moving mass and the change of speed. In addition to obtain the traditional continuous increasing function relationship, a step function relationship with stepped discontinuous changes is also obtained. At the same speed, the mass can have two values, such as a ladder upgrade one level; the same mass can be matched with two different speeds, such as one step extension forward on the same step stair. From the perspective of the increase in speed, the mass is stagnant on the step platform (the speed increases, the mass does not change), and it jumps in the step up ladder (the speed does not change, the mass has a jump change). This obviously incorporates the main image of quantum theory into the theory of relativity, which is the result that all physics researchers care about and expect.

Aperture measurement based on a conic invariant.

With the advantages of low cost, universal applicability, and in situ detection, the conic invariant of the tested aperture diameter was obtained by ellipse geometric fitting on the aperture surface. The world coordinate system was established, and the transformation relationship between the world coordinate system and the camera coordinate system was obtained by the calibration. The improved Candy algorithm and coordinate transformation relationship could be used to project the sub-pixel coordinates of the aperture edge onto the aperture surface. Then, the ellipse geometric fitting was performed on the aperture edge curve surface to obtain the conic invariant. Finally, the conic invariant was used to measure the aperture diameter on the test bench.

Control technology of stable gaze scanning based on airborne platform

Stable gaze scanning control technology is the key to realize the integration of stable imaging, search, and tracking on airborne platforms. We investigate the control technology of stable gaze scanning on an airborne platform. The working principle of a stable staring scanning system is analyzed, and a servo system control algorithm is modeled. The position loop, velocity loop, and acceleration loop are designed. A stability model of the space with inclination angle is established. The coordinate transformation relationship between inertial coordinate system and airborne axis coordinate system is obtained. The designed control model and algorithm are used to control the single-lens reflex mirror mounted at an angle of 15 deg for spatial gaze pointing and step scanning. A test system is built for performance verification. Results show that the root-mean-square accuracy of the proposed algorithm is higher than 10 μrad in a dynamic staring step scan with ±30 deg and a step length of 2.16 deg. The single-step time is <52 ms, the stabilization time is >53 ms, and the servo system overshoot is small. The system step accuracy root mean square is better than 52 μrad. These findings confirm the effectiveness of the integrated search and follow technology under an airborne platform.

Pose Estimation of GIS Pipeline Based on Spatial Transformation Network

The manual flange structure alignment between GIS pipelines in the power system is inefficient and difficult to accurately align. To solve this problem, combined with the research results in the field of deep learning named spatial transformation network, a new pose estimation method based on single camera is proposed. In view of the high similarity between the moving flange and the static flange at the pixel level, the spatial transformation network is used to find the pixel mapping relationship of the two flange images. Thereby establishing the mapping relationship between the pixel coordinates of the two flange images and then using multiple points. In the perspective method, the pixel coordinates are mapped to the world coordinates to obtain the estimation of the position of the key point in the flange, and then the direction vector of the flange is calculated according to the position of the key point. Since there is a pixel coordinate transformation relationship between the static flange and the movable flange. Only the position of the key point in the static flange can be inversely solved by measuring the position of the key point in the static flange. Experiments show that, compared to the traditional method of measuring flange pose based on instrument measurement and linear regression, the method proposed in this paper can accurately measure the pose of the flange structure. And it can rely as little as possible on the measurement of the key points of the moving flange by the instrument.

Hand–Eye Calibration Algorithm Based on an Optimized Neural Network

A robot can identify the position of a target and complete a grasping based on the hand–eye calibration algorithm, through which the relationship between the robot coordinate system and the camera coordinate system can be established. The accuracy of the hand–eye calibration algorithm affects the real-time performance of the visual servo system and the robot manipulation. The traditional calibration technique is based on a perfect mathematical model AX = XB, in which the X represents the relationship of (A) the camera coordinate system and (B) the robot coordinate system. The traditional solution to the transformation matrix has a certain extent of limitation and instability. To solve this problem, an optimized neural-network-based hand–eye calibration method was developed to establish a non-linear relationship between robotic coordinates and pixel coordinates that can compensate for the nonlinear distortion of the camera lens. The learning process of the hand–eye calibration model can be interpreted as B=fA, which is the coordinate transformation relationship trained by the neural network. An accurate hand–eye calibration model can finally be obtained by continuously optimizing the network structure and parameters via training. Finally, the accuracy and stability of the method were verified by experiments on a robot grasping system.

Geometrical Size Detection on Key Contours of Safety Seat Base

According to the plastic base without clear benchmark, the contour features are extracted by the image processing method such as image matching and feature extraction. With the reference of the waist groove, the measuring coordinate system is established. The coordinate transformation relation is determined by the calibration of visual inspection system. Thus, the geometric relation of the arc groove with respect to the measuring coordinate system is obtained. The geometric dimensions of the safety seat base are measured. The experiment result shows that the relative error of measuring the waist-shaped groove’s width is 2.7%, the one of measuring the length is 2.1%. And the relative error of measuring the arc-shaped groove’s width is 0.7%.

Improving Positioning Accuracy of the Mobile Laser Scanning in GPS-Denied Environments: An Experimental Case Study

The positioning accuracy of the mobile laser scanning (MLS) system can reach the level of centimeter under the conditions where GPS works normally. However, in GPS-denied environments this accuracy can be reduced to the decimeter or even the meter level because the observation mode errors and the boresight alignment errors of MLS cannot be calibrated or corrected by the GPS signal. To bridge this research gap, this paper proposes a novel technique that appropriately incorporates the robust weight total least squares (RWTLS) and the full information maximum likelihood optimal estimation (FIMLOE) to improve the positioning accuracy of the MLS system under GPS-denied environment. First of all, the coordinate transformation relationship and the observation parameters vector of MLS system are established. Secondly, the RWTLS algorithm is used to correct the 3D point observation model; then the uncertainty propagation parameter vector and the boresight alignment errors between the laser scanner frame and the IMU frame are calibrated by FIMLOE. Lastly, experimental investigation in indoor scenarios was performed to evaluate the effectiveness of the proposed method. The experimental results demonstrate that the proposed method is able to significantly improve the positioning accuracy of an MLS system in GPS-denied environments.

Two-order approximate and large stepsize numerical direction based on the quadratic hypothesis and fitting method

Many effective optimization algorithms require partial derivatives of objective functions, while some optimization problems ʼ objective functions have no derivatives. According to former research studies, some search directions are obtained using the quadratic hypothesis of objective functions. Based on derivatives, quadratic function assumptions, and directional derivatives, the computational formulas of numerical first-order partial derivatives, second-order partial derivatives, and numerical second-order mixed partial derivatives were constructed. Based on the coordinate transformation relation, a set of orthogonal vectors in the fixed coordinate system was established according to the optimization direction. A numerical algorithm was proposed, taking the second order approximation direction as an example. A large stepsize numerical algorithm based on coordinate transformation was proposed. Several algorithms were validated by an unconstrained optimization of the two-dimensional Rosenbrock objective function. The numerical second order approximation direction with the numerical mixed partial derivatives showed good results. Its calculated amount is 0.2843 % of that of without second-order mixed partial derivative. In the process of rotating the local coordinate system 360 ° , because the objective function is more complex than the quadratic function, if the numerical direction derivative is used instead of the analytic partial derivative, the optimization direction varies with a range of 103.05 ° . Because theoretical error is in the numerical negative gradient direction, the calculation with the coordinate transformation is 94.71 % less than the calculation without coordinate transformation. If there is no theoretical error in the numerical negative gradient direction or in the large-stepsize numerical optimization algorithm based on the coordinate transformation, the sawtooth phenomenon occurs. When each numerical mixed partial derivative takes more than one point, the optimization results cannot be improved. The numerical direction based on the quadratic hypothesis only requires the objective function to be obtained, but does not require derivability and does not take into account truncation error and rounding error. Thus, the application scopes of many optimization methods are extended.

Derivation and simulation verification of the relationship between world coordinates and local coordinates under virtual reality engine

As a new human–computer interaction technology, virtual reality technology has been widely used in education, military, industry, art and entertainment, etc. Unity3D is one of the most popular virtual reality product development engines in the world. Coordinate transformation is the mathematical basis for space transformation in virtual reality technology. This paper explains the mechanism of Euler rotation causing the phenomenon of gimbal lock from the perspective of mathematical principles and derives the importance of Unity3D using quaternion for rotation calculation. Based on the Unity3D quaternion rotation calculation, the world–local coordinate transformation relationship of the child object under the Unity3D engine is deeply deduced and verified, which lays a theoretical foundation for the in-depth development of virtual reality products based on Unity3D.