Coordinate Frame Research Articles

An Advancement in Truck-Tire–Road Interaction Using the Finite Element Analysis

This paper aimed to investigate the cornering characteristics of a Regional Haul Steer II, RHS 315/80 R22.5 truck tire traveling on a dry, hard surface using the Finite element analysis (FEA). This research was carried out using commercial Finite Element software and Pam-Crash in an Explicit Environment. A finite element truck tire model was developed to apply the tire terrain cornering condition. The concentrated loads and boundary conditions for the rim and wheel were applied to the model. The rubber material was defined using the Mooney–Rivlin model. The truck tire cornering operating conditions, including three different speeds with respect to various positive slip angles, were investigated. Several simulations were repeated at various operating conditions, including three different inflation pressures and three different vertical loads. Subsequently, the tire lateral force was computed using the local and global frame coordinates. Additionally, the self-aligning moment was extracted from the tire cross-section at each operating condition. Finally, a comparison between the simulation results showed that the tire lateral force was highly sensitive to the variation of the slip angles at the higher domain, and also that the tire inflation pressure, regardless of the speed, was considered to be one of the main parameters directly affecting the tire-cornering properties.

Efficient coordination of radio frames to mitigate cross-link interference in 5G D-TDD systems

Dynamic time division duplexing (D-TDD) is widely used in 5G to support various services and short-latency communications, where uplink (UL) and downlink (DL) traffic may be highly asymmetric and fast-varying. In particular, D-TDD allows each cell to arrange subframes in terms of selecting link directions, which betters the utilization of spectrum resources based on instantaneous traffic demand. However, the inter-cell subframe misalignment, which is caused by different link directions on the same frequency band in neighboring cells, leads to notable cross-link interference (CLI). Especially, CLI has a negative impact on UL performance. Hence, this paper proposes a cluster-based radio frame coordination using codebooks (CRCC) framework to mitigate CLI efficiently. CRCC first clusters cells and formulates a codebook of radio frame configuration for each cluster, where cells pick their configuration of subframes. Then, the cluster is divided into subclusters, where the cells in each subcluster adjust subframes to reduce misalignments. Finally, CRCC combines subclusters by deciding the subframes of those cells located on the boundaries between subclusters. Simulation results reveal that CRCC greatly increases UL throughput and keeps high DL throughput, thereby improving the performance of a 5G D-TDD system.

An equivariant neural operator for developing nonlocal tensorial constitutive models

Developing robust constitutive models is a fundamental and longstanding problem for accelerating the simulation of multiscale physics. Machine learning provides promising tools to construct constitutive models based on various calibration data. However, with either traditional or machine learning techniques, the constitutive model for tensorial quantities has been much less studied than scalar quantities due to more complicated physics, even though the former plays an important role in many scientific and engineering applications. In this work, we propose a neural operator to develop nonlocal constitutive models for tensorial quantities through a vector-cloud neural network with equivariance (VCNN-e). The VCNN-e respects all the invariance properties desired by constitutive models, faithfully reflects the region of influence in physics, and is applicable to different spatial resolutions. By design, the model guarantees that the predicted tensor is invariant to the frame translation and ordering (permutation) of the neighboring points. Furthermore, it is equivariant to the frame rotation, i.e., the output tensor co-rotates with the coordinate frame. We evaluate the VCNN-e by using it to emulate the Reynolds stress transport model for turbulent flows, which directly computes the Reynolds stress tensor to close the Reynolds-averaged Navier–Stokes (RANS) equations. The evaluation is performed in two situations: (1) emulating the Reynolds stress model through synthetic data generated from the Reynolds stress transport equations with closure models, and (2) predicting the Reynolds stress by learning from data generated from direct numerical simulations. Such a priori evaluations of the proposed network on realistic and challenging datasets pave the way for developing and calibrating robust and nonlocal, non-equilibrium constitutive models for the RANS equations and other mechanical problems.

A low-cost indoor positioning system based on data-driven modeling for robotics research and education

AbstractThis paper presents a low-cost, accurate indoor positioning system that integrates image acquisition and processing and data-driven modeling algorithms for robotics research and education. Multiple overhead cameras are used to obtain normalized image coordinates of ArUco markers, and a new procedure is developed to convert them to the camera coordinate frame. Various data-driven models are proposed to establish a mapping relationship between the camera and the world coordinates. One hundred fifty data pairs in the camera and world coordinates are generated by measuring the ArUco marker at different locations and then used to train and test the data-driven models. With the model, the world coordinate values of the ArUco marker and its robot carrier can be determined in real time. Through comparison, it is found that a straightforward polynomial regression outperforms the other methods and achieves a positioning accuracy of about 1.5 cm. Experiments are also carried out to evaluate its feasibility for use in robot control. The developed system (both hardware and algorithms) is shared as an open source and is anticipated to contribute to robotic studies and education in resource-limited environments and underdeveloped regions.

Teamwork solutions for complex problems in psychotherapy: A systems thinking-based commentary.

Most psychological treatments are administered in a one-to-one therapy format, which has proven effective but has limitations in complex clinical situations. Teamwork can help address these limitations by going beyond the one-to-one therapy approach and involving the client's professional and relational network in therapy interventions to promote and secure change. In this issue of Journal of Clinical Psychology: In Session five effective teamwork practices are presented illustrating how clinicians integrate teamwork into treatment delivery to improve outcomes in an array of cases presenting high complexity. In this commentary section, we describe the role and essence of these teamwork practices from a systems thinking approach as a theoretical umbrella to understand the diversity of processes hindering and facilitating effective teamwork CONCLUSSION: From this approach we discuss the core skills that psychotherapists should train to master team working and interprofessional collaboration. The basic professional competence consists in the ability to foster and coordinate shared frames of understanding in case formulation. An advanced systemic skill is based on the ability to formulate and change relational patterns, given that interpersonal processes are the main key factor to understand barriers and facilitators of effective teamwork to overcome stalemated complex clinical situations.

2-D distributed pose estimation of multi-agent systems using bearing measurements

This article studies distributed pose (orientation and position) estimation of leader–follower multi-agent systems over κ-layer graphs in 2-D plane. Only the leaders have access to their orientations and positions, while the followers can measure the relative bearings or (angular and linear) velocities in their unknown local coordinate frames. For the orientation estimation, the local relative bearings are used to obtain the relative orientations among the agents, based on which a distributed orientation estimation algorithm is proposed for each follower to estimate its orientation. For the position estimation, the local relative bearings are used to obtain the position constraints among the agents, and a distributed position estimation algorithm is proposed for each follower to estimate its position by solving its position constraints. Both the orientation and position estimation errors converge to zero asymptotically. A simulation example is given to verify the theoretical results.

Analytical Green's function for the acoustic scattering by a flat plate with a serrated edge

An analytical Green's function is developed to study the acoustic scattering by a flat plate with a serrated edge. The scattered pressure is solved using the Wiener–Hopf technique in conjunction with the adjoint technique. It is shown that the kernel decomposition proposed in recent literature appears only valid at high frequencies. We focus on this high-frequency regime and obtain the scattered pressure in the form of a contour integral. We show that such an integral, although complicated, can be evaluated exactly for any arbitrary piecewise linear serrations, for which closed-form analytical Green's functions are obtained. The derivation is validated by performing numerical integration of the contour integral showing excellent agreement. The Green's function is shown to agree well with the numerical results obtained using the finite element method at high frequencies. The noise directivity patterns are studied as a function of the frequency, serration amplitude, source position and Mach number. It is found that noise is often enhanced at low observer angles and may be slightly reduced at high observer angles, which may be understood from the perspective of an extended or removed rigid reflection surface. It is found that increasing the mean-flow Mach number leads to increasingly evident noise amplification at side angles, a seemingly strange Doppler behaviour exhibited in source-fixed coordinate frames. The analytical Green's function is applicable to both leading- and trailing-edge scatterings, and is particularly suitable for developing a three-dimensional trailing-edge noise model that is not only highly efficient but also capable of including non-frozen turbulence effects.

A Hybrid Approach to 3D Shape Estimation of Catheters Using Ultrasound Images

Catheter-based cardiac interventions have substantially improved the efficacy of the treatment. However, catheter navigation still poses several challenges including its poor visualization and localisation. Therefore, various imaging methods have been used to localize the catheter and estimate its shape. The use of ultrasound imaging is superior to other modalities in many aspects, but suffers from poor spatial resolution. Hence, we present a hybrid approach involving deep learning and classical approach to 3D shape estimation of catheters. Our novel approach uses two stages. First, a UNet-3D model is proposed to estimate the catheter centroid in the ultrasound image. Then, an adaptive Kalman Filter (AKF) is used to fuse the points into the 3D world coordinate frame. Simulation studies, phantom and ex-vivo experimentation results demonstrate the robustness of the method to ultrasound noise and extreme configurations (sharp curves).

Kinematic geometry of spatial RSSR mechanisms

Two different novel methods to derive the input–output (IO) equation of arbitrary RSSR linkages are described. Both methods share some common elements, i.e., they use the standard Denavit–Hartenberg notation to first describe the linkage as an open kinematic chain, and Study’s kinematic mapping to describe the displacement of the coordinate frame attached to the end-effector of the chain with respect to the relatively non-moving base frame. The kinematic closure equation is obtained in the seven-dimensional projective kinematic mapping image space by equating the eight Study soma coordinates to the identity array. Then two methods are successfully applied to eliminate the intermediate joint angle parameters leading to the degree four biquadratic implicit algebraic IO equation: (a) the linear implicitisation algorithm, which can be applied after rearranging the closure equation such that the linkage can be viewed as two serial RS chains, and (b) numerical elimination theory using pseudowitness sets. Both approaches lead to the same IO equation. The utility of this algebraic form of the IO equation is illustrated with three detailed application examples.

Economic bifurcations in pandemic leadership: Power in abundance or agency amid scarcity?

Social psychological scholarship has emphasized the importance of effective leadership during the COVID-19 pandemic. However, the wider material contexts of these dynamics have often remained understudied. Through a critical discursive lens, this paper investigates differences in the social constructions used by leaders of richer and poorer nations during the COVID-19 pandemic. We identify a sharp economic bifurcation in global discourses of pandemic leadership. Pandemic leadership in wealthier nations exercises power in abundance by mobilizing institutions and inspiring communities through discursive frames of coordination and collaboration. Conversely, pandemic leadership in poorer settings negotiates agency amid scarcity by tactically balancing resources, freedoms and dignity within discursive frames of restriction and recuperation. Implications of these findings are unpacked for understanding leadership especially during an international crisis, highlighting the need for critical sensitivities to wider societal structures for a genuinely global social psychology.

Dynamics of a 3-UPS-UPU-S Parallel Mechanism

In this paper, a parallel mechanism with two rotational degrees of freedom is proposed. It could rotate freely and continuously around the two coordinate axes at the fixed origin of the coordinate frame. The structure of the mechanism is a second-order over constraint parallel structure and the moving platform and base platform are connected by five kinematic chains. The motion characteristics of this structure are analyzed by reciprocal screw equation. Then, the kinematics and dynamics modelling are carried out systematically in a unified way. The kinematics of the mechanism is established by means of screws, the displacements and accelerations of each joint and any point on a link could be calculated by the kinematic screw equation directly. The analysis of acceleration and its mathematical expression in screw form are given, and the acceleration matrix could be applied into the dynamic analysis based on the Newton–Euler equation. All the constraint forces and torques could be obtained by a single set of Newton–Euler equations.

An analytical envelope model for space charge in cyclotrons

The statistical σ-matrix approach is used to derive general envelope equations for ellipsoidal bunches with space charge in isochronous and non-isochronous fixed-field accelerators (FFAs) These accelerators couple the radial and longitudinal phase spaces due to momentum dispersion induced by the space charge effect. This generates a rotation of the bunch around the local vertical axis which is known in the field as the vortex effect. A special invariant of the vortex is found which represents its total angular momentum with respect to its center. For the isochronous cyclotron, a special solution of the envelope equations is found which describes a circular bunch with equal radial and longitudinal RMS sizes. The existence of this solution is a direct consequence of the circular symmetry of the single particle Hamiltonian in a co-moving coordinate frame. The stationary solution of the circular bunch fixes the relation between bunch sizes and accelerated current (or the total charge per bunch) for given emittances. The general envelope equations may easily be implemented in existing numerical envelope codes.

Novel Fiducial Fiber Scanning Measurement Method Based on a Polar Coordinate System for LAMOST

The multiobject fiber-fed spectrograph is the core scientific instrument for large-scale spectroscopic surveys. For closed-loop control of fiber positioning, fiber metrology systems are implemented in numerous fiber-fed spectrographs. The position accuracy of the fiducial fiber in the focal plate directly affects the performance of the fiber metrology system. However, there are currently no suitable methods and devices for measuring the fiducial fibers with high accuracy in the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). To solve this problem, this study proposed a novel online scanning measurement method for fiducial fibers in which a scanning camera was set up in front of the focal plate, and the rotation and translation movements of the focal plate were combined to set a polar coordinate measurement system. First, the pole and polar axis of the polar coordinate frame were determined, and the compensation values of the polar radius and angle of the polar coordinate of the fiducial fibers were solved in the field of view of the scanning camera. A prototype measurement platform was set up to verify the feasibility and scientific validity of the method. Experiment results show that the polar radius accuracy of the proposed method met the measurement requirements. The X–Y measurement accuracy can be further improved when a higher-precision rotary stage is adopted. Thus, the difficulties in online accurate measurement for fiducial fibers can be tackled by the proposed method with good operability in LAMOST.

A High-Order Compact Gas-Kinetic Scheme in a Rotating Coordinates Frame and on Sliding Mesh

This paper extends the high-order compact gas-kinetic scheme (CGKS) to flow simulations on a rotating coordinate frame. The kinetic equation with the inclusion of centrifugal and Coriolis accelerations is used in the construction of the scheme. With the updates of both cell-averaged flow variables and their gradients in the rotating and stationary domains, a third-order compact reconstruction is developed with sliding interface between them. To capture shock waves and complicated wave interactions, the HWENO-type non-linear reconstruction and gradient compression factors are incorporated in the scheme. For achieving high-order time accuracy, based on the time-accurate flux function the multi-stage multi-derivative time stepping method is implemented in the scheme for the fourth-order time accuracy with two stages. The CGKS is validated in cases from subsonic acoustic wave propagation to high Mach number shock interaction. The compact scheme achieves high-order accuracy and remarkable robustness.

A digital geometry on the tetrakis square tiling—Distance and coarsening

AbstractThere are various tessellations of the plane, including three regular and eight semi‐regular tilings. The square grid is self‐dual, and the hexagonal and triangular tilings are dual to each other. The semi‐regular tessellations are based on more than one type of regular tiles, while their dual tilings are based on a sole but not a regular tile. In various applications, including Geographical Information Systems, it is worth considering non‐regular grids instead of the most used square grid. In this article, we are interested in the dual of the semi‐regular truncated quadrille tiling, T(8,8,4), which is also known as the Khalimsky grid due to its connectedness structure. In our grid, which is called the tetrakis square or kisquadrille tiling, while it is denoted by D(8,8,4), we consider the right‐angled triangle regions of the usual two‐dimensional Khalimsky graph as tiles/pixels. We give an easy‐to‐use coordinate frame addressing the triangles of all the four different orientations. Neighbor relations are described mathematically based on this frame. Based on the shortest path algorithm, a closed formula is proven to compute the digital, that is, path‐based distance on this grid. Some properties of the distance function have also been studied. Hierarchical coarsening is a frequently used technique both in Geometric and Geographical Information Systems to rescale some parts of the map. The tetrakis square grid is apt for hierarchical coarsening, and thus, it can easily be used in image compression and multigrid and other related methods.

A Switched Systems Approach to Multiagent System Consensus: A Relay–Explorer Perspective

The rendezvous or position consensus problem is a fundamental topic within the multiagent system (MAS) literature and has numerous engineering applications. The majority of recent results that solve the position consensus problem rely on communication networks and each agent's ability to obtain position information via direct measurements and communication. Distributed coordination strategies for MASs that are network free and have agents that cannot directly measure position information are scarce. In this work, we develop a relay–explorer strategy to achieve position consensus at a common, desired location. In particular, a group of explorer agents, lacking global position sensors, use open-loop estimators of their position to independently dead reckon toward the desired location. To prevent the difference between the estimated and true position of each explorer from growing beyond a user-defined threshold, a mobile information service provider (relay agent) that is capable of measuring its position in the global coordinate frame, intermittently visits each explorer to provide position information as determined by a maximum dwell-time condition. The relay agent has a position estimator for each explorer, and each estimator is synchronized with the corresponding explorer. The relay agent uses these position estimators to locate each explorer, maneuver to them, and provide position feedback. The contribution of this work over our precursory results is the consideration of uncertain explorer agent dynamics, which are estimated online using recurrent neural networks and integral concurrent learning. The estimated dynamics serve as feed-forward model approximations in the position estimators used by the explorers and relay agent, which generate more accurate position estimates once a finite excitation condition is satisfied. The MAS is modeled as a switched system, and a Lyapunov-based analysis is used to derive a maximum dwell-time condition for each explorer, prove the MAS is exponentially regulated to the desired location, and show the error between the estimated and true explorer dynamics is uniformly ultimately bounded. Experiments and multiple simulation examples are provided to verify the theoretical development, explore the scalability and learning performance of the approach, and shed light on future extensions.

Toward a robust detection of viscous and turbulent flow regions using unsupervised machine learning

We propose an invariant feature space for the detection of viscous-dominated and turbulent regions (i.e., boundary layers and wakes). The developed methodology uses the principal invariants of the strain and rotational rate tensors as input to an unsupervised Machine Learning Gaussian mixture model. The selected feature space is independent of the coordinate frame used to generate the processed data, as it relies on the principal invariants of the strain and rotational rate, which are Galilean invariants. This methodology allows us to identify two distinct flow regions: a viscous-dominated, rotational region (a boundary layer and a wake region) and an inviscid, irrotational region (an outer flow region). We have tested the methodology on a laminar and a turbulent (using Large Eddy Simulation) case for flows past a circular cylinder at Re = 40 and Re = 3900 and a laminar flow around an airfoil at Re=1×105. The simulations have been conducted using a high-order nodal Discontinuous Galerkin Spectral Element Method. The results obtained are analyzed to show that Gaussian mixture clustering provides an effective identification method of viscous-dominated and rotational regions in the flow. We also include comparisons with traditional sensors to show that the proposed clustering does not depend on the selection of an arbitrary threshold, as required when using traditional sensors.

Open-source software package for on-the-fly deskewing and live viewing of volumetric lightsheet microscopy data.

Oblique plane microscopy, OPM, is a form of lightsheet microscopy that permits volumetric imaging of biological samples at high temporal and spatial resolution. However, the imaging geometry of OPM, and related variants of light sheet microscopy, distorts the coordinate frame of the presented image sections with respect to the real space coordinate frame in which the sample is moved. This makes live viewing and practical operation of such microscopes difficult. We present an open-source software package that utilises GPU acceleration and multiprocessing to transform the display of OPM imaging data in real time to produce a live extended depth of field projection. Image stacks can be acquired, processed and plotted at rates of several Hz, making live operation of OPMs, and similar microscopes, more user friendly and intuitive.

Fundamentally different representations of color and motion revealed by individual differences in perceptual scaling

The coordinate frames for color and motion are often defined by three dimensions (e.g., responses from the three types of human cone photoreceptors for color and the three dimensions of space for motion). Does this common dimensionality lead to similar perceptual representations? Here we show that the organizational principles for the representation of hue and motion direction are instead profoundly different. We compared observers' judgments of hue and motion direction using functionally equivalent stimulus metrics, behavioral tasks, and computational analyses, and used the pattern of individual differences to decode the underlying representational structure for these features. Hue judgments were assessed using a standard "hue-scaling" task (i.e., judging the proportion of red/green and blue/yellow in each hue). Motion judgments were measured using a "motion-scaling" task (i.e., judging the proportion of left/right and up/down motion in moving dots). Analyses of the interobserver variability in hue scaling revealed multiple independent factors limited to different local regions of color space. This is inconsistent with the influences across a broad range of hues predicted by conventional color-opponent models. In contrast, variations in motion scaling were characterized by more global factors plausibly related to variation in the relative weightings of the cardinal spatial axes. These results suggest that although the coordinate frames for specifying color and motion share a common dimensional structure, the perceptual coding principles for hue and motion direction are distinct. These differences might reflect a distinction between the computational strategies required for the visual analysis of spatial vs. nonspatial attributes of the world.

Relativistic Fermion and Boson Fields: Bose-Einstein Condensate as a Time Crystal

In a basis of the space-time coordinate frame four quaternions discovered by Hamilton can be used. For subsequent reproduction of the coordinate frame these four quaternions are expanded to four 4 × 4 matrices with real-valued matrix coefficients −0 and 1. This group set is isomorphic to the SU(2) group. Such a matrix basis introduces extra six degrees of freedom of matter motion in space-time. There are three rotations about three space axes and three boosts along these axes. Next one declares the differential generating operators acting on the energy-momentum density tensor written in the above quaternion basis. The subsequent actions of this operator together with its transposed one on the above tensor lead to the emergence of the gravitomagnetic equations that are like the Maxwell equations. Wave equations extracted from the gravitomagnetic ones describe the propagation of energy density waves and their vortices through space. The Dirac equations and their reduction to two equations with real-valued functions, the quantum Hamilton-Jacobi equations and the continuity equations, are considered. The Klein-Gordon equations arising on the mass shell hints to the alternation of the paired fermion fields and boson ones. As an example, a Feynman diagram of an electron–positron time crystal is illustrated.