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Report discusses applicability of conjugate-gradient algorithms to computation of forward dynamics of robotic manipulators. Rapid computation of forward dynamics essential to teleoperation and other advanced robotic applications. Part of continuing effort to find algorithms meeting requirements for increased computational efficiency and speed. Method used for iterative solution of systems of linear equations.
A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves.
The influence of vane sweep in rotor-stator interaction noise is investigated. In an analytical approach, the interaction of a convected gust representing the rotor viscous wake, with a cascade of cascade of finite span swept airfoils, representing the stator, is analyzed. The analysis is based on the solution of the exact linearized equations of motion. High frequency convected gusts for which noise generation is concentrated near the leading edge of airfoils is considered. In a preliminary study, the problem of an isolated finite span swept airfoil interacting with a convected gust is analyzed. Results indicate that sweep can substantially reduce the farfield noise levels for a single airfoil. Using the single airfoil model, an approximate solution to the problem of noise radiation from a cascade of finite span swept airfoils interacting with a convected gust is derived. A parametric study of noise generated by gust cascade interaction is carried out to assess the effectiveness of vane sweep in reducing rotor-stator interaction noise. The results show that sweep is beneficial in reducing noise levels. Rotor wake twist or circumferential lean substantially influences the effectiveness of vane sweep. The orientation of vane sweep must be chosen to enhance the natural phase lag caused by wake lean, in which case rather small sweep angles substantially reduce the noise levels.
A numerical method is developed for the minimization of deviations of real tooth surfaces from the theoretical ones. The deviations are caused by errors of manufacturing, errors of installment of machine-tool settings and distortion of surfaces by heat-treatment. The deviations are determined by coordinate measurements of gear tooth surfaces. The minimization of deviations is based on the proper correction of initially applied machine-tool settings. The contents of accomplished research project cover the following topics: (1) Descriptions of the principle of coordinate measurements of gear tooth surfaces; (2) Deviation of theoretical tooth surfaces (with examples of surfaces of hypoid gears and references for spiral bevel gears); (3) Determination of the reference point and the grid; (4) Determination of the deviations of real tooth surfaces at the points of the grid; and (5) Determination of required corrections of machine-tool settings for minimization of deviations. The procedure for minimization of deviations is based on numerical solution of an overdetermined system of n linear equations in m unknowns (m much less than n ), where n is the number of points of measurements and m is the number of parameters of applied machine-tool settings to be corrected. The developed approach is illustrated with numerical examples.
The linearized equation of motion is given in a Lagrangian representation for a rotating plasma with anisotropic pressure. A WKB theory is developed for large-n ballooning modes in an axisymmetric configuration with field-aligned and rigid toroidal flows. In the presence of field-aligned flows, it is shown that a resonance occurs which is strongly suggestive of a generalized mirror instability. In the presence of toroidal rotation, a possible stabilizing effect is identified for P(normal) greater than P(parallel). Finally, as a special case of the theory, the necessary and sufficient conditions for stability in a static, anisotropic plasma are obtained.
The relative performance of two iterative schemes, based on projection techniques, is compared on a shared memory multiprocessor - VAX 6240. The CG accelerated Block-SSOR method and the CG accelerated Symmetric-Kaczmarz method are considered for the solution of large sparse nonsymmetric systems of linear equations. It is shown that the regular structure of many matrices can be exploited by the CG-accelerated Block-SSOR method to provide good speedup in a multiprocessing environment. However, the CG accelerated Symmetric-Kaczmarz method, while being a viable alternative on a scalar machine, is unable to benefit from multiprocessing.
While the direct solution of systems of linear equations resulting from fluid dynamic problems has generally not been practical in the past, it is presently demonstrated that the direct method is often more efficient than the most popular iterative schemes when constructed in such a way as to take advantage of presently available vector processing capabilities and large memory. The vertical line Gauss-Seidel algorithm was chosen as the iterative method to be compared with the direct method. It is fond that the direct method becomes efficient only when large residual reductions are desired.
A new derivation is presented for the bounds on the size of a multilayer neural network to exactly implement an arbitrary training set; namely, the training set can be implemented with zero error with two layers and with the number of the hidden-layer neurons equal to no.1 is greater than p - 1. The derivation does not require the separation of the input space by particular hyperplanes, as in previous derivations. The weights for the hidden layer can be chosen almost arbitrarily, and the weights for the output layer can be found by solving no.1 + 1 linear equations. The method presented exactly solves (M), the multilayer neural network training problem, for any arbitrary training set.
The aim is to develop a 3-D computational fluid dynamics (CFD) code for the analysis of fluid flow in cylindrical seals and evaluation of the dynamic forces on the seals. This code is expected to serve as a scientific tool for detailed flow analysis as well as a check for the accuracy of the 2D industrial codes. The features necessary in the CFD code are outlined. The initial focus was to develop or modify and implement new techniques and physical models. These include collocated grid formulation, rotating coordinate frames and moving grid formulation. Other advanced numerical techniques include higher order spatial and temporal differencing and an efficient linear equation solver. These techniques were implemented in a 2D flow solver for initial testing. Several benchmark test cases were computed using the 2D code, and the results of these were compared to analytical solutions or experimental data to check the accuracy. Tests presented here include planar wedge flow, flow due to an enclosed rotor, and flow in a 2D seal with a whirling rotor. Comparisons between numerical and experimental results for an annular seal and a 7-cavity labyrinth seal are also included.
An expert system has been developed using the C Language Integrated Production System (CLIPS) that automates the process of constructing DNA sequence based phylogenies (trees or lineages) that indicate evolutionary relationships. LinkFinder takes as input homologous DNA sequences from distinct individual organisms. It measures variations between the sequences, selects appropriate proportionality constants, and estimates the time that has passed since each pair of organisms diverged from a common ancestor. It then designs and outputs a phylogenic map summarizing these results. LinkFinder can find genetic relationships between different species, and between individuals of the same species, including humans. It was designed to take advantage of the vast amount of sequence data being produced by the Genome Project, and should be of value to evolution theorists who wish to utilize this data, but who have no formal training in molecular genetics. Evolutionary theory holds that distinct organisms carrying a common gene inherited that gene from a common ancestor. Homologous genes vary from individual to individual and species to species, and the amount of variation is now believed to be directly proportional to the time that has passed since divergence from a common ancestor. The proportionality constant must be determined experimentally; it varies considerably with the types of organisms and DNA molecules under study. Given an appropriate constant, and the variation between two DNA sequences, a simple linear equation gives the divergence time.
A fast, accurate Choleski method for the solution of symmetric systems of linear equations is presented. This direct method is based on a variable-band storage scheme and takes advantage of column heights to reduce the number of operations in the Choleski factorization. The method employs parallel computation in the outermost DO-loop and vector computation via the loop unrolling technique in the innermost DO-loop. The method avoids computations with zeros outside the column heights, and as an option, zeros inside the band. The close relationship between Choleski and Gauss elimination methods is examined. The minor changes required to convert the Choleski code to a Gauss code to solve non-positive-definite symmetric systems of equations are identified. The results for two large scale structural analyses performed on supercomputers, demonstrate the accuracy and speed of the method.
A method is developed for prediction of ozone levels in planetary atmospheres. This method is formulated in terms of error covariance matrices, and is associated with both direct measurements, a priori first guess profiles, and a weighting function matrix. This is described by the following linearized equation: y = A(matrix) x X + eta, where A is the weighting matrix and eta is noise. The problems to this approach are: (1) the A matrix is near singularity; (2) the number of unknowns in the profile exceeds the number of data points, therefore, the solution may not be unique; and (3) even if a unique solution exists, eta may cause the solution to be ill conditioned.
Recently reported experimental results demonstrate that restabilization of the low-Reynolds-number flow past a circular cylinder can be achieved by the placement of a smaller cylinder in the wake of the first at particular locations. Traditional numerical procedures for modeling such phenomena are computationally expensive. An approach is presented here in which the properties of the adjoint solutions to the linearized equations of motion are exploited to map quickly the best positions for the small cylinder's placement. Comparisons with experiment and previous computations are favorable. The approach is shown to be applicable to general flows, illustrating how strongly control mechanisms that involve sources of momentum couple to unstable (or stable) modes of the system.
A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves.
The fully coupled, systematically linearized equations of motion are used for attitude control system design of an early Space Station Freedom flight configuration. These equations are valid around any estimated spacecraft equilibrium point. A full state feedback controller, incorporating gain scheduled adaptation of the attitude gains, is developed for use during spacecraft on-orbit operations characterized by significant mass properties variations. Feasibility of the gain adaptation is demonstrated via a Space Station Freedom/Orbiter berthing operation scenario. The attitude controller transient performance during gain adaptation appear satisfactory.
Nonlinear and linear equations of motions were derived. The preliminary investigation consisted of model beam as truss structure, effects of truss structure on control design, and effects of reflector offset on control design. It was concluded that the offset of the reflector c.g. from the beam reflector attach point is dynamically significant. Also, truss effects may also significantly effect the performance of the controller if ignored. If the truss is included in the modeling of the NASA/SCOLE configuration, a practically implementable scheme is available to reduce the model order.
Robotic surface missions to the Moon should be capable of measuring mineral as well as chemical abundances in regolith samples. Although much is already known about the lunar regolith, our data are far from comprehensive. Most of the regolith samples returned to Earth for analysis had lost the upper surface, or it was intermixed with deeper regolith. This upper surface is the part of the regolith most recently exposed to the solar wind; as such it will be important to resource assessment. In addition, it may be far easier to mine and process the uppermost few centimeters of regolith over a broad area than to engage in deep excavation of a smaller area. The most direct means of analyzing the regolith surface will be by studies in situ. In addition, the analysis of the impact-origin regolith surfaces, the Fe-rich glasses of mare pyroclastic deposits, are of resource interest, but are inadequately known; none of the extensive surface-exposed pyroclastic deposits of the Moon have been systematically sampled, although we know something about such deposits from the Apollo 17 site. Because of the potential importance of pyroclastic deposits, methods to quantify glass as well as mineral abundances will be important to resource evaluation. Combined x ray diffraction (XRD) and x ray fluorescence (XRF) analysis will address many resource characterization problems on the Moon. XRF methods are valuable for obtaining full major-element abundances with high precision. Such data, collected in parallel with quantitative mineralogy, permit unambiguous determination of both mineral and chemical abundances where concentrations are high enough to be of resource grade. Collection of both XRD and XRF data from a single sample provides simultaneous chemical and mineralogic information. These data can be used to correlate quantitative chemistry and mineralogy as a set of simultaneous linear equations, the solution of which can lead to full characterization of the sample. The use of Rietveld methods for XRD data analysis can provide a powerful tool for quantitative mineralogy and for obtaining crystallographic data on complex minerals.
The large-angle magnetic suspension test fixture (LAMSTF) research project is described which is based on a sophisticated finite element computer program, VF/GFUN, for calculating magnetic fields. The LAMSTF design includes eddy current paths the effect of which on system dynamics is being studied to modify the system dynamic model and the digital controller. Linearized equations of motions have been developed for system modelling and analysis of controllers.