Search NASA⌕ Search

SEARCH · Search NASA

Results for “Matrix inversion”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Kinematics of an in-parallel actuated manipulator based on the Stewart platform mechanism

This paper presents kinematic equations and solutions for an in-parallel actuated robotic mechanism based on Stewart's platform. These equations are required for inverse position and resolved rate (inverse velocity) platform control. NASA LaRC has a Vehicle Emulator System (VES) platform designed by MIT which is based on Stewart's platform. The inverse position solution is straight-forward and computationally inexpensive. Given the desired position and orientation of the moving platform with respect to the base, the lengths of the prismatic leg actuators are calculated. The forward position solution is more complicated and theoretically has 16 solutions. The position and orientation of the moving platform with respect to the base is calculated given the leg actuator lengths. Two methods are pursued in this paper to solve this problem. The resolved rate (inverse velocity) solution is derived. Given the desired Cartesian velocity of the end-effector, the required leg actuator rates are calculated. The Newton-Raphson Jacobian matrix resulting from the second forward position kinematics solution is a modified inverse Jacobian matrix. Examples and simulations are given for the VES.

Williams, Robert L., II↗
NASA NTRS1983

On obtaining the forward phase functions of Saturn ring features from radio occultation observations

It is noted that the near-forward scattering functions of particles in Saturn ring features are related to 3.6 cm radio occultation power spectra by a Fredholm integral equation of the first kind. The equation reduces to an algebraic system of equation whose solution by usual inversion techniques (that is, least mean squares) is ruled out by the near singularity of the forward transformation matrix. A combination of constrained linear inversion and a filtering algorithm based on eigenvector decomposition of the matrix reduces the instabilities; this yields derived phase functions valid over the range of zero to about 12 mrad. It is noted that these functions represent the collective forward diffraction lobe of particles greater than about 1 m in radius. Since multiple scattering of the signal is a significant effect, the measured phase functions must be adjusted to obtain the singly scattered component. This single-scattering correction is examined for two physical models, namely the monolayer and the classical discrete random slab; in addition, the fraction of opacity in submeter particles for each model for particular ring features is estimated.

Zebker, H. A.↗
NASA NTRS1989

Minimal inversion, command matching and disturbance decoupling in multivariable systems

The present treatment of the related problems of minimal inversion and perfect output control in linear multivariable systems uses a simple analytical expression for the inverse of a square multivariate system's transfer-function matrix to construct a minimal-order inverse of the system. Because the poles of the minimal-order inverse are the transmission zeros of the system, necessary and sufficient conditions for the inverse system's stability are simply stated in terms of the zero polynomial of the original system. A necessary and sufficient condition for the existence of the required controllers is that the plant zero polynomial be neither identical to zero nor unstable.

Seraji, H.↗
NASA NTRS1977

The incomplete inverse and its applications to the linear least squares problem

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

Morduch, G. E.↗
NASA NTRS1988

A spatial operator algebra for manipulator modeling and control

A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.

Rodriguez, G.↗
NASA NTRS1996

Design of Robust Adaptive Unbalance Response Controllers for Rotors with Magnetic Bearings

Experimental results have recently demonstrated that an adaptive open loop control strategy can be highly effective in the suppression of unbalance induced vibration on rotors supported in active magnetic bearings. This algorithm, however, relies upon a predetermined gain matrix. Typically, this matrix is determined by an optimal control formulation resulting in the choice of the pseudo-inverse of the nominal influence coefficient matrix as the gain matrix. This solution may result in problems with stability and performance robustness since the estimated influence coefficient matrix is not equal to the actual influence coefficient matrix. Recently, analysis tools have been developed to examine the robustness of this control algorithm with respect to structured uncertainty. Herein, these tools are extended to produce a design procedure for determining the adaptive law's gain matrix. The resulting control algorithm has a guaranteed convergence rate and steady state performance in spite of the uncertainty in the rotor system. Several examples are presented which demonstrate the effectiveness of this approach and its advantages over the standard optimal control formulation.

Knospe, Carl R.↗
NASA NTRS1987

An optimal resolved rate law for kindematically redundant manipulators

The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution was found to cause large joint rates in some case. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to nonplanar manipulators.

Bourgeois, B. J.↗
NASA NTRS1982

Alternative ways for formulation of hybrid stress elements

An element stiffness matrix can be derived by the conventional potential energy principle and, indirectly, also by generalized variational principles, such as the Hu-Washizu principle and the Hellinger-Reissner principle. The present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle. It is found that the resulting scheme is equivalent to that considered by Tong (1982) for the construction of hybrid stress elements. In Tong's scheme the inversion of a large flexibility matrix can be avoided. It is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the Hellinger-Reissner principle and the Hu-Washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method.

Pian, T. H. H.↗
NASA NTRS1987

An optimal resolved rate law for kinematically redundant manipulators

The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution has been found to cause large joint rates in some cases. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to non-planar manipulators.

Bourgeois, B. J.↗
NASA NTRS1972

On the computation of the generalized inverse by classical minimization.

An alternative method for deriving the generalized inverse of an arbitrary rectangular matrix with real or complex coefficients is described. The method applies a classical minimization procedure without iteration processes and is readily applicable in digital computer programming.

Voith, R. P.↗
NASA NTRS1976

An aid to the development of Botswana's resources: Section on hydrology

The author has identified the following significant results. It is proved that FCC's can be used for a simple estimate of the total evaportranspiring area of the Okavango Delta, sufficiently accurate for preliminary inputs for the development of mathematical model of the surface hydrology of the delta. The color coded matrix has shown as interesting inverse correlation with an array on the same grid prepared by ecologists from air photography study, for percent liable to flood.

Dickson, W. L.↗
NASA NTRS1977

Estimation of the geophysical properties of the ocean surface using aircraft microwave measurements

An improved model of the effects of sea state on microwave signature has been developed which incorporates the different effects of whitecaps and streaks to define the response of microwave channels to wind speed. This model has been demonstrated to agree with recent measurements. An approximation model has also been incorporated to describe the effects of precipitation on microwave radiation through a computationally rapid routine. The use of these models and a new technique to allow the selection of the most climatologically appropriate D-matrix is demonstrated in the inversion of data collected over the bering Sea. Surface wind speed agrees very well with observations while good results are obtained for integrated water vapor, and liquid water.

Fowler, M. G.↗
NASA NTRS1977

Diagonal dominance using function minimization algorithms

A new approach to the design of multivariable control systems using the inverse Nyquist array method is proposed. The technique utilizes a conjugate direction function minimization algorithm to achieve dominance over a specified frequency range by minimizing the ratio of the moduli of the off-diagonal terms to the moduli of the diagonal term of the inverse open loop transfer function matrix. The technique is easily implemented in either a batch or interactive computer mode and will yield diagonalization when previously suggested methods fail. The proposed method has been successfully applied to design a control system for a sixteenth order state model of the F-100 turbofan engine with three inputs.

Leininger, G. G.↗
NASA NTRS1985

The San Fernando Observatory video Stokes polarimeter

A study was conducted to determine the suitability of the San Fernando Observatory's 61 cm (24 inch) aperture vacuum solar telescope and 3 m (118 inch) focal length vacuum spectroheliograph for Stokes Polarimetry measurements. The polarization characteristics of these two instruments was measured by determining their Mueller matrices as a function of telescope orientation, field angle, wavelength, grating type, and position of the measuring beam in the telescope entrance window. In general, the polarizing and depolarizing properties are small so that inversion of the system Mueller matrix will permit the accurate measurement of Stokes profiles for vector magnetic field determination. A proposed polarimeter design based on the use of a TV camera system to simultaneously scan six different polarization components of a given line profile is described. This design, which uses no rotating optics or electronic modulators and makes efficient use of the available irradiance, promises to yield high quality vector magnetograms.

Richter, P. H.↗
NASA NTRS1994

Computationally efficient multibody simulations

Computationally efficient approaches to the solution of the dynamics of multibody systems are presented in this work. The computational efficiency is derived from both the algorithmic and implementational standpoint. Order(n) approaches provide a new formulation of the equations of motion eliminating the assembly and numerical inversion of a system mass matrix as required by conventional algorithms. Computational efficiency is also gained in the implementation phase by the symbolic processing and parallel implementation of these equations. Comparison of this algorithm with existing multibody simulation programs illustrates the increased computational efficiency.

Ramakrishnan, Jayant↗
NASA NTRS1998

3D Navier-Stokes Time Accurate Solutions Using Multipartitioning Parallel Computation Methodology

A parallel CFD code solving 3D time accurate Navier-Stokes equations with multipartitioning parallel Methodology is being developed in collaboration with Ohio State University within the Air Vehicle Directorate, at Wright Patterson Air Force Base. The advantage of the multipartitioning parallel method is that the domain decomposition will not introduce domain boundaries for the implicit operators. A ring structure data communication is employed so that the implicit time accurate method can be implemented for multi-processors with the same accuracy as for the single processor. No sub-iteration is needed at the domain boundaries. The code has been validated for some typical unsteady flows, which include Coutte Flow, flow passing a cylinder. The code now is being employed for a large scale time accurate wall jet transient flow computation. 'ne preliminary results are promising. The mesh has been refined to capture more details of the flow field. The mesh refinement computation is in progress and would be difficult to successfully implement without the parallel computation techniques used. A modified version of the code with more efficient inversion of the diagonalized block matrix is currently being tested.

Zha, Ge-Cheng↗