Multiple Coordinate Systems Research Articles

Decentralized vibration control of a multi-link flexible robotic manipulator using smart piezoelectric transducers

The work in this paper is aimed to investigate the use of a decentralized control system for suppressing vibration of a multi-link flexible robotic manipulator using embedded smart piezoelectric transducers. To achieve this, a non-linear dynamic model of a flexible robotic manipulator with smart piezoelectric actuators/sensors, is developed based on the co-rotational finite element method. The method incorporates multiple co-ordinate (co-rotational) systems which rotate and translate with each element, so that the geometric non-linearity present in rotating manipulator system can be dealt with efficiently. The placement of piezoelectric actuators and sensors over the flexible links are considered for the application of decentralized control system. A numerical study shows that the developed co-rotational finite element method can be utilized to investigate the piezoelectric actuator/sensor placement and vibration control performances for a multi-link flexible manipulator undertaking complicated motion.

Adaptation of scanning saccades co-occurs in different coordinate systems

Plastic changes of saccades (i.e., following saccadic adaptation) do not transfer between oppositely directed saccades, except when multiple directions are trained simultaneously, suggesting a saccadic planning in retinotopic coordinates. Interestingly, a recent study in human healthy subjects revealed that after an adaptive increase of rightward-scanning saccades, both leftward and rightward double-step, memory-guided saccades, triggered toward the adapted endpoint, were modified, revealing that target location was coded in spatial coordinates (Zimmermann et al. 2011). However, as the computer screen provided a visual frame, one alternative hypothesis could be a coding in allocentric coordinates. Here, we questioned whether adaptive modifications of saccadic planning occur in multiple coordinate systems. We reproduced the paradigm of Zimmermann et al. (2011) using target light-emitting diodes in the dark, with and without a visual frame, and tested different saccades before and after adaptation. With double-step, memory-guided saccades, we reproduced the transfer of adaptation to leftward saccades with the visual frame but not without, suggesting that the coordinate system used for saccade planning, when the frame is visible, is allocentric rather than spatiotopic. With single-step, memory-guided saccades, adaptation transferred to leftward saccades, both with and without the visual frame, revealing a target localization in a coordinate system that is neither retinotopic nor allocentric. Finally, with single-step, visually guided saccades, the classical, unidirectional pattern of amplitude change was reproduced, revealing retinotopic coordinate coding. These experiments indicate that the same procedure of adaptation modifies saccadic planning in multiple coordinate systems in parallel-each of them revealed by the use of different saccade tasks in postadaptation.

Fast Ellipse Detection and Automatic Marking in Planar Target Image Sequences

A fast method of detecting and automatic marking ellipses in the circle array target image sequences with high quality and strong regular pattern is proposed in this paper. This method collects a small amount of edge points from the ellipse by directly scanning the target image and searching for jumpy-changing of pixels, which can be used to identify the rest of other edge points by combining with the block properties of the elliptical regions, so that the expected ellipses can be calculated. The ellipse raster conversion process is then used to optimize and obtain the correct parameters of ellipses. After this, the multiple coordinate systems can be created based on the corner ellipses on the boundary of the ellipse array, and the fast marking of topological position of ellipses can also be achieved by mapping the ellipses between the different coordinate systems. The main advantage of the proposed method is that it significantly reduces the time complexity as it does not require the complex edge detection and spatial transformation operation. In addition, it is not restricted to any specific target models, and so it has very strong universality. This method is easy to be implemented, and has the high accuracy of detection. Thus, it can meet the requirements of the fast detection of the target image.

VGIS-AntiJitter: an effective framework for solving jitter problems in virtual geographic information systems

With the proposition of the Digital Earth (DE) concept, Virtual Geographic Information System (VGIS) has started to play the role of a Digital Earth prototype system. Many core problems involved in VGIS, such as out-of-core management and interactive rendering of very large scale terrain and image data, have been well studied in the past decades. However, the jitter problem, a common problem in VGIS that often causes annoying visual artefacts and deteriorates the output image quality, draws little attention. In this paper, after an intensive analysis of the jitter problem, a comprehensive framework is proposed to address such a problem while accounting for the characteristics of different data types in VGIS, such as terrain or ocean mesh data, vector data and 3-D model data. Specifically, this framework provides an improved dynamic local coordinate system (DLCS) method for terrain or ocean mesh data. For vector data, the framework provides a simple and effective multiple local coordinate systems (MLCS) method. The framework provides a MLCS method for 3-D model data making full use of the existing local coordinate system of the model. The advantages of the proposed methods over current approaches are analysed and highlighted through case studies involving large GIS datasets.

Transformation between different local coordinate systems of the scapula

The existence of multiple local coordinate systems (LCSs) for the scapula makes it difficult to compare the kinematics of the scapula across various studies and reports. This study aimed to build transformation matrices between different LCSs for the scapula and to provide the coordinates of previously measured muscles and ligaments around the scapula with respect to the International Society of Biomechanics (ISB) recommended LCS. The bony landmarks necessary for building various local coordinate systems were digitized on 13 CT scanned scapulae. The LCSs were built based on the digitized bony landmarks and then used for calculating the transformation equations. The approximate coordinates of 28 muscles and ligaments of the scapula were expressed with respect to the ISB-recommended LCS using the derived transformation equations. The results of this study may be used for the comparison of scapula kinematics data with respect to various LCSs and for building a scapula biomechanical model with respect to ISB-recommended LCS.

Thermal Impacts of Electromagnetic Proximity Effects in Induction Cooking System With Distributed Planar Multicoils

This paper investigates the thermal impacts of electromagnetic proximity effects among the coils of domestic induction heating system (DIHS) with distributed planar spiral multicoils. A combined coordinates system is developed in the computation, consisting of a master Cartesian coordinate system and multiple slave cylindrical coordinate systems. The proposed computing method is implemented with different effecting parameters so as to analyze the impacts of proximity effects and eddy currents distribution in the DIHS. Computation results are validated through comparing against those from the finite element method (FEM). Furthermore, the temperature field is calculated to study the thermal impacts of proximity effects on the thermal distribution in the induction plate.

Auto-configuration and self-calibration in flexible robot-based micro-/nanohandling cells

AbstractMobile robots capable of micro- and nanohandling are a valuable research tool and can be effortlessly integrated into different microscope systems. In this paper, this effortless integration is extended to automated closed-loop positioning based on different external sensors. In three steps, a robot can automatically characterize the employed sensors, determine its location and orientation within the sensors’ coordinate systems and determine its own motion behavior, which is influenced by the specific environment. Additionally, an automated mapping between multiple sensor coordinate systems can be performed simplifying later automation steps. With the described techniques, the integration of mobile microrobots into a specific system can be done fully automatically.

A generalized advection formalism for relativistic fluid simulations

While it is possible to numerically evolve the relativistic fluid equations using any chosen coordinate mesh, typically there will be computational advantages associated with certain choices. For example, astrophysical flows that are governed by rotation tend to give rise to advection variables that are naturally conserved when a cylindrical mesh is used. On the other hand, Cartesian-like coordinates afford a more straightforward implementation of adaptive mesh refinement and avoid the appearance of coordinate singularities. Here we show how it may be possible to reap the benefits associated with multiple coordinate systems simultaneously in numerical simulations. This could be accomplished by implementing a hybrid numerical scheme: one that evolves a set of state variables adapted to one set of coordinates on a mesh defined by an alternative set of coordinates. We provide a formalism (a generalization of the much-used Valencia formulation) by which this can be done. We suggest that a preferred approach to modeling astrophysical flows that are dominated by rotation involves the evolution of inertial-frame cylindrical momenta (i.e. radial momentum, angular momentum and vertical momentum) and the Jacobi energy on a corotating Cartesian coordinate grid.

Singular perturbation techniques in the gravitational self-force problem

Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this situation by explicating the foundations and geometrical structure of singular perturbation theory in general relativity. Within that context, I sketch precise formulations of the methods used in the self-force problem: dual expansions (including matched asymptotic expansions), for which I identify precise matching conditions, one of which is a weak condition arising only when multiple coordinate systems are used; multiscale expansions, for which I provide a covariant formulation; and a self-consistent expansion with a fixed worldline, for which I provide a precise statement of the exact problem and its approximation. I then present a detailed analysis of matched asymptotic expansions as they have been utilized in calculating the self-force. Typically, the method has relied on a weak matching condition, which I show cannot determine a unique equation of motion. I formulate a refined condition that is sufficient to determine such an equation. However, I conclude that the method yields significantly weaker results than do alternative methods.

Influence of inverse dynamics methods on the calculation of inter-segmental moments in vertical jumping and weightlifting

BackgroundA vast number of biomechanical studies have employed inverse dynamics methods to calculate inter-segmental moments during movement. Although all inverse dynamics methods are rooted in classical mechanics and thus theoretically the same, there exist a number of distinct computational methods. Recent research has demonstrated a key influence of the dynamics computation of the inverse dynamics method on the calculated moments, despite the theoretical equivalence of the methods. The purpose of this study was therefore to explore the influence of the choice of inverse dynamics on the calculation of inter-segmental moments.MethodsAn inverse dynamics analysis was performed to analyse vertical jumping and weightlifting movements using two distinct methods. The first method was the traditional inverse dynamics approach, in this study characterized as the 3 step method, where inter-segmental moments were calculated in the local coordinate system of each segment, thus requiring multiple coordinate system transformations. The second method (the 1 step method) was the recently proposed approach based on wrench notation that allows all calculations to be performed in the global coordinate system. In order to best compare the effect of the inverse dynamics computation a number of the key assumptions and methods were harmonized, in particular unit quaternions were used to parameterize rotation in both methods in order to standardize the kinematics.ResultsMean peak inter-segmental moments calculated by the two methods were found to agree to 2 decimal places in all cases and were not significantly different (p > 0.05). Equally the normalized dispersions of the two methods were small.ConclusionsIn contrast to previously documented research the difference between the two methods was found to be negligible. This study demonstrates that the 1 and 3 step method are computationally equivalent and can thus be used interchangeably in musculoskeletal modelling technology. It is important that future work clarifies the influence of the other inverse dynamics methods on the calculation of inter-segmental moments. Equally future work is needed to explore the sensitivity of kinematics computations to the choice of rotation parameterization.

Scattering of flexural wave in a thin plate with multiple circular holes by using the multipole Trefftz method

The scattering of flexural wave by multiple circular holes in an infinite thin plate is analytically solved by using the multipole Trefftz method. The dynamic moment concentration factor (DMCF) along the edge of circular holes is determined. Based on the addition theorem, the solution of the field represented by multiple coordinate systems centered at each circle can be transformed into one coordinate system centered at one circle, where the boundary conditions are given. In this way, a coupled infinite system of simultaneous linear algebraic equations is derived as an analytical model for the scattering of flexural wave by multiple holes in an infinite plate subject to the incident flexural wave. The formulation is general and is easily applicable to dealing with the problem containing multiple circular holes. Although the number of hole is not limited in our proposed method, the numerical results of an infinite plate with three circular holes are presented in the truncated finite system. The effects of both incident wave number and the central distance among circular holes on the DMCF are investigated. Numerical results show that the DMCF of three holes is larger than that of one, when the space among holes is small and meanwhile the specified direction of incident wave is subjected to the plate.

Block Modeling with Connected Fault-Network Geometries and a Linear Elastic Coupling Estimator in Spherical Coordinates

Geodetic observations of interseismic deformation provide constraints on the partitioning of fault slip across plate boundary zones, the spatial distribution of both elastic and inelastic strain accumulation, and the nature of the fault system evolution. Here we describe linear block theory, which decomposes surface velocity fields into four components: (1) plate rotations, (2) elastic deformation from faults with kinematically consistent slip rates, (3) elastic deformation from faults with spatially variable coupling, and (4) homogeneous intrablock strain. Elastic deformation rates are computed for each fault segment in a homogeneous elastic half-space using multiple optimal planar Cartesian coordinate systems to minimize areal distortion and triangular dislocation elements to accurately represent complex fault system geometry. Block motions, fault-slip rates, elastic coupling, and internal block strain rates are determined simultaneously using a linear estimator with constraints from both geodetically determined velocity fields and geologic fault-slip rate estimates. We also introduce algorithms for efficiently implementing alternative fault-network geometries to quantify parameter sensitivity to nonlinear perturbations in model geometry.

Development of the Triple Theta Assembly Station with Machine Vision Feedback

Increased requirements for tighter tolerances on assembled target components in complex three-dimensional geometries with only days to assemble complete campaigns require the implementation of a computer-controlled high-precision assembly station. Over the last year, an 11-axis computer-controlled assembly station has been designed and built with custom software to handle the multiple coordinate systems and automatically calculate all relational positions. Preliminary development efforts have also been done to explore the benefit of a machine vision feedback module with a dual-camera viewing system to automate certain basic features like crosshair calibration, component leveling, and component centering.

The Milky Way Model

In this article, I describe constructing a scale model of our galaxy—the Milky Way—and using this model to teach modern astronomy. The Milky Way model expands on concepts usually explored in the more common solar system model. The Milky Way model presents an opportunity to probe a broad array of physical processes and astrophysical systems, as well as multiple astronomical coordinate systems and far more expansive spatial scales. This exercise is kinetic, interactive, and designed to be done in large spaces (such as a gymnasium floor) with students at the middle school to high school levels.

Interaction between Polymer-Grafted Particles

Previous self-consistent field theory (SCFT) calculations have predicted that the steric interaction between two polymer-grafted particles in good solvent can become attractive, but this conclusion has since been questioned. Here we reexamine the problem with a new numerical scheme using multiple coordinate systems, and find that the interaction remains repulsive regardless of the particle size, brush thickness, or particle separation. The erroneous attraction in the earlier calculations can be attributed to numerical inaccuracy and a subtle issue with how the chains were grafted to the particles. Using our corrected SCFT solution, we also investigate the accuracy of a previous calculation based on strong-stretching theory (SST) and the applicability of the Derjaguin approximation, where the interaction between large particles is estimated from the one-dimensional uniform compression of polymer brushes.

Neural Ensemble Decoding Reveals a Correlate of Viewer- to Object-Centered Spatial Transformation in Monkey Parietal Cortex

The parietal cortex contains representations of space in multiple coordinate systems including retina-, head-, body-, and world-based systems. Previously, we found that when monkeys are required to perform spatial computations on objects, many neurons in parietal area 7a represent position in an object-centered coordinate system as well. Because visual information enters the brain in a retina-centered reference frame, generation of an object-centered reference requires the brain to perform computation on the visual input. We provide evidence that area 7a contains a correlate of that computation. Specifically, area 7a contains neurons that code information in retina- and object-centered coordinate systems. The information in retina-centered coordinates emerges first, followed by the information in object-centered coordinates. We found that the strength and accuracy of these representations is correlated across trials. Finally, we found that retina-centered information could be used to predict subsequent object-centered signals, but not vice versa. These results are consistent with the hypothesis that either area 7a, or an area that precedes area 7a in the visual processing hierarchy, is performing the retina- to object-centered transformation.

3D Monte Carlo modelling of edge plasmas in fusion experiments

A three-dimensional model for the numerical simulation of transport in the edge plasma of modern fusion devices is developed. The model is based on the Braginskii set of equations which are solved with the help of a Monte Carlo method by three-dimensional plasma transport code E3D. The multiple coordinate system approach and interpolated cell mapping technique used in E3D allow us to avoid artificial numerical cross-field transport due to a high anisotropy of Braginskii equations in the case of general magnetic configurations including ergodic regions. The complete self-consistent set of fluid equations (equations for the density, parallel momentum, ion and electron temperatures) has been successfully implemented in E3D. A stabilization method for iterating coupled momentum and density equations is discussed.

Control networks and hemispheric asymmetries in parietal cortex during attentional orienting in different spatial reference frames

Neuropsychological research has consistently demonstrated that spatial attention can be anchored in one of several coordinate systems, including those defined with respect to an observer (viewer-centered), to the gravitational vector (environment-centered), or to individual objects (object-centered). In the present study, we used hemodynamic correlates of brain function to investigate the neural systems that mediate attentional control in two competing reference frames. Healthy volunteers were cued to locations defined in either viewer-centered or object-centered space to discriminate the shape of visual targets subsequently presented at the cued locations. Brain responses to attention-directing cues were quantified using event-related functional magnetic resonance imaging. A fronto-parietal control network was activated by attention-directing cues in both reference frames. Voluntary shifts of attention produced increased neural activity bilaterally in several cortical regions including the intraparietal sulcus, anterior cingulate cortex, and the frontal eye fields. Of special interest was the observation of hemispheric asymmetries in parietal cortex; there was significantly greater activity in left parietal cortex than in the right, but this asymmetry was more pronounced for object-centered shifts of attention, relative to viewer-centered shifts of attention. Measures of behavioral performance did not differ significantly between the two reference frames. We conclude that a largely overlapping, bilateral, cortical network mediates our ability to orient spatial attention in multiple coordinate systems, and that the left intraparietal sulcus plays an additional role for orienting in object-centered space. These results provide neuroimaging support for related claims based on findings of deficits in object-based orienting in patients with left parietal lesions.

Extensions of the 3‐Dimensional Plasma Transport Code E3D

AbstractOne important aspect of modern fusion research is plasma edge physics. Fluid transport codes extending beyond the standard 2‐D code packages like B2‐Eirene or UEDGE are under development. A 3‐dimensional plasma fluid code, E3D, based upon the Multiple Coordinate System Approach and a Monte Carlo integration procedure has been developed for general magnetic configurations including ergodic regions. These local magnetic coordinates lead to a full metric tensor which accurately accounts for all transport terms in the equations. Here, we discuss new computational aspects of the realization of the algorithm.The main limitation to the Monte Carlo code efficiency comes from the restriction on the parallel jump of advancing test particles which must be small compared to the gradient length of the diffusion coefficient. In our problems, the parallel diffusion coefficient depends on both plasma and magnetic field parameters. Usually, the second dependence is much more critical. In order to allow long parallel jumps, this dependence can be eliminated in two steps: first, the longitudinal coordinate x3 of local magnetic coordinates is modified in such a way that in the new coordinate system the metric determinant and contra‐variant components of the magnetic field scale along the magnetic field with powers of the magnetic field module (like in Boozer flux coordinates). Second, specific weights of the test particles are introduced. As a result of increased parallel jump length, the efficiency of the code is about two orders of magnitude better. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

VISRAD—A 3-D view factor code and design tool for high-energy density physics experiments

The 3-D view factor code VISRAD is used to both design high-energy density physics experiments, and to simulate the multi-dimensional radiation environment within target systems, i.e., hohlraums and associated components such as diagnostic holes, capsules, and backlighters. VISRAD target systems are built using a variety of geometric primitives, and surface removal algorithms (e.g., drilling holes in cylinders) can be employed to build complex targets. Laser beam parameters—power profiles, pointing, and focusing—can be specified for either individual beams or groups of beams. At present, the OMEGA and National Ignition Facility laser systems are supported by VISRAD. The use of multiple coordinate systems is supported so that target components can be positioned and oriented, and laser beams can be pointed, in the target chamber coordinate system or in the coordinate system of any target component. Radiation flux distributions about the target system are computed by solving a coupled set of power balance equations in which the emission from a given surface element in the target grid is coupled to all other surface elements. Accurate algorithms are used in computing the configuration (view factor) integrals. At any point in the grid, the time- and frequency-dependent flux incident onto that point can be viewed and/or written to a file to be used as input to radiation-hydrodynamics simulations. Energy source models include laser energy deposition—computed using 3-D ray-trace algorithms—and self-radiating target components. To aid designers in setting up targets, pointing beams, and viewing results, VISRAD has an easy-to-use graphical user interface and interactive 3-D graphics. The code has been designed for cross-platform use on Windows, Unix, and Mac OS X platforms.