Relative Coordinate System Research Articles

Multi-season evaluation of hurricane analysis and forecast system (HAFS) quantitative precipitation forecasts

Quantitative precipitation forecasts (QPF) from numerical weather prediction models need systematic verification to enable rigorous assessment and informed use, as well as model improvements. The United States (US) National Oceanic and Atmospheric Administration (NOAA) recently made a major update to its regional tropical cyclone modeling capabilities, introducing two new operational configurations of the Hurricane Analysis and Forecast System (HAFS). NOAA performed multi-season retrospective forecasts using the HAFS configurations during the period that the Hurricane Weather and Forecasting (HWRF) model was operational, which was used to assess HAFS performance for key tropical cyclone forecast metrics. However, systematic QPF verification was not an integral part of the initial evaluation. The first systematic QPF evaluation of the operational HAFS version 1 configurations is presented here for the 2021 and 2022 season re-forecasts as well as the first HAFS operational season, 2023. A suite of techniques, tools, and metrics within the enhanced Model Evaluation Tools (METplus) software suite are used. This includes shifting forecasts to mitigate track errors, regridding model and observed fields to a storm relative coordinate system, as well as object oriented verification. The HAFS configurations have better performance than HWRF for equitable threat score (ETS), but larger over forecast biases than HWRF. Storm relative and object oriented verification show the HAFS configurations have larger precipitation areas and less intense precipitation near the TC center as compared to observations and HWRF. HAFS QPF performance decreased for the 2023 season, but the general spatial patterns of the model QPF were very similar to 2021-2022.

Assessing the consistency and reliability of the line intercept transect method in coral cover estimation using structure from motion photogrammetry techniques

Appropriate coral reef monitoring methods and descriptors determine the effectiveness of ecosystem status assessment. We combined line intercept transect (LIT) and SfM technologies for image acquisition, and the POS information of images is defined and assigned in the relative coordinate system we build. Then, constructed high-resolution orthomosaics of coral reefs along measuring tapes in Metashape. We compared the estimates of coral cover by three methodologies (LIT, LIT on orthomosaic (LITO), surface analyses on orthomosaic (SAO)) and used virtual transects on orthomosaics and their estimates of coral cover to assess the consistency and reliability of LIT. The results show that the estimation of coral cover by LITO or LIT is more consistent and reliable when coral cover is higher, and the probability of overestimation is lower. SfM technology is increasingly used in coral reef survey and assessment, and has the potential to become the new standard for coral reef survey.

Волны Рэлея на гладкой кривой поверхности

A model has been developed that describes the propagation of surface waves on smooth curved surfaces. This model is developed using the hyperbolic wave equation and is applicable to studying the propagation of surface waves on any curved surface described by a related orthogonal curvilinear coordinate system and for any values of the product of the wave vector and the radius of curvature. The behavior of Rayleigh waves on canonical curved surfaces (cylinder, sphere) is simulated, and the results are used to quantify the effect of curvature on the speed of Rayleigh waves. The condition for the existence of a Rayleigh wave is the validity of the values of the wave vectors K obtained from the dispersion equations. The actual values of the wave vectors K determine the waves propagating along the surface without carrying the energy deep into the body. The speed of the surface wave increases with increasing curvature of the concave surface, and decreases on the concave surface. The Rayleigh wave has limited growth as the positive radius of curvature decreases. At positive values of the radius of curvature (outer surface), as the radius decreases, a maximum is observed, and then the speed of waves decreases and breaks of curves are observed at negative curvature (inner surface), which is associated with resonance along the circumference of the envelope of a cylinder or great circle of a sphere.

The vortex dynamics characteristics in a pump-turbine: A rigid vorticity analysis while varying guide vane openings in turbine mode

In off-design conditions, pump-turbines generate vortex structures of varying scales and intensities, jeopardizing energy conversion due to unstable flow phenomena. While off-design pump-turbine internal flow dynamics have been analyzed, understanding the spatiotemporal evolution of complex vortex structures within runner blade passages, which are prone to inducing hydraulic instabilities, has to be still addressed properly. This paper applies the rigid vorticity theory, also known as Liutex, to explore vortex characteristics in the pump-turbine under different guide vane openings during turbine mode operation. The investigation focuses on three main aspects: i) spatial distribution characteristics, ii) temporal evolution characteristics, and iii) vortex morphological features along with deformation mechanisms. Results showed that the suction surface side of the blade's trailing edge commonly experiences significant shear effects, while vortices tend to emerge on both pressure and suction surface sides. Under small Guide Vane Opening (GVO) condition, vortices in blade passages show periodic evolution, and Enstrophy of the Rigid Vorticity Dilatation Term (ERDT) predominantly contributes to the helical deformation of these vortices. Conversely, under large GVO condition, vortices maintain high helicity and remain stable. This study provides insights to reduce hydraulic instability in pump-turbines and optimize energy conversion efficiency. The proposed Reynolds-averaged transport equation for enstrophy of the rigid vorticity and the relative streamline coordinate system provide advanced tools for analyzing unstable flow structures.

Motion capture based calibration for industrial robots

Path accuracy of industrial robotic systems is of paramount importance for manufacturing applications. Many robot vendors provide guarantees of locational repeatability for robot arms down to 0.01 mm, however, this level of precision is meaningless if the system is not well calibrated. In many cases, where an offline programming environment is used, the physical system needs to match the behavior of the digital twin with minimal error. Calibration is thus required to ensure that the position and motion of the robot matches that of what was programmed. One approach is to use relative coordinate systems to offset the programmed path to account for any consistent deviations across the path. These offset coordinate systems can be created using techniques such as touch-based, laser-based, and/or vision-based systems. The offset coordinate system approach is used by major robot manufacturers and NC machines to arrive at a well-defined path. However, this approach assumes that the workspace is uniformly shifted, which is not always the case for industrial robots. Such systems can suffer from distortion in their coordinate space due to mechanical flexure, gearing backlash, and other factors that distort their workspace. To correct this distortion, we propose the use of a commercially available motion capture system that precisely monitors and reports the location of a Yaskawa industrial robotic arm. The positional and rotational information of the robot end-effector can be captured using this motion capture system and compared with that of the expected TCP (Tool Center Point) location derived from the forward kinematics model. The difference between these coordinates can then be used to determine and correct offsets from paths created using the digital twin. With motion capture driven path corrections, the accuracy of offline programed robots can be greatly improved without the need for exhaustively complex calibration processes.

SUNDER: Self-organized grouping and entrapping method for swarms in multitarget environments

For swarm robots moving in a harsh or uncharted outdoor environment without GPS guidance and global communication, algorithms that rely on global-based information are infeasible. Typically, traditional gene regulatory networks (GRNs) that achieve superior performance in forming trapping pattern towards targets require accurate global positional information to guide swarm robots. This article presents a gene regulatory network with Self-organized grouping and entrapping method for swarms (SUNDER-GRN) to achieve adequate trapping performance with a large-scale swarm in a confined multitarget environment with access to only local information. A hierarchical self-organized grouping method (HSG) is proposed to structure subswarms in a distributed way. In addition, a modified distributed controller, with a relative coordinate system that is established to relieve the need for global information, is leveraged to facilitate subswarms entrapment toward different targets, thus improving the global multi-target entrapping performance. The results demonstrate the superiority of SUNDER-GRN in the performance of structuring subswarms and entrapping 10 targets with 200 robots in an environment confined by obstacles and with only local information accessible.

Improved Three-Variable Control for Electromagnetic Mass Damper System Considering Control–Structure Interaction

Current methods account for control–structure interaction (CSI) in structural control design, which may be unavailable in the preliminary design phase of actively controlled structures due to the unknown dynamic characteristic of an actuator. Therefore, it may result in significant difference in the design and evaluation of an active structural control system when ignoring or considering CSI at different phases. To eliminate the CSI effects of electromagnetic mass damper (EMD) system and thus decouple the tracking control of EMD from the control design of structure, in this paper, an improved three-variable control (ITVC) combining a signal convertor, a typical three-variable controller, and a voltage compensator is developed. The voltage compensator counteracts the influence of lower-order CSI including viscous damping force and Coulomb friction. The three-variable controller reduces the higher-order CSI effects, while the signal convertor converts all command and feedback signals to the relative coordinate system and eliminates the additional CSI effects. Performance tests and frequency response tests of the EMD system show that the CSI effects are basically eliminated by ITVC. In addition, shake table tests are performed on a one-story actively controlled structure to further verify ITVC. Experimental results suggest that ITVC can apply accurate control force on the structure and achieve ideal structural response control.

A high-accuracy positioning method for mobile robotic grasping with monocular vision and long-distance deviation

It is difficult for mobile robot to position and grasp large-sized objects accurately because the vision acquisition camera deviates from the rotation axis of the robot with a long distance, which leads to the magnification of the calibration error. A method of identifying target objects by positioning marked targets with monocular vision was developed. The marked target was placed in a fixed position within the field of view, which was no longer limited by the specific size of the target object. And the corresponding relation between the displacement of the robot relative coordinate system and the image coordinate system was established. Based on the surface fitting method of Gaussian process regression (GPR), the error compensation model was constructed to effectively compensate and correct the operating errors of the robot once again, so that the accuracy of the error compensation model can meet the goal of accurate positioning and grasping for large-sized objects. Specifically, the error data of each positioning was collected by comparing the real value of the robot's positioning with the estimated value of vision, and the error distribution model of the whole field of vision can be obtained. More than 1000 times of printed circuit board (PCB) board accurate loading and unloading tests were carried out with PCB board moving rack and mobile robot operating platform. The results showed that it could achieve precise visual positioning, which met the industrial application requirements for the mobile robot operating platform.

Numerical study on the mechanism of fluid energy transfer in an axial flow pump impeller under the rotating coordinate system

It is a necessary condition to obtain the fluid movement law and energy transfer and loss mechanism in the impeller of the axial pump for achieving an efficient and accurate design of the axial flow pump. Based on the shear stress transport k-ω turbulence model, a three-dimensional unsteady numerical simulation of the whole flow field of an axial flow pump was presented at different flow rates. Combined with the Bernoulli equation of relative motion, the flow field structure in the impeller under design condition was studied quantitatively in the rotating coordinate system. The fluid movement law and energy transfer and loss mechanism in the impeller of the axial flow pump was described in detail. In the relative coordinate system, the mechanical energy of the fluid on the same flow surface conserves. The dynamic energy is continuously transformed into pressure energy from the leading edge to the trailing edge and the dynamic energy is continuously transformed into pressure energy from the leading edge to the trailing edge. The energy conversion is mainly completed in the front half of the blade. The friction loss and the mixing loss are the basic sources of losses in the impeller flow passage. Most hydraulic losses of impeller flow passage are caused by friction and the hydraulic losses near the trailing edge are dominated by mixing loss. This research has certain reference significance for further understanding the flow field structure in the impeller of the axial flow pump, improving its design theory and method, and then realizing its efficient and accurate design of the axial flow pump.

Evolution equations of multi-planet systems with variable masses

In celestial mechanics and astrodynamics, the study  of the  dynamical evolution of exoplanetary systems is the   relevant topics.    For today more than 3,000 exoplanetary systems are known. In this paper, we study the dynamic evolution of extrasolar systems, when the leading factor of evolution  is the variability of the masses of gravitating bodies. The problem of spherically symmetric bodies with  variable masses is considered in a relative coordinate system, this bodies inter-gravitating according to Newton's law. The quasi-elliptical motions of planets whose orbits do not intersect during evolution are investigated. It is believed that the mass of bodies under consideration  varies isotropically by various known laws with different velocities. The mass of the parent star is considered to be the most massive than its planets and the origin of the relative coordinate system is in the center of the parent star.. Due to the variability of the masses, the differential equations of motion become non-autonomous and the task is difficult. The problem is investigated by methods of perturbation theory. The canonical perturbation theory based on a periodic motion over a quasi-canonical section is used.  Canonical equations of motion are obtained in analogues of the second Poincare system, which are effective in the case when the analogues of eccentricities and the analogues of the inclination of the orbital plane of planets are sufficiently small.  The secular perturbations of the planets, which determine the behavior of the orbital parameters over long time intervals, are studied. The evolutionary equations of many planetary systems with isotropically varying masses in analogues of the second system of Poincare variables are derived in an analytical form which are obtained using the Wolfram Mathematica computer algebra system. This takes into account the effects of the decreasing mass of the parent star and the growth of the masses of the planets due to the accretion of matter from the remnants of the protoplanetary disk. For the three-planetary problem of four bodies with variable masses, the evolutionary equations in dimensionless variables are obtained explicitly. In the future, these results will be used to study the dynamics of the three-planet system K2-3 in the non-stationary stage of its evolution.

Numerical investigation of contact loads of unsynchronised, dry-running screw machines

Unsynchronised, dry-running screw machines have advantages compared to conventional oil-injected and synchronised, dry-running screw machines. Because of the absence of an additional timing gear and no injected lubricant, the effort for manufacturing and assembly can be reduced and lubricant residues in the process gas are avoided. In this design the female rotor torque resulting from the gas pressure is transferred directly to the male rotor by the contacting rotor surfaces. To investigate this contact, a two-dimensional boundary element method contact algorithm is developed to calculate the loads in terms of contact tractions and sliding velocities. The contact kinematics of the screw rotors and the non-constant curvature of the rotor surfaces are considered. The movement between the screw rotors is transformed into a relative coordinate system fixed on the male rotor. Furthermore, the influence of manufacturing tolerances to the occurring contact loads are investigated.

Real-time hybrid testing for active mass driver system based on an improved control strategy against control-structure-interaction effects

General real-time hybrid testing (RTHT) for active mass driver (AMD) system requires shake table to achieve boundary conditions between the numerical and experimental substructures, which may be unavailable in some situations. Simplified RTHT is free of shake table, but it cannot consider control-structure-interaction (CSI) effects, and may result in an inaccurate performance evaluation of AMD system due to a significant influence of CSI on control performance. In this study, to eliminate the CSI effects, an improved control strategy is proposed, by incorporating the acceleration of control floor into the AMD controller and transforming all the control commands and feedbacks from the geocentric coordinate system to the relative coordinate system. Based on this strategy, the implementations of general and simplified RTHTs for AMD system are described. Experimental investigations are conducted on a two-story structure equipped with an AMD. It is confirmed that the general RTHT can be used to evaluate the actual performances of different control strategies. The CSI effects are essentially eliminated by the improved control strategy, but adversely affect the performance of traditional control strategy. In addition, the simplified RTHT is inappropriate for the performance evaluation of the traditional control strategy, but is available to that of the improved control strategy. Finally, an AMD control scheme is presented for a seismically excited 20-story benchmark building, and is evaluated through the simplified RTHT. Experimental results demonstrate the effectiveness of the proposed AMD control scheme. The maximum roof displacement and acceleration decrease from 0.175 m and 3.059 m/s2 to 0.116 m and 1.356 m/s2, respectively, when subjected to the El Centro earthquake.

Formation control for connected and automated vehicles on multi‐lane roads: Relative motion planning and conflict resolution

Existing research has revealed that multi-vehicle coordinated decision making and control can achieve an improvement in both traffic efficiency and driving safety. In the multi-lane scenarios, a typical coordination method is multi-vehicle formation control. The existing formation control methods predefine the formation switching process and have not considered or explained the collision-free behaviour of vehicles in detail. In this paper, a multi-lane formation control strategy for connected and automated vehicles (CAVs) is proposed. The planning framework is bi-level, which can switch the structure of multi-vehicle formation in different scenarios smoothly and effectively. In the upper-level, the relative coordinate system is built to plan the collision-free relative paths for vehicles. In the lower-level, multi-stage trajectory planning and tracking are modelled as an optimal control problem with path constraints. The case study verifies the function of the formation control method in three lane-number-changing scenarios. Large-scale simulations in the lane-drop bottleneck scenario are conducted under different input traffic volumes, and the numerical results indicate that the proposed formation control method reduces congestion and improves both traffic efficiency and fuel economy at high traffic volumes.

Design and evaluation of a dual-beam read/write configuration for optical storage

Increasing the number of read/write layers and ensuring the quality of read/write signals are the key factors to enhance the optical storage capacity. However, limited by the single optical path, the structure, and the material of the disk, the existing system reads and writes up to 16 layers. In the existing optical storage system design, the optical path design and the signal model are independent of each other, so the signal quality based on the signal model can only be evaluated after the implementation of the optical path. We propose a dual-beam read/write optical path for the optical storage system, which breaks through the limitation of the single optical path and can read/write multilayers. The servo detection signals and servo margins show that the dual-beam read/write system has good error detection capability and strong robustness. The servo error signal is calculated according to the relationship between the wavefront aberration, relative coordinate system displacement difference, and servo error of the optical system, thus deriving a quantifiable signal evaluation model. The effectiveness of the model is verified by experiments. The signal evaluation model breaks through the limitations of the traditional optical design method for the optical storage system and can guide the optical design from the signal perspective. The dual-beam optical path for multilayer optical storage systems provides a broader range of ideas for enhancing optical storage capacity.

Optimal Unmanned Ground Vehicle—Unmanned Aerial Vehicle Formation-Maintenance Control for Air-Ground Cooperation

This paper investigates the air–ground cooperative time-varying formation-tracking control problem of a heterogeneous cluster system composed of an unmanned ground vehicle (UGV) and an unmanned aerial vehicle (UAV). Initially, the structure of the UAV–UGV formation-control system is analyzed from the perspective of a cooperative combat system. Next, based on the motion relationship between the UAV–UGV in a relative coordinate system, the relative motion model between them is established, which can clearly reveal the physical meaning of the relative motion process in the UAV–UGV system. Then, under the premise that the control system of the UAG is closed-loop stable, the motion state of the UGV is modeled as an input perturbation. Finally, using a linear quadratic optimal control theory, a UAV–UGV formation-maintenance controller is designed to track the reference trajectory of the UGV based on the UAV–UGV relative motion model. The simulation results demonstrate that the proposed controller can overcome input perturbations, model-constant perturbations, and linearization biases. Moreover, it can achieve fast and stable adjustment and maintenance control of the desired UAV–UGV formation proposed by the cooperative combat mission planning system.

A Relative Coordinate-Based Topology Shaping Method for UAV Swarm with Low Computational Complexity

Functional topology shaping is crucial for unmanned aerial vehicles (UAVs) swarm applications, such as remote sensing, precision agriculture, and emergency wireless communication. However, the current research on topology shaping is mostly based on the assumption that the target positions of the nodes are known or have been pre-defined. Moreover, the computational complexity of existing shaping methods is still high. In this paper, a topology shaping method based on a relative coordinate system is proposed to solve the problem of UAV swarm topology shaping with no external source of localization information. Based on the relative coordinates of nodes and target topology shape of the swarm, the topology shaping is transformed into a problem of optimal coordinate mapping from initial relative coordinates to target relative coordinates of nodes with minimized global energy consumption. The Jonker–Volgenant algorithm is employed to solve the optimization problem. As verified by simulations, the proposed method can achieve UAV swarm topology shaping with no external localization information. Furthermore, simulation results show that the proposed method has an average reduction in computation time of 94% in the case of 1000 nodes compared with existing methods with the same level of global energy consumption.

Secular perturbations of the translational-rotational motion in a nonstationary three-body problem

A non-stationary three-body problem with axisymmetric dynamic structure, shape, and variable compression is considered. The Newtonian interaction force is characterized by an approximate expression of the force function accurate to the second harmonic. The masses of bodies change isotropically at different rates. The axes of inertia of the proper coordinate system of nonstationary axisymmetric three bodies coincide with the principal axes of inertia of the bodies, and it is assumed that their relative orientations remain unchanged during the evolution. Differential equations of translational and rotational motion of three non-stationary axisymmetric bodies with variable masses and dimensions in the relative coordinate system with the origin in the center of the more massive body are presented. The analytical expression for the Newtonian force function of the interaction of three bodies with variable masses and dimensions is given. The canonical equations of translational-rotational motion of three bodies in the Delaunaye-Andouye analogues have been obtained. The equations of secular perturbations of translational-rotational motion of unsteady axisymmetric three-bodies in the analogue of the Delaunaye-Andouye osculating elements have been obtained. The problem is investigated by methods of perturbation theory.

Decoupled coordinates for machine learning-based molecular fragment linking

Recent developments in machine learning-based molecular fragment linking have demonstrated the importance of informing the generation process with structural information specifying the relative orientation of the fragments to be linked. However, such structural information has so far not been provided in the form of a complete relative coordinate system. We present a decoupled coordinate system consisting of bond lengths, bond angles and torsion angles, and show that it is complete. By incorporating this set of coordinates in a linker generation framework, we show that it has a significant impact on the quality of the generated linkers. To elucidate the advantages of such a coordinate system, we investigate the amount of reliable information within the different types of degrees of freedom using both detailed ablation studies and an information-theoretical analysis. The presented benefits suggest the application of a complete and decoupled relative coordinate system as a standard good practice in linker design.

A parallel shape formation method for swarm robotics

In order to cope with diversified tasks and unstructured environments, a parallel shape formation method for swarm robotics is introduced to adjust the system’s configuration autonomously and flexibly with the user-specified 2-D shape. Given the desired shape to be formed in the form of analytic functions, the forming task of the swarm system is divided into two sub-tasks: the edge robot forming task and the internal robot forming task. Then, the seed robot is selected through the generation and transmission of the gradient to establish the relative coordinate system, and the initial coordinates of robots are obtained through trilateral positioning. Based on that, using the artificial potential field method, under the action of gravitational force generated by the objective analytic functions and repulsion forces generated by other individuals in the neighborhood, edge individuals move to the target boundary; at the same time, internal individuals spread evenly in the target area under the action of the repulsion forces generated by each other. During the forming process, the two sub-tasks are executed in parallel, and the individuals continue to update their real-time positions by dead-reckoning until the desired shape is formed. We evaluate the feasibility and scalability of this novel method in simulation-based experiments, and implement the parallel shape formation algorithm on the Cilibot robot, a hardware system developed in our lab.

An Orthogonal Wheel Odometer for Positioning in a Relative Coordinate System on a Floating Ground

This paper introduces a planar positioning sensing system based on orthogonal wheels and encoders for some surfaces that may float (such as ship decks). The positioning sensing system can obtain the desired position and angle information on any such ground that floats. In view of the current method of using the IMU gyroscope for positioning, the odometer data on these floating grounds are not consistent with the real-time data in the world coordinate system. The system takes advantage of the characteristic of the orthogonal wheel, using four vertical omnidirectional wheels and encoders to position on the floating ground. We design a new structure and obtain the position and angle information of a mobile robot by solving the encoder installed on four sets of omnidirectional wheels. Each orthogonal wheel is provided with a sliding mechanism. This is a good solution to the problem of irregular motion of the system facing the floating grounds. In the experiment, it is found that under the condition that the parameters of the four omnidirectional wheels are obtained by the encoder, the influence of the angle change of the robot in the world coordinate system caused by the flotation of the ground can be ignored, and the position and pose of the robot on the fluctuating ground can be well obtained. Regardless of straight or curved motion, the error can reach the centimeter level. In the mobile floating platform experiment, the maximum error of irregular movement process is 2.43 (±0.075) cm and the RMSE is 1.51 cm.