Showing papers on "Degrees of freedom published in 1996"

Efficient generation of motion transitions using spacetime constraints

Abstract: This paper describes the application of space time constraints to creating transitions between segments of human body motion. The motion transition generation uses a combination of spacetime constraints and inverse kinematic constraints to generate seamless and dynamically plausible transitions between motion segments. We use a fast recursive dynamics formulation which makes it possible to use spacetime constraints on systems with many degrees of freedom, such as human figures. The system uses an interpreter of a motion expression language to allow the user to manipulate motion data, break it into pieces, and reassemble it into new, more complex, motions. We have successfully used the system to create basis motions, cyclic data, and seamless motion transitions on a human body model with 44 degrees of freedom. Additional

Method and apparatus for determining position and orientation

Abstract: A method for determining degrees of freedom of an object, and in particular, to a device for determining up to six degrees of freedom of a head mount display and a handle. A first camera is attached to a head mount display and senses an optically modulated target. The first camera's video output signal is processed with a digital computer to determine the position and orientation of the head mount display. A second camera is attached to a head mount display and senses an optically modulated target attached to a handle. The second camera's video output signal is processed with a digital computer to determine the position and orientation of the handle.

Understanding radio polarimetry. II. Instrumental calibration of an interferometer array.

Abstract: In a companion paper, a mathematical formalism to describe the polarimetric response of a radio interferometer was presented. Some of the instrumental parameters, however, are either unknown or poorly known. Here we consider the determination of these parameters both by a traditional radio-interferometry instrumental approach as well as by using optical polarimetry principles. In doing so, we establish links between the two fields. We show that some degrees of freedom cannot be solved for with various calibration or self-calibration schemes. These degrees of freedom are identified with instrumental parameters and physical source properties. The number of unsolvable degrees of freedom is reduced for a long synthesis with alt-az antennas. We also consider the effect of errors in the assumed instrumental parameters on the resultant calibrated data. The polarimetric calibration procedure for some telescopes is reviewed in the context of this analysis.

A Parallel Manipulator with Only Translational Degrees of Freedom

Abstract: This paper presents a novel three degree of freedom parallel manipulator that employs only revolute joints and constrains the manipulator output to translational motion. Closed-form solutions are developed for both the inverse and forward kinematics. It is shown that the inverse kinematics problem has up to four real solutions, and the forward kinematics problem has up to 16 real solutions.

Non-crystalline solids: glasses and amorphous solids

Abstract: Zachariasen's concept of glass formation has been extended to rationalize the relative ease of different compositions for formation of non-crystalline solids. It is shown that non-crystalline solids can be divided in to two thermodynamically distinct classes: glasses and amorphous solids. Further, it is argued that they behave differently upon heating. Based on Zachariasen's notion of glass as a topologically disordered network with short range order equivalent to that in the corresponding crystal, quantitative structure-based definitions are proposed for glasses and amorphous solids. In addition, a previous formalism based on degrees of freedom in topologically disordered networks has been extended to examine the relative abilities of compositions to form non-crystalline solids.

Generating optimized motion transitions for computer animated objects

Abstract: A method and system which simplifies the process of constructing new basis motions and transitions between them for animation of articulated figures with many degrees of freedom using existing basis motion data. The system uses an interpreter of a motion expression language called motion algebra to allow a user to manipulate basis motion data, break it into components, and reassemble it into new, more complex motions. The system provides two methods for generating motion: motion transition generation and cyclification. Motion transition generation uses a combination of space/time constraints and inverse kinematic constraints to generate transitions between basis motions. These transitions minimize the torque required while maintaining kinematic constraints. A fast dynamics formulation makes it possible to use spacetime constraints on systems with many degrees of freedom. Cyclification helps to eliminate discontinuities in cyclic motions and distributes the discontinuity error over an entire time interval.

Method and apparatus for determining degrees of freedom of a camera

Abstract: A method for determining up to six degrees of freedom of a camera relative to a reference frame comprises sensing an optically modulated target with the camera and processing the camera's video output signal with a digital computer. The target may have a single pattern, multiple patterns, or patterns of varying size. Multiple targets may also be used. A very wide field of view camera may be used in conjunction with a method for removing geometric distortion from the camera's view. Target patterns may be transmissive, reflective, or retroreflective, or may actively emit light. Asymmetric patterns are used to eliminate ambiguity in the recovery of the degrees of freedom.

System for manipulating digitized image objects in three dimensions

Abstract: This invention relates to a method and apparatus for displaying photo-realistic three-dimensionally projected views of real objects in real scenes and enabling the viewer to manipulate these objects and the scene with several degrees of freedom, such as rotation, zooming, or otherwise "handling" them as though they were physically manipulated.

Existence of local degrees of freedom for higher dimensional pure Chern-Simons theories

Abstract: The canonical structure of higher dimensional pure Chern-Simons theories is analyzed. It is shown that these theories have generically a nonvanishing number of local degrees of freedom, even though they are obtained by means of a topological construction. This number of local degrees of freedom is computed as a function of the spacetime dimension and the dimension of the gauge group.

Design and Control Degrees of Freedom

Abstract: One of the central problems in developing a steady-state process flowsheet is finding the number of variables that must be specified to completely define the process. This number is called the design degrees of freedom. Once this number has been found, the number of design optimization variables can be calculated by subtracting all variables that are set by specifications on production rate, product qualities, safety constraints, and environmental limitations. In principle, the design degrees of freedom are easily calculated by simply subtracting the number of equations from the number of variables. However, for typically complex industrial processes, there are many hundreds of variables and equations, and it is not a trivial job to make sure that the correct variables and equations have been defined. In addition, this conventional variables-minus-equations approach requires that a detailed model of the process be available. Once the plant has been specified, the design of a control structure requires tha...

Damage Detection in Beam Structures Using Subspace Rotation Algorithm with Strain Data

Abstract: Motivated by a smart structures philosophy of self-health monitoring in structural systems, a damage detection system for beam structures using subspace rotation techniques is presented. In doing so, the subspace rotation is extended from displacement-based data to strain-based data. Methods for accommodating the additional degrees of freedom of beam elements are presented. Using simulated data, the ability to locate and quantify single and multiple damage events is investigated. It has been found that the higher-order vibration modes are required to locate damage events in beams because the frequency response of beams is much less sensitive to a damage event than that of truss structures. It has also been found that condensation methods cannot be used to remove rotational degrees of freedom in the beam because of the coupled nature of the rotational degrees of freedom to the translational degrees of freedom.

Random-lattice models and simulation algorithms for the phase equilibria in two-dimensional condensed systems of particles with coupled internal and translational degrees of freedom.

Abstract: In this work we concentrate on phase equilibria in two-dimensional condensed systems of particles where both translational and internal degrees of freedom are present and coupled through microscopic interactions, with a focus on the manner of the macroscopic coupling between the two types of degrees of freedom. First, an unconventional description of the translational degrees of freedom is developed, in which the randomly varying spatial connectivity of the particles is represented by a random lattice whose dynamic structure is given by triangulating the spatial configurations. Based on this random-lattice description, a series of three statistical-mechanical models are then constructed. All of the three models are in essence spin-\textonehalf{} Ising models where the spins, representing internal degrees of freedom, are associated with hard-disk particles and nearest-neighbor particles interact through spin-spin interactions that may have spatial dependence. The fluctuating number of nearest neighbors and the possible spatial dependence of the spin-spin interactions couple microscopically the spin degrees of freedom to the translational degrees of freedom. The first model (I) is a random-lattice Ising model with conventional nearest-neighbor spin-spin interactions. The second model (II) is an extension of this model to include a spatial dependence of the nearest-neighbor spin-spin interactions. The third model (III) is a modification of the second model that accounts for spin states with different internal degeneracy. Monte Carlo simulation techniques, including both a special algorithm for the random-lattice description and histogram and finite-size scaling analysis, are used to investigate the phase behavior of all three models. It is shown that the order-disorder spin transition in model I is decoupled from a first-order singularity---lattice melting---associated with the translational degrees of freedom and remains critical and falls in the universality class of the standard two-dimensional Ising model on regular lattices. Model II is shown to exhibit a phase diagram that has a region where the spin degrees of freedom are slaved by the translational degrees of freedom and develop a first-order singularity in the order-disorder transition that accompanies the lattice-melting transition. The internal degeneracy of the spin states in model III implies that the spin order-disorder singularity can be of first order throughout the phase diagram. It is found that this first-order singularity can be either coupled to or decoupled from the lattice-melting singularity, depending on the strength of the microscopic coupling. The calculated phase diagram and the associated thermodynamic transitional properties for model III are discussed in relation to experiments on planar bilayers of lipid-chain molecules whose properties are determined by a subtle coupling between the translational variables and the intrachain conformational states.

Chaos in ocean ambient ‘‘noise’’

Abstract: Using a data analysis toolkit designed to explore data from nonlinear systems using time domain methods, it has been determined that the observed number of degrees of freedom in one pristine measurement of ocean ambient background pressure fluctuations or ‘‘noise’’ is nine. While the true number of degrees of freedom in the ocean is probably large, the observed measurements have nine degrees of freedom. There is a positive Lyapunov exponent, which identifies the system as being chaotic. The largest exponent is very large, indicating that the prediction horizon for these data is confined to a few samples. Determination of the degrees of freedom is important for the construction of physical models and nonlinear noise reduction filters, which may be based on characteristics of the observed few degrees of freedom from the background acoustic source. The magnitude of the largest Lyapunov exponent provides a measure of confidence for signal state prediction and mitigation.

p-ADIC HILBERT SPACE REPRESENTATION OF QUANTUM SYSTEMS WITH AN INFINITE NUMBER OF DEGREES OF FREEDOM

Abstract: Gaussian measures on infinite-dimensional p-adic spaces are introduced and the corresponding L2-spaces of p-adic valued square integrable functions are constructed. Representations of the infinite-dimensional Weyl group are realized in p-adic L2-spaces. p-adic Hilbert space representations of quantum Hamiltonians for systems with an infinite number of degrees of freedom are constructed. Many Hamiltonians with potentials which are too singular to exist as functions over reals are realized as bounded symmetric operators in L2-spaces with respect to a p-adic Gaussian measure.

A new way of averaging with applications to MRI

Abstract: Averaging is often used to increase the quality of an image degraded by noise or artifacts. A method is developed in which several degrees of freedom are introduced in the averaging process, this freedom making possible the choice of different weighting factors for different portions of the Fourier space. If a weighting factor is associated with each line of a magnetic resonance acquisition, we show that we obtain some freedom to eliminate motion artifacts. The process minimizes a quantity called the gradient energy over a region of interest in the image plane. A processed image is obtained from a mosaic of such regions of interest scanned over the whole image plane. The method is shown to yield greater motion artifact suppression in magnetic resonance images than that achieved with regular averaging. The main strength of the method is probably its ability to diminish the intensity of unstructured artifacts which are usually poorly managed by other postprocessing methods of artifacts suppression.

The Quantum theory of general relativity at low-energies

Abstract: In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions appropriate for those energies. Whether or not general relativity is truly fundamental, at low energies it is automatically described as a quantum effective field theory and this allows a consistent framework for quantum gravity at ordinary energies. I briefly describe the nature and limits of the technique.

Automatic Motion Planning for Complex Articulated Bodies

Abstract: Much research has been devoted to path planning during the past decade, i.e. the geometrical problem of finding a collision-free path between two given postures (configurations) of an articulated body (robot) among obstacles. This problem has straightforward applications in robotic automation, computer aided design, and computer graphics animation. Current global techniques compute explicitly the non-colliding zones in configuration space. Thus, they require exponential space and time in the number of Degrees of Freedom (DOF) of the body. These methods are therefore untractable for more than 4 DOF. This report presents a new approach to path planning which does not require construction of an explicit description of the configuration space. The method consists of building and searching a graph connecting the local minima of a potential function defined over the configuration space. The graph is explored by means of a randomization technique that escapes the local minima by executing Brownian motions. This planner is considerably faster than previous path planners and it solves problems with many more degrees of freedom. Experiments are reported for several computer simulated robots, including rigid objects with 3 DOF (in 2D workspaces) and 6 DOF (in 3D workspaces) and articulated bodies with up to 30 DOF (in 2D and 3D workspaces).

Canonical parameterization of excess motor degrees of freedom with self-organizing maps

Abstract: The problem of sensorimotor control is underdetermined due to excess (or "redundant") degrees of freedom when there are more joint variables than the minimum needed for positioning an end-effector. A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps. The parameterization approximates the topological structure of the joint space, which is that of a fiber bundle. The fibers represent the "self-motion manifolds" along which the manipulator can change configuration while keeping the end-effector at a fixed location. The method is demonstrated for the case of the redundant planar manipulator. Data samples along the self-motion manifolds are selected from a large set of measured input-output data. This is done by taking points in the joint space corresponding to end-effector locations near "query points", which define small neighborhoods in the end-effector work space. Self-organizing maps are used to construct an approximate parameterization of each manifold which is consistent for all of the query points. The resulting parameterization is used to augment the overall kinematics map so that it is locally invertible. Joint-angle and end-effector position data, along with the learned parameterizations, are used to train neural networks to approximate direct inverse functions.

Noise induced phase transitions

Abstract: Models of macroscopic systems with an infinite number of microscopic degrees of freedom perturbed by external noise can undergo sharp phase transitions which are however modified or even induced by the external noise These non-equilibrium phase transitions exhibit the features characteristic of equilibrium phase transitions such as symmetry breaking and non ergodicity, which are absent in the transitions studied in zero-dimensional systems

The nuclear effects in $g_{1^3\rm{He}}$ and the Bjorken sum rule for A=3

Abstract: The Bjorken sum rules for the $A=3$ and $A=1$ are used as a guide to estimate nuclear effects in extracting $g_{1n}(x,Q^{2})$ from the $\vec{e}\,\vec{^3\rm{He}}$ data. We estimate that the combination of the spin depolarization, the nonnucleonic degrees of freedom in the $A=3$ system and nuclear shadowing is likely to reduce $g_{1^3\rm{He}}(x\le 0.05)$ by $\sim 15 \%$ while a significant enhancement of the structure functions $g_{1^3\rm{He}}, g_{1^3\rm{H}}$ at $x \sim 0.1$ is predicted.

Combining Cauchy and characteristic codes. III. The interface problem in axial symmetry.

Abstract: This paper is part of a long term program to develop combined Cauchy and characteristic codes as investigative tools in numerical relativity. In this, the third stage of the program, attention is devoted to axisymmetric systems possessing two spatial degrees of freedom. The method relies on being able to pass information backwards and forwards across an interface exterior to any central source present. Formulas are obtained which show how it is possible to relate the canonical forms of the interior Cauchy and exterior characteristic metric functions, and their derivatives, on the interface.

Power-supply system for a manipulator

Abstract: Power-supply system for a manipulator, for example an industrial robot, which manipulator comprises a plurality of drive means (1) for moving the manipulator in its plurality of degrees of freedom Each drive means (1c,1d) comprises at least one electric driving motor (2c,2d) and a reduction gear (3c,3d) The driving motors are supplied and controlled via a rectifier (6) and drive devices (7c,7d) According to the invention at least one of said drive devices (7) is arranged on the manipulator adjacent to its associated drive means (1c,1d) Also the rectifier may consist of a plurality of smaller units arranged on the manipulator and each provided for supplying only one or only a group of drive devices