Multiple Coordinate Systems Research Articles

Tracking the topology of neural manifolds across populations

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

Error analysis and accuracy evaluation method for coordinate measurement in transformed coordinate system

Multiple coordinate system transformations are required for engineering measurements of multi-faceted components. Traditional engineering measurements neglect coordinate errors after transformations, leading to inaccurate accuracy evaluations for coordinates. In this study, the effects of angular deviation and coordinate value magnitude on coordinate errors during transformations are first analyzed. Additionally, the transformation deviation of the three-point method is examined. Subsequently, an accuracy evaluation method for coordinate measurements is proposed to determine the scale scaling factor and the formula for calculating the variance of measuring coordinate errors. Finally, a coordinate accuracy evaluation method and evaluation formula that consider coordinate system transformation errors are proposed by self-checking. The validity of the proposed accuracy evaluation formula is confirmed through experiments. The coordinate measurement accuracy of the low-cost binocular camera is higher than that of the total station, whether or not coordinate system transformations are considered. Stereo-vision measurement technology is more suitable for small-scale engineering measurements.

Numerical study on hydrodynamic interaction between two parallel surge-released ships advancing in head regular waves based on the hybrid method

This study examines the hydrodynamic interaction between two parallel surge-released ships in head regular waves. A hybrid approach combining potential flow theory and functional-decomposition URANS is used for an efficient and accurate simulation. The methodology involves a surge-released module, 4DOF motion equations, multiple coordinate systems, and a dynamic structured grid. Two ship models are used for validation, comparing numerical and experimental results in ship motions and wave loads. The analysis shows good agreement, with differences of less than 5 % in heave and pitch motions, less than 8 % in roll motions, and less than 15 % in total resistance and sway interference forces. Present study also observes consistent trajectories of the wave system between the two ships. The influence of surge motion and wave height on wave-ship-ship interaction is investigated, emphasizing the importance of considering surge motion in seakeeping performance and longitudinal separation. The occurrence of parametric roll in Ship B is accurately resolved by the hybrid method and the parametric roll amplitude is smaller under ship-to-ship interaction conditions. Wave-induced moments play a limited role in this phenomenon, while the dominating roll restoring moment exhibits a hardening effect. Accordingly, roll motion and moments remain relatively unchanged with increasing wave height, indicating the strong nonlinear nature of parametric roll.

Influence of tunnel cone angle and lip deflection on the performance of coaxial twin propeller

Abstract To investigate the influence of the culvert cone angle and the angle of the mouth on the aerodynamic performance of the culvert coaxial twin rotor and its mechanism, the quasi-steady numerical simulation of the flow field of the culvert coaxial twin rotor under a hovering state was carried out based on the Reynolds mean Navier-Stokes (RANS) equation and the multiple reference coordinate system method (MRF). The influence of cone angle from -6° to 9° and lip deflection angle from -20° to 30° on the aerodynamic performance of coaxial double-rotors with ducted passages is analyzed. The results show that the contractile culvert can generate a large gain lift force, which is conducive to improving the aerodynamic efficiency of the system. The inward deflection of the lip obstructs the flow of air into the culvert, which will worsen the local aerodynamic environment and lead to serious air separation, increasing the power consumption of the system. However, the structure of the outward deflection of the lip (open culvert) better complies with the flow trend of air, helps to reduce aerodynamic interference, and improves the additional lift of the culvert, which is beneficial to improving the aerodynamic performance of the system.

Stability Analysis of Planetary Rotor with Variable Speed Self Rotation and Uniform Eccentric Revolution in the Rubber Tapping Machinery

Natural rubber is a critical material that is essential to industry and transportation. In order to reduce the cost of rubber tapping and improve the efficiency and profitability of rubber production, the 4GXJ-2 portable electric rubber cutter and automatic rubber tapping robot have been developed. In their vibration tool holder, the planetary rotor with variable speed self rotation and uniform eccentric revolution is the most important transmission component, and its instability will cause irregular vibration of the tapping tool, thereby reducing the accuracy of vibration cutting and increasing noise. Base on the ANCF (Absolute Nodal Coordinate Formulation) 3D-beam element and 3D REF (3D Ring on Elastic Foundation), a novel eccentric 3D REF model of a planetary rotor is proposed. By introducing multiple coordinate systems, the coupled motion of uniform eccentric revolution, variable speed self rotation and flexible deformation is decomposed and the influences of these motions on the centrifugal force and Coriolis force are more clearly derived. The model is degraded and validated by comparing with other examples of a rotating circular ring model and uniformly eccentrically revolving annular plate. According to the Floquet theory and Runge−Kutta method, the unstable region of revolution speed of a planetary rotor in rubber tapping machinery is predicted as [817 rad/s, 909 rad/s], [1017 rad/s, 1095 rad/s] and [1263 rad/s,1312 rad/s]. Compared with the rubber-tapping experiment of rubber tapping machinery, the validity of the proposed model is further verified. This model provides important design references for the speed settings of those rubber tapping machines.

Multiplexed representation of others in the hippocampal CA1 subfield of female mice

Hippocampal place cells represent the position of a rodent within an environment. In addition, recent experiments show that the CA1 subfield of a passive observer also represents the position of a conspecific performing a spatial task. However, whether this representation is allocentric, egocentric or mixed is less clear. In this study we investigated the representation of others during free behavior and in a task where female mice learned to follow a conspecific for a reward. We found that most cells represent the position of others relative to self-position (social-vector cells) rather than to the environment, with a prevalence of purely egocentric coding modulated by context and mouse identity. Learning of a pursuit task improved the tuning of social-vector cells, but their number remained invariant. Collectively, our results suggest that the hippocampus flexibly codes the position of others in multiple coordinate systems, albeit favoring the self as a reference point.

A Wear Prediction Framework for Ball-Screw of Electro-Mechanical Brake Unit on Railway Trains

The electro-mechanical brake is a new advancement in railway train braking. Ball-screws are important components of electro-mechanical braking units (EMBUs), and their wear can cause EMBUs to degrade in performance or even fail to function. In this paper, we present a framework for prediction of ball-screw wear with discrete operating conditions as inputs, taking into account the time-varying characteristics of EMBUs. The framework includes determining the contact type, analyzing relative motion, calculating contact deformations, and estimating wear. The contact type is determined based on the quasi-static approach of Hertz theory. A dynamics model using multiple coordinate systems is established to analyze how balls and raceways move in relation to each other. The contact deformations of the ball–raceway contact are determined using numerical calculation. Then, the wear depth increment is calculated using the Archard model. The results of the calculation and the endurance test indicate that the wear on the screw raceway is greater than that on the nut raceway. The effect of velocity is greater than the effect of axial force. The presented calculation framework is reasonable and can be used for predicting EMBU ball-screw wear.

Dynamic Analysis and Numerical Simulation of Arresting Hook Engaging Cable in Carried-Based UAV Landing Process

Carrier-based unmanned aerial vehicles (UAVs) require precise evaluation methods for their landing and arresting safety due to their high autonomy and demanding reliability requirements. In this paper, an efficient and accurate simulation method is presented for studying the arresting hook engaging arresting cable process. The finite element method and multibody dynamics (FEM-MBD) approach is employed. By establishing a rigid–flexible coupling model encompassing the UAV and arresting gear system, the simulation model for the engagement process is obtained. The model incorporates multiple coordinate systems to effectively capture the relative motion between the rigid and flexible components. The model considers the material properties, arresting gear system characteristics, and UAV state during engagement. Verification is conducted by comparing simulation results with experimental data from a referenced arresting hook rebound. Finally, simulations are performed under different touchdown points and roll angles of the UAV to analyze the stress distribution of the hook, center of gravity variations, and the tire touch and rollover cable response. The proposed rigid–flexible coupling arresting dynamics model in this paper enables the effective analysis of the dynamic behavior during the arresting hook engaging arresting cable process.

Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem

This paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a posteriori framework for computer assisted existence proofs. Our framework is applied to the study collision and near collision orbits in the circular restricted three body problem. In this case the coordinate systems are the standard rotating coordinates, and the two Levi-Civita coordinate systems regularizing collisions with each of the massive primaries. The proposed framework is used to prove the existence of a number of orbits which have long been studied numerically in the celestial mechanics literature, but for which there are no existing analytical proofs at the mass and energy values considered here. These include transverse ejection/collisions from one primary body to the other, Strömgren's asymptotic periodic orbits (transverse homoclinics for L4,5), families of periodic orbits passing through collision, and orbits connecting L4 to ejection or collision.

A geometric optimal control approach for imitation and generalization of manipulation skills

Daily manipulation tasks are characterized by regular features associated with the task structure, which can be described by multiple geometric primitives related to actions and object shapes. Only using Cartesian coordinate systems cannot fully represent such geometric descriptors. In this article, we consider other candidate coordinate systems and propose a learning approach to extract the optimal representation of an observed movement/behavior from these coordinates. This is achieved by using an extension of Gaussian distributions on Riemannian manifolds, which is used to analyze a small set of user demonstrations statistically represented in different coordinate systems. We formulate the skill generalization as a general optimal control problem based on the (iterative) linear quadratic regulator ((i)LQR), where the Gaussian distribution in the proper coordinate systems is used to define the cost function. We apply our approach to object grasping and box-opening tasks in simulation and on a 7-axis Franka Emika robot using open-loop and feedback control, where precision matrices result in the automatic determination of feedback gains for the controller from very few demonstrations represented in multiple coordinate systems. The results show that the robot can exploit several geometries to execute the manipulation task and generalize it to new situations. The results show high variation along the do-not-matter direction, while maintaining the invariant characteristics of the task in the coordinate system(s) of interest. We then tested the approach in a human–robot shared control task. Results show that the robot can modify its grasping strategy based on the geometry of the object that the user decides to grasp.

Coverage Motion Planning Based on 3D Model’s Curved Shape for Home Cleaning Robot

Research on the automated control of robots for wiping curved surfaces includes studies on cleaning contaminated areas and controlling the end-effector posture to apply a constant force along curved surfaces. However, such robots should also clean difficult-to-find contaminants such as dust and dirt. One of previous studies has considered motion generation as a generalized traveling salesman problem. In particular, a point cloud is acquired from an RGBD camera, and a large graph is created to represent the surface based on the point cloud. The system then finds an appropriate end-effector posture for each node and sets up multiple coordinate systems. Consequently, an efficient cleaning motion can be generated; however, path generation using the previous study is a highly time-consuming process. Therefore, in this study, a 3D model is used to generate cleaning actions more efficiently. A point cloud is then generated from the mesh data of the 3D model, based on which the surface is represented as a simple graph that can be solved as a traveling salesman problem, thereby reducing the computational time. The optimal end-effector posture is determined based on the shape of the surface and is set as the coordinate system for each node. Finally, experiments are conducted to compare the cleaning results with the previous study results, thereby verifying that results can be obtained in less than one-tenth the computational time required for the previous study results.

Three-dimensional vibration analysis of rotating pre-twisted variable thickness blades composed of spanwise graded functional materials

In this study, the isogeometric method is used to obtain a three-dimensional (3-D) solution for the vibration of rotating pre-twisted blades composed of spanwise functionally graded materials (SFGM). The material properties are assumed to change continuously in the spanwise direction according to a mixture rule. Nonuniform rational B–splines (NURBS) are used to describe the unknown displacement and geometry of the rotating blades, whose thickness linearly tapers along the spanwise direction. A typical isogeometric element for a rotating pre-twisted variable thickness SFGM blade is introduced to prevent transformations among multiple coordinate systems. This model considers centrifugal stiffening, centrifugal softening, and Coriolis force effects. Several cases are studied, including rotating rectangular plates, partial cylindrical shells and conical shells with different material properties and geometric parameters. The predicted vibration behaviors are verified by comparisons with results from the literature and commercial finite element software. The comparisons show that the current model has good accuracy. Finally, the influence of material properties, rotating speeds, installation angles, pre-twist angles, and variable thicknesses on the vibrational characteristics of rotating pre-twisted SFGM blades are examined.

A robot-driven automatic scribing method via three-dimensional measurement sensor

The evaluation of the complex workpiece allowance and the scribing the datum line now extremely rely on manual operation. The manual operation is time-consuming and prone to misjudgment, and has a large blind area. To solve these problems, the robot-driven automatic scribing via three-dimensional (3D) measurement sensor method (RAS3DM) is proposed. In this study, we solve the key technology of calibrating the rigid transformation between the 3D measurement coordinate system and laser scribing coordinate system. And a fast and accurate multiple coordinate systems calibration and unification method is proposed, a fixed calibration target and a mobile calibration target are designed. Hence, a structured-light 3D shape measurement sensor driven by an industrial robot with six-degree of freedom (6-DOF) is utilized to obtain the complete 3D shape of the complex workpiece automatically, and then by comparing the 3D measurement result and the standard CAD model, the laser scribing equipment can automatically scribe the mechanical processing datum line to assist further processing. The experiment results illustrate that the proposed method is accurate and efficient: the complex workpiece allowance evaluation and scribing time is about 5 times faster than that of manual operation, and the scribing accuracy is 0.15mm, which can effectively solve various problems of manual scribing. The proposed RAS3DM can be widely applied in factories and laboratories.

Sound Localization of World and Head-Centered Space in Ferrets.

The location of sounds can be described in multiple coordinate systems that are defined relative to ourselves, or the world around us. Evidence from neural recordings in animals point towards the existence of both head-centered and world-centered representations of sound location in the brain; however, it is unclear whether such neural representations have perceptual correlates in the sound localization abilities of non-human listeners. Here, we establish novel behavioral tests to determine the coordinate systems in which ferrets can localize sounds. We found that ferrets could learn to discriminate between sound locations that were fixed in either world-centered or head-centered space, across wide variations in sound location in the alternative coordinate system. Using probe sounds to assess broader generalization of spatial hearing, we demonstrated that in both head and world-centered tasks, animals used continuous maps of auditory space to guide behavior. Single trial responses of individual animals were sufficiently informative that we could then model sound localization using speaker position in specific coordinate systems and accurately predict ferrets’ actions in held-out data. Our results indicate that an animal model in which neurons are known to be tuned to sound location in egocentric and allocentric reference frames can also localize sounds in multiple head and world-centered spaces.

Research on Multicamera Photography Image Art in BERT Motion Based on Deep Learning Mode.

In order to improve the artistic expression effect of photographic images, this article combines the deep learning model to conduct multicamera photographic image art research in BERT motion. Moreover, this article analyzes the external parameter errors caused in the calibration process and uses the checkerboard in the common field of view to calibrate the spatial coordinates of the corners of the board in multiple camera coordinate systems. In addition, this article aims to match the spatial coordinates of the corresponding points to each other and solve the rotation and translation matrix in the transformation process. Finally, this article uses the LM algorithm to optimize the calibration parameters of the camera and combines the deep learning algorithm to perform image processing. The experimental research results show that the research method of multicamera photography image art in BERT motion based on the deep learning mode proposed in this article can effectively improve the expression effect of image art.

Robust Camera Distortion Calibration via Unified RPC Model for Optical Remote Sensing Satellites

On-orbit geometric calibration (GC) is always performed to compensate for geometric distortion from the satellite’s camera. However, the traditional GC method is complex and difficult to apply broadly due to its reliance on a rigorous physical model (RPM), which involves not only complex processing of attitude, orbit, and time, but also the transformation among multiple coordinate systems. Additionally, the RPM is closely related to designs of satellites and cameras, which increases the complexity of the GC, and thus reduces generalizability. This paper proposes a practical and robust GC method to prevent camera distortion based on a standardized rational polynomial coefficient (RPC) model. Through a series of innovations, including stepwise optimization, a priori gross error elimination, the adjustment model with angular resolution, and the correction for the bias field-of-view (FOV) distortion, we were able to achieve robust GC for camera distortion, as well as accurate splicing and registration among segmented images. Method validation using data from the linear-array camera of the ZiYuan3-02 satellite, and the area-array camera of the GaoFen-4 satellite, produced satisfactory results, indicating that our method effectively compensates for systematic geometric distortion such that consistent GC and accuracy comparable with that of traditional RPM-based methods can be obtained.

A Position and Attitude Measurement Method Based on Laser Displacement Sensor and Infrared Vision Camera

The position and attitude measurement of objects plays an important role in industrial manufacture and inspection. However, in the existing measurement methods, the challenges brought by the environmental uncertainty to the visual measurement algorithm and the coordinate conversion errors caused by the joint measurement of various precision equipment will lead to poor accuracy and stability. In this paper, a measurement method is proposed to measure the object’s position and attitude based on laser displacement sensor and infrared vision camera. Firstly, when measuring the position and attitude, the combination of infrared vision camera and measurement target is an effective method to solve the challenges brought by environmental changes and measurement target changes in visual measurement methods. In addition, the measurement results and data of the whole system need not be converted between multiple coordinate systems, which avoids the complexity of system calculation and coordinate conversion errors. Through position and attitude measuring experiments, the position measurement error is 2.6 mm and the attitude angle measurement error is 1.1°, which verifies the feasibility and stability of the method.

Model-Data Co-Driven Integration of Detection and Imaging for Geosynchronous Targets With Wideband Radar

The high orbit height and long coherent processing interval (CPI) of geosynchronous (GEO) targets lead to the problems of ultralow signal-to-noise ratio (ULSNR) and complex signal modulation, posing great challenges to the traditional radar target detection and imaging algorithms. To address the problems, this article proposes a novel model-data codriven integration algorithm of detection and imaging for GEO targets with wideband radar. In this technique, underpinned by the transformation relationships between multiple spatial coordinate systems and the orbit prior information of GEO targets, we deduce the analytical expressions of the effective rotational vector of GEO targets so as to accomplish the model-driven optimal subaperture selection for integration of detection and imaging (OSASIDI). This considerably improves the processing performance and algorithm efficiency compared with traditional data-driven methods at ULSNR. In addition, we derive the radar equation of GEO targets for integration of detection and imaging in detail, which guides OSASIDI by analyzing the impacts of different parameters on detection and imaging performance. Aiming at the complex signal modulation problem caused by ultralong CPI (ULCPI) during the optimal subaperture (OSA) at ULSNR, we innovatively propose a model-data codriven integration of detection and imaging algorithm (MDCDIDI), which can eliminate the complex spatial-time-variant motion errors caused by the dual time-variant characteristic (DTVC) of effective rotational vector, so as to realize the focus-before-detection and obtain the well-focused inverse synthetic aperture radar (ISAR) images. Extensive experimental results from simulated data, which are generated from actual GEO parameters and the computer-aided-design (CAD) model of the Tiangong-I (TG-I) satellite, corroborate the effectiveness of the proposed algorithm.

Theory of Nonradiative Energy Transfer between Two Optical Ions Using the Proper Adiabatic Approximation

Using adiabatic approximation of polyatomic molecules and methods of molecular quantum electrodynamics, we have derived the Förster-Dexter theory of energy transfer between two optical ions. Although we have assumed a single configurational coordinate, the theory can be easily formulated for multiple normal coordinate system. This approach leads smoothly to the energy transfer rates originally derived by Dexter1 for electric dipole-electric dipole interaction without any additional assumptions regarding the normalization of the wavefunctions in the energy space. Using the transfer rates thus derived, and the band shape functions, Wp , a new function F(T) has been proposed to study the temperature dependence of energy transfer rates due to the overlap of the emission and absorption line shapes of the donor and acceptor ions, respectively. This function has been studied for various scenarios of the relative alignment of the zero phonon lines of these ions in order to understand the participation of phonons in the energy transfer process. We have also compared this quantum mechanically derived F(T) function with that derived using semiclassical theory. The agreements are very good at high temperatures. D. L. Dexter, J. Chem. Phys. 21, 836(1953)

VariantStore: an index for large-scale genomic variant search

Efficiently scaling genomic variant search indexes to thousands of samples is computationally challenging due to the presence of multiple coordinate systems to avoid reference biases. We present VariantStore, a system that indexes genomic variants from multiple samples using a variation graph and enables variant queries across any sample-specific coordinate system. We show the scalability of VariantStore by indexing genomic variants from the TCGA project in 4 h and the 1000 Genomes project in 3 h. Querying for variants in a gene takes between 0.002 and 3 seconds using memory only 10% of the size of the full representation.