Plane Coordinate System Research Articles

QGIS‐based support tools to simplify the complex design challenges of subsurface drainage systems

AbstractWe developed a comprehensive set of tools to simplify the design and layout of subsurface drainage systems. These tools, which utilize publicly available LiDAR (light detection and ranging) datasets, may also be used for other applications. The tool streamline operations include harmonizing geographic information system (GIS) layers into a single State Plane or Universal Transverse Mercator Coordinate System, clipping and thinning LiDAR data within a defined boundary, generating drainage networks with contour lines and laylines for surface flow visualization, identifying depressions and creating gridlines with user‐specified angles and spacings. To showcase their use, an illustrative example using a diverse dataset from the University of Illinois’ South Farm is provided. These user‐friendly tools, optimized for compatibility with all versions of QGIS3 (quantum geographic information system 3), are freely accessible for download or installation from the official QGIS plugin repository. A user manual with step‐by‐step instructions is available online on the Illinois Drainage Guide website.

Experience and effectiveness of the no-loft linking shape and dimension method using laser optical systems in aircraft production

The object of research is the application of the no-loft linking shapes and dimension method using laser measuring tools to reduce the labor intensity and cycle of mounting work. The study of the accuracy of the geometric parameters of cantilever wing and technological equipment at various stages of production was carried out. The problem is to create a method of using laser optical systems in aircraft production at the stage of mounting of technological equipment to minimize the impact on the accuracy of the dimensions of assembled parts of aggregates. The following results were obtained: the advantages of using the no-loft linking method in the modern production of aviation equipment were analyzed, which makes it possible to reduce the preparation cycle by 2–3 times. A study was conducted on the effective use of the Coordinate Measuring Machine (CMM) of laser tracker in the manufacture of the cantilever wing (CW) of the AN series airplane at all stages of mounting, as well as on the accuracy inspection of geometric parameters in comparison with the theoretical master geometry (MG). The practical significance of the research is that the proposed method of using laser optical systems during the installation of equipment allows to reduce to a minimum the impact on the accuracy of low rigidity frames. And also, to reduce the equipment deformation due to the mass of the parts of the assembled aggregates and temperature deformations, which allows to ensure a reduction of the mounting error to ±0.1 mm. Also, the application of this technique allows to enter the plane's coordinate system without prior leveling, to mounting and inspection the installation of the wing, fin, stabilizer, engines and landing gear on the fuselage. In general, the application of the no-loft linking shape and dimension method with using laser optical systems in aircraft production allows to reduce the labor intensity and cycle of mounting work up to 10 times.

S-shaped rolling gait designed using curve transformations of a snake robot for climbing on a bifurcated pipe

In this work, we focus on overcoming the challenge of a snake robot climbing on the outside of a bifurcated pipe. Inspired by the climbing postures of biological snakes, we propose an S-shaped rolling gait designed using curve transformations. For this gait, the snake robot’s body presenting an S-shaped curve is wrapped mainly around one side of the pipe, which leaves space for the fork of the pipe. To overcome the difficulty in constructing and clarifying the S-shaped curve, we present a method for establishing the transformation between a plane curve and a 3D curve on a cylindrical surface. Therefore, we can intuitively design the curve in 3D space, while analytically calculating the geometric properties of the curve in simple planar coordinate systems. The effectiveness of the proposed gait is verified by actual experiments. In successful configuration scenarios, the snake robot could stably climb on the pipe and efficiently cross or climb to the bifurcation while maintaining its target shape.

Orbit constraint of a small bead on a rotating large circular hoop in a horizontal plane

Orbit constraint problems can be encountered in mechanical equipment and amusement equipment. Mechanics exercises generally consider the ideal physical model, and the practical problems also consider the influence of friction, which makes the problem more complex and and practical. The problem of the force and oscillation of objects on orbit needs to be deeply discussed. In order to simulate the orbital motion of objects more realistically and help students expand their theoretical mechanics beyond class, we study the orbit constraint of a small bead on a rotating large circular hoop in a horizontal plane about an axis passing through a point on the circumference. The coupling equations followed by the bead on the hoop are derived using Newton’s second law in a planar polar coordinate system and solved by numerical methods. We found that under the action of friction, when the initial angular velocity of the bead is greater than the critical angular velocity, the bead will rotate on the ring, and the number of rotations is related to the initial angular velocity and influenced by the friction coefficient. At different initial angular velocities, the number of oscillations of the bead on the hoop is basically the same and ultimately stops near the fixed point.

Solar Radiation Tracking Design Based on Photoelectric Sensor for Tracing Signal Reconstruction Algorithm

Due to the high precision, low power requirements, and maintenance-free nature, the four-quadrant photoelectric sensor (FQPS) and the laser displacement sensor are employed in the development of the two-axis solar tracker. Among them, when designing the optical path of the FQPS, a cavity-wandering optical path is introduced to control the spot size of the direct sunlight falling on the sensor. The sensor interface has five data transmission lines, of which four positive poles correspond to the four quadrants of the planar two-dimensional coordinate system. AD7793 is used as the signal collector and a differential amplifier with small clutter is integrated. A laser displacement sensor is installed in the solar radiation tracker to realize the self-correction of movement error. The main control circuit adopts DSP chip TMS320F28335 for the whole dual-axis sun tracker. In the experiment, Code Composer Studio was used for development, and SPA algorithm was used to measure the position. A number of error correction variables, such as year, month, day, time, minute, second, ΔT, time zone, longitude, latitude, etc., are added to the algorithm. After debugging the hardware and software, the sunrise and sunset times of a certain place on the solar terms such as spring equinox, summer solstice, autumn equinox and winter solstice in 2022 are tested, and compared with those released by the Meteorological Bureau. The tracking signal is rebuilt using proximal gradient descent technology. The results demonstrate that the signal-to-noise ratio under the reconstruction algorithm is continuously enhanced and tends to stabilize with an increase in sampling rate without noise, and it exhibits good signal reconstruction performance in the presence of noise and growing noise.

Developing a universal and reliable temporomandibular joint reference system for quantifying morphological and positional changes.

This study aimed to provide a universal and reliable reference system quantifying temporomandibular joint (TMJ) morphological and positional changes. Large field-of-view (FOV) cone-beam computed tomography (CBCT) images (20 TMJs) from 10 preorthognathic surgery patients and limited FOV CBCT images (40 TMJs) from 20 splint therapy-treated patients with temporomandibular disorders were collected. TMJ-specific reference system including a TMJ horizontal reference plane (TMJHP) and a local coordinate system (TMJCS) was constructed with landmarks on cranial base. Its application for TMJ measurements and its spatial relationship to common Frankfort horizontal plane (FHP) and maxillofacial coordinate system (MFCS) were evaluated. Five relevant landmarks were selected to optimally construct TMJ-specific reference system. General parallelism between TMJHP and FHP was demonstrated by minimal angular and constant distance deviation (1.714 ± 0.811º; 2.925 ± 0.817 mm). Additionally, tiny axial orientational deviations (0.181 ± 6.805º) suggested TMJCS rivaled MFCS. Moreover, small deviations in orientations and distances (1.232 ± 0.609º; 0.310 ± 0.202 mm) indicated considerable reliability for TMJCS construction, with intraclass correlation coefficients (ICCs) ranging from 0.999 to 1.000. Lastly, slight discrepancies in translations and rotations revealed high reliability for condylar positional and morphological measurements (ICC, 0.918-0.999). TMJ-specific reference system was merely tested in two representative FOVs. This study provides a universal and reliable reference system for TMJ assessment that is applicable to both limited and large FOV CBCT. It would improve comparability among diverse studies and enable comprehensive evaluations of TMJ positional and morphological changes during TMJ-related treatment follow-up such as splint therapy and disease progression.

Modeling and Analysis of a Multidimensional Planar Monoreactive Oscillator

The work belongs to the field of mechanical engineering, namely: to oscillating mechanical systems. The relevance of the study is determined by the fact that fluctuations of inertial masses are found everywhere. In the field of construction and use of aviation and rocket technology, this topic is of particular importance. Like a three-dimensional plane coordinate system in the coordinate plane Z, a multidimensional system with n axes shifted relative to each other by angles can be considered. There is an arbitrary vector emanating from the origin. It is proved that the points which are the coordinates of the end of the vector in the coordinate system are the vertices of a regular polygon. The shape and dimensions of the polygon are not related to the coordinates of the vector i.e. are unchanged. The center of a regular polygon in all cases coincides with the middle of the vector. In the considered (idealized) case, the polygon, at the vertices of which there are oscillating weights of masses m, lies in the Z plane multi-piston mechanism. In the considered multidimensional plane monoreactive oscillator, free harmonic linear oscillations of loads can occur. In this case, only kinetic energy is involved in the energy exchange. There is no need for elastic elements. The oscillator does not have a fixed natural oscillation frequency. The frequency depends on the initial speeds and positions of the weights. A regular polygon makes a double rotation - around the point 0 and around the point r. At the same time, the loads carry out linear harmonic oscillations with amplitude R. The use of a crank-slider or crank-and-rod mechanism will allow organizing the parallel movement of goods.

Synchronized Tracking Control of Dynamic System of Unmanned Rear-Wheel Vehicles Based on Dynamic Analysis

From the classic automatic guided vehicle system, the system of the unmanned rear-wheel drive vehicle (URWDV) based on a dynamic analysis is studied. In the URWDV system, the relationship among the position information, velocity, and the heading angular velocity of the unmanned vehicle is established in the plane coordinate system and the coordinate system centered vehicle itself. The velocity and heading angular velocity values are obtained through a dynamic analysis and are used as control parameters. The synchronized tracking control of the unmanned vehicle is realized by the control scheme of the velocity and the heading angular velocity. Finally, the simulation examples show the effectiveness of the tracking control.

Method for real-time reconstruction of a transmission line based on the LiDAR point cloud data of a partial line segment

In a light detection and ranging (LiDAR) anti-external force damage monitoring system, the LiDAR installed on an electric power tower can only collect some point cloud data from the transmission line within a few tens of meters. Consequently, its anti-break system fails to calculate the distance between the transmission line and ground objects. In this study, a real-time reconstruction method for a transmission line based on a catenary mathematical model is proposed. Based on the three-dimensional (3D) point cloud data of the local power line, a 3D point cloud is mapped to a two-dimensional (2D) plane. In the 3D plane coordinate system, the catenary equation is fitted and calculated using the catenary model, and the 2D point cloud dataset of the transmission line is calculated according to this equation. Subsequently, the transmission line of the 2D plane is restored to the 3D space, and finally, the entire transmission line is restored to the 3D point cloud data. The field test results reveal that the proposed method can be used to effectively calculate and reconstruct the 3D transmission line model in real time and solve the spatial distance calculation problem of the anti-external force damage monitoring system.

Trajectory Tracking Control of the Wheeled Mobile Robot based on the Curve Tracking Algorithm

A controller based on the curve tracking algorithm is offered as a solution to the issue of the wheeled mobile robot’s trajectory not be precisely monitored. First, Utilizing a planar global coordinate system, the kinematics and dynamics models of the wheeled mobile robot is created. Then, the kinematic model of the actual and predicted trajectories is utilized to determine the trajectory tracking error of the wheeled mobile robot. By the trajectory tracking error system model, The curve tracking algorithm controller is employed in the outer loop control to remove the robot’s position and attitude deviation during trajectory tracking, while the PI controller is utilized in the inner loop control to precisely track the robot’s speed. The simulation results demonstrate that the suggested control technique can regulate the wheeled mobile robot’s pose error [xq yq θq]T within the ranges of 0.1m, 0.03m, and 0.03rad, which demonstrates the efficacy of the control approach.

An Improved Calibration Method of Grating Projection Measurement System

In the traditional fringe projection profilometry system, the projector and the camera light center are both spatially virtual points. The spatial position relationships specified in the model are not easy to obtain, leading to inaccurate system parameters and affecting measurement accuracy. This paper proposes a method for solving the system parameters of the fringe projection profilometry system, and the spatial position of the camera and projector can be adjusted in accordance with the obtained calibration parameters. The steps are as follows: First, in accordance with the conversion relationship of the coordinate system in the calibration process, the calculation formula of the vertical distance from the camera light center to the reference plane and the calculation formula of the distance between the projector and the camera light center are given respectively. Secondly, according to the projector calibration principle, the position of the projector light axis perpendicular to the reference plane is gained by comparing the parallel relationship between the reference plane coordinate system and the projector coordinate system’s Z-axis. Then, in order to fulfill the position restriction that the line between the projector light center and the camera light center must be parallel to the reference plane, the camera’s spatial location is adjusted so that the vertical distance between it and the reference plane tends to that between the projector light center and the reference plane. And finally, the three-dimensional (3D) reconstruction of the target object can be finished using the phase height model’s system parameters once the aforementioned position limitations are put into practice. Experimental results demonstrate that the method improves the measurement accuracy, and verifies that it is effective and available in 3D shape measurement.

Wavelet based tone mapping (TM) enhancement to a detection system for faint and compact sources in HDR and large FOV radio scenes

For high dynamic range (HDR) and large field-of-view (FOV) radio scenes, detection of faint sources with compact support and tiny sizes in comparatively extensive celestial areas is a challenging task. In the era of the Square Kilometer Array (SKA), it will be of particular concern, and data-targeted systematic methods are put on the agenda. This paper proposes a systematic method to solve this problem. From the perspective of image processing, a multiscale image contrast enhancement (ICE) is proposed to normalize the HDR. Source representation is realized by a starlet framework, where a two-step tone mapping (TM) including an arc-tangent function compression and an aggregated gain function enhancement are embedded. According to two bionic principles, the gain function is designed to highlight faint sources, remove artifacts (e.g., halos), and avoid feature distortions. For source detection, an integration method is proposed for projections between the celestial and the planar coordinate systems. It serves for coordinate transform and source location. A detection indicator system is built, and elaborate discrimination principles are drawn up. In the experiments, this method is dedicated to the dataset of the TIFR GMRT Sky Survey (TGSS) alternative data release 1 (ADR1) to facilitate the scientific goal of discovering new sources. Results show its advantages over the state of the art methods in visual inspections and detection ratios, and preliminarily prove that it has prospects for future HDR and large FOV radio data.

Evaluation of training efficiency of table tennis players based on computer video processing technology

In this paper to improve the training efficiency of table tennis players, this paper applies computer video processing technology to the evaluation of training efficiency of table tennis players, and uses intelligent video processing to identify the training process of table tennis players. Moreover, this paper introduces the curve coordinates to mathematicalize the projection problem, establishes the spherical coordinate system and the plane coordinate system, obtains the spherical quadrilateral and the plane quadrilateral, obtains Euler's idea of establishing a projection suitable for table tennis, and obtains the road map of Euler's projection theory. In addition, this paper builds a training efficiency of table tennis players evaluation system based on projection algorithm and athlete feature recognition. Through the experimental research, it can be seen that the training efficiency evaluation system of table tennis based on computer video processing technology proposed in this paper can effectively improve the training efficiency of table tennis players.

Unscented Kalman filter for long-distance vessel tracking in geodetic coordinates

This paper describes a unique instantiation of the unscented Kalman filter (UKF) that is particularly well-suited to long-distance surface vessel tracking. The proposed filter leverages a nonlinear process model to predict the position, speed, and heading of targets directly in geodetic coordinates, obviating the need for intermediate coordinate frame transformations, and enabling the use of a simple linear observer. These features differentiate the proposed filter from prior architectures, most of which require the definition of a planar coordinate system in order to describe the linearized state kinematics in an easily differentiable form. Reliance upon local Earth-tangent frames is acceptable in confined operating regions, but incurs substantial estimation error when the target is far from the local origin. It is shown that this error grows with distance-cubed from the local origin. By tracking targets directly in geodetic coordinates, the proposed filter is able to achieve more consistent performance, and a three-fold reduction in computational cost. A series of numerical simulations and field exercises are performed to ground these claims, and verify the efficacy of the proposed filter.

Feasibility study for using the fillers in the bearing structure components of a gondola car

Purpose. To study the feasibility of using the fillers for the gondola car bearing structure components. This makes it possible to reduce both damage to the gondola car bearing structure components during operating modes of loading and the cost of unscheduled repairs. In addition, it can improve the efficiency of railway transport operation. Methodology. In order to substantiate the use of aluminium foam as a filler for the gondola car bearing structure components with a closed box-section, a computational modeling of loading under the most unfavorable operating mode, such as shunting collision, has been performed. Gondola car 12-757 model built at PJSC Kryukovsky Railway Car Building Works is chosen as a prototype. The calculation is performed using the finite element method implemented in the SolidWorks Simulation (CosmosWorks) software package. The fatigue strength and natural vibration frequencies of the gondola car bearing structure with a filler of its components have been calculated. The natural vibration frequencies of the bearing structure of the gondola car are calculated. The design service life of the gondola car bearing structure has been determined. The main indicators of the gondola car bearing structure dynamics have been studied. The calculation is made in a plane coordinate system. In this case, the mathematical model is solved by the Runge-Kutta method. Findings. The results of the conducted research have revealed that the use of aluminium foam as a filler for the gondola car bearing structure components contributes to reduction of their load-bearing capacity from 12 to 47% compared to the prototype wagon. Originality. The expediency of using aluminium foam as a filler of the gondola car bearing structure components by modeling its load-bearing capacity under the most unfavorable operating conditions has been scientifically substantiated. Practical value. By reducing the loading on the gondola car bearing structure, using aluminium foam as filler for its components, it is possible to increase fatigue strength, reduce the amount of damages, and, consequently, the cost of unscheduled repairs of the wagon. The conducted research can contribute to the creation of recommendations for developing the innovative rolling stock designs with improved technical-and-economic, as well as operational performance.

Minimizing Root-Mean-Square Linear Distortion in Common Conformal Map Projections

AbstractThe upcoming State Plane Coordinate System of 2022 has spurred considerable interest in design, development, and implementation of large-scale conformal map projections designed at Earth’s ...

Robotics-based vineyard water potential monitoring at high resolution

The purpose of this research is deploying a proximal sensing solution using non-invasive and cost-effective sensors onboard an Autonomous Ground Vehicle (AGV) as a feasible way for building high-resolution maps of water potential in vineyards. The final objective is offering growers a practical system to make decisions about water management, especially for arid climatic conditions. The monitoring AGV was entirely developed within this research context, and as a result, it is a machine specifically designed to endure off-road conditions and harsh environments. The autonomous vehicle served as a massive, non-invasive, and on-the-go data collector robotic platform. The sensors used for measuring the relevant field variables were two spectral reflectance sensors (SRS), an infrared radiometer, and an on-board weather sensor. The collected data were displayed on comprehensible grid maps using the Local Tangent Plane (LTP) coordinate system. The proposed model has a coefficient of determination R2 of 0.69, and results from combining six parameters: the canopy and air temperatures (as the temperature difference), the relative humidity, the altitude difference, the Normalized Difference Vegetation Index (NDVI), and the Photochemical Reflectance Index (PRI). The strongest relationships found in this study were between the temperature difference and PRI, with an R2 of 0.75, and the temperature difference with the leaf water potential with an R2 of 0.61. The practical use of these high-resolution maps includes irrigation scheduling and harvest zoning for sorting grape quality, with a further use as inputs to complex artificial intelligence algorithms considering larger areas or complementing airborne data. Future improvements to make the models more robust and versatile will entail considering additional variables, locations, or grapevine cultivars, and even other crops grown in vertical trellis systems.

Route-Planning Method for Plant Protection Rotor Drones in Convex Polygon Regions.

Aiming at the problem of low operating efficiency due to the poor endurance of plant protection rotor drones and the small volume of pesticide carried, this paper proposes a route-planning algorithm for convex polygon regions based on the initial heading angle. First, a series of coordinate conversion methods ranging from the Earth coordinate system to the local plane coordinate system are studied. Second, in the local plane coordinate system, a route generation method based on subregion is proposed; therefore, multiple routes can be generated with different initial heading angles. Lastly, the optimal route and the best initial heading angle can be obtained after the comparison according to the three evaluation criteria: number of turns, route distance, and pesticide waste rate. The simulation results show that, compared with the common grid method, the route generation method based on subregion reduces the route distance and pesticide waste rate by 2.27% and 13.75%, respectively. Furthermore, it also shows that, compared with the route generated by the initial heading angle of 0°, the optimal route reduces the number of turns, route distance, and pesticide waste rate by 60%, 17.65%, and 38.18%, respectively. The route was optimized in three aspects and reached the best overall result using this method, which in turn proved its feasibility.

An Accurate Geocoding Method for GB-SAR Images Based on Solution Space Search and Its Application in Landslide Monitoring

Although ground-based synthetic aperture radar (GB-SAR) interferometry has a very high precision with respect to deformation monitoring, it is difficult to match the fan-shaped grid coordinates with the local topography in the geographical space because of the slant range projection imaging mode of the radar. To accurately identify the deformation target and its position, high-accuracy geocoding of the GB-SAR images must be performed to transform them from the two-dimensional plane coordinate system to the three-dimensional (3D) local coordinate system. To overcome difficulties of traditional methods with respect to the selection of control points in GB-SAR images in a complex scattering environment, a high-resolution digital surface model obtained by unmanned aerial vehicle (UAV) aerial photogrammetry was used to establish a high-accuracy GB-SAR coordinate transformation model. An accurate GB-SAR image geocoding method based on solution space search was proposed. Based on this method, three modules are used for geocoding: framework for the unification of coordinate elements, transformation model, and solution space search of the minimum Euclidean distance. By applying this method to the Laoguanjingtai landslide monitoring experiment on Hailuogou Glacier, a subpixel geocoding accuracy was realized. The effectiveness and accuracy of the proposed method were verified by contrastive analysis and error assessment. The method proposed in this study can be applied for accurate 3D interpretation and analysis of the spatiotemporal characteristic in GB-SAR deformation monitoring and should be popularized.

Research of the Vertical Dynamics of the Supporting Structures of Freight Cars Made of Round Pipes

Purpose. This study is aimed at determining the vertical dynamics of supporting structures of freight cars made of round pipes. Methodology. Mathematical modeling of the dynamic loading of the supporting structures of the main types of freight cars made of round pipes (gondola car, covered car, flat car, hopper car) was carried out. The studies were carried out in a plane coordinate system – the XZ plane. At the same time, it was taken into account that the car is moving in an elastic-viscous track so that the reactions of the track are proportional to both its deformation and the rate of this deformation. The studies were carried out for the case of empty cars. The joint inequality is described by a periodic function. The calculation was performed at a speed of 80 km/h. Differential equations of motion were solved in the MathCad software package using the Runge-Kutta method. Findings. Based on the mathematical modeling of the dynamic loading of the supporting structures of cars made of round pipes, the main indicators of their dynamics were obtained: accelerations acting on the supporting structures in the mass center, forces acting in the spring suspension of bogies, dynamics coefficients. For gondola car, covered car, and hopper car, the acceleration at the mass center of the supporting structure is within 0.4 g, and for a flat car – 0.5 g. It was found that the obtained indicators of the dynamics of cars made of round pipes are within the permissible limits. The accelerations acting on the supporting structures of cars made of round pipes are almost the same as those obtained for prototype cars. At the same time, the motion of cars is assessed as "excellent" for gondola car, covered car, and hopper car and "good" for flat car. Originality. Mathematical modeling of the dynamic loading of the supporting structures of cars from round pipes was carried out and the main indicators of their dynamics were obtained. Practical value. The research carried out will contribute to the creation of recommendations for the design of supporting structures of freight cars of round pipes, and can also be useful developments in the creation of innovative car designs.