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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.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Collision-free trajectory planning algorthm for manipulators

Collision-free trajectory planning for robotic manipulators is investigated. The task of the manipulator is to move its end-effector from one point to another point in an environment with polyhedral obstacles. An on-line algorithm is developed based on finding the required joint angles of the manipulator, according to goals with different priorities. The highest priority is to avoid collisions, the second priority is to plan the shortest path for the end effector, and the lowest priority is to minimize the joint velocity for smooth motion. The pseudo-inverse of the Jacobian matrix is applied for inverse kinematics. When a possible collision is detected, a constrained inverse kinematic problem is solved such that the collision is avoided. This algorithm can also be applied to a time-variant environment.

Pourboghrat, F.↗
NASA NTRS2002

On-Line, Gyro-Based, Mass-Property Identification for Thruster-Controlled Spacecraft Using Recursive Least Squares

Spacecraft control, state estimation, and fault-detection-and-isolation systems are affected by unknown v aerations in the vehicle mass properties. It is often difficult to accurately measure inertia terms on the ground, and mass properties can change on-orbit as fuel is expended, the configuration changes, or payloads are added or removed. Recursive least squares -based algorithms that use gyro signals to identify the center of mass and inverse inertia matrix are presented. They are applied in simulation to 3 thruster-controlled vehicles: the X-38 and Mini-AERCam under development at NASA-JSC, and the SAM, an air-bearing spacecraft simulator at the NASA-Ames Smart Systems Research Lab (SSRL).

Wilson, Edward↗
NASA NTRS2001

Maximally Informative Statistics for Localization and Mapping

This paper presents an algorithm for localization and mapping for a mobile robot using monocular vision and odometry as its means of sensing. The approach uses the Variable State Dimension filtering (VSDF) framework to combine aspects of Extended Kalman filtering and nonlinear batch optimization. This paper describes two primary improvements to the VSDF. The first is to use an interpolation scheme based on Gaussian quadrature to linearize measurements rather than relying on analytic Jacobians. The second is to replace the inverse covariance matrix in the VSDF with its Cholesky factor to improve the computational complexity. Results of applying the filter to the problem of localization and mapping with omnidirectional vision are presented.

Deans, Matthew C.↗
NASA NTRSDate not supplied

Graphical and Numerical Description of Strain-Gage Balance Interactions

A new approach for the graphical and numerical description of balance interactions is presented. The approach uses data from single-component loads as input. This choice has the two advantages. First, the number of applied loads is at the minimum needed for interactions to be observed. In addition, the loads used for the description of interactions can easily be repeated at different sites. Output differences relative to the outputs of the zero load point of a load series are used for the description of interactions. Similarly, load differences relative to the loads of the zero load point of a load series are used for the description of the loads. Interactions are plotted versus the load differences for each load component while omitting the outputs of the primary gage of the chosen load component. The resulting plots have a characteristic star pattern as interactions are zero at zero load. Numerical estimates of the slopes of the interactions can be reverse-engineered from the load prediction equations of a balance if calibration data is examined. The slopes are the off-diagonal coefficients of the inverse of the matrix that has the coefficients of the linear terms of the fitted loads if the Non-Iterative Method is used for the analysis. Similarly, the slopes are the off-diagonal coefficients of the inverse of the matrix that is the non-iterative part of the primary load iteration equation if the Iterative Method is used for the analysis. Data from the calibration of a force balance is processed to illustrate the proposed graphical and numerical description of interactions.

wind tunnel test↗
NASA NTRSDate not supplied

Graphical and Numerical Description of Strain-Gage Balance Interactions

A new approach for the graphical and numerical description of strain-gage balance interactions is presented. The approach uses data from single-component loads as input. This choice has the two advantages. First, the number of applied loads is at the minimum needed for interactions to be observed. In addition, the loads used for the description of interactions can easily be repeated at different sites. Output differences relative to the outputs of the zero load point of a load series are used for the description of interactions. Similarly, load differences relative to the loads of the zero load point of a load series are used for the description of the loads. Interactions are plotted versus the load differences for each load component while omitting outputs of the primary gage of the chosen load component. The resulting plots have a star pattern as all interactions are zero at zero load. Estimates of the slopes of the interactions can be obtained from the load prediction equations of a balance if calibration data is examined. The slopes are the off-diagonal coefficients of the inverse of the matrix that has the coefficients of the linear terms of the fitted loads if the Non-Iterative Method is used for the analysis. Similarly, the slopes are the off-diagonal coefficients of the inverse of the matrix that is the non-iterative part of the primary load iteration equation if the Iterative Method is used for the analysis. Data sets from a manual and a machine calibration of a force balance are processed to illustrate the proposed description of interactions.

strain-gage balance↗
NASA NTRS1985

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

Chu, W. P.↗
NASA NTRS1991

Turbulence modeling in supersonic combusting flows

To support the National Aerospace Plane project, the RPLUS3D CFD code has been developed at NASA Lewis. The code has the ability to solve three-dimensional flowfields with finite rate combustion of hydrogen and air. The combustion processes of the hydrogen-air system are simulated by an 18-reaction path, 8-species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though it uses a fully implicit numerical algorithm. A k-epsilon (two equation) turbulence model is incorporated into the RPLUS3D code.

Chitsomboon, Tawit↗
NASA NTRS1992

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Chitsomboon, Tawit↗
NASA NTRS2019

Matrix Exponential in C/C++ Version of Vector Radiative Transfer Code IPOL

We use only left eigenvectors to evaluate the matrix exponential in the method of discrete ordinates for the vector radiative transfer equation, which neglects circular polarization, in a plane-parallel atmosphere. This is contrary to a common practice of using the right eigenvectors to evaluate the matrix exponential combined with the left eigenvectors to avoid the inversion of the matrix of the right ones. Two numerical tests for Rayleigh and Aerosol scattering confirm our idea. For better explanation of our approach and for independent crosscheck of our results, we distribute an example in C/C++.

Sergey Korkin↗
NASA NTRS2019

Meshless Local Petrov-Galerkin (MLPG) Method with Orthogonal Polynomials for Euler-Bernoulli Beam Problems

In this paper, the feasibility of orthogonal polynomials in the meshless local Petrov Galerkin method (MLPG) method is studied. The orthogonal polynomials, Chebyshev and Legendre polynomials, are used in this MLPG method as trial functions. The test functions used were power functions with smooth derivatives at their ends. The performance of these methods is studied by applying these methods to Euler-Bernoulli beam problems. The MLPG-Galerkin and Legendre methods passed all the patch tests for simple beam problems. Next the formulations are tested on complex beam problems such as beams with partial loadings and continuous beam problems. Problems with load discontinuities and additional supports require special attention. Near discontinuities, judicious choice of number of nodes and nodal placements are needed to obtain accurate deflections, slopes, moments and shear forces. As polynomial functions are used, the large number of nodes can create a transformation matrix that is ill-conditioned, resulting in problems with the inversion of the matrix. The conditioning worsens as the number of nodes are increased beyond 20. Quadruple precision was needed for models to obtain accurate solutions. Even with quadruple precision the accuracy of the method suffers as the number of nodes is increased beyond 20. This appears to be a drawback of the MLPG-Chebyshev and MLPG-Legendre methods.

Raju, Ivatury S.↗
NASA NTRS1972

On estimating the Venus spin vector

The improvement in spin vector and probe position estimates one may reasonably expect from the processing of such data is indicated. This was done by duplicating the ensemble calculations associated with a weighed least squares with a priori estimation technique applied to range rate data that were assumed to be unbiased and uncorrelated. The weighting matrix was assumed to be the inverse of the covariance matrix of the noise on the data. Attention is focused primarily on the spin vector estimation.

Argentiero, P. D.↗
NASA NTRS1993

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Fijany, Amir↗
NASA NTRS2011

Constraint Embedding Technique for Multibody System Dynamics

Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with closure-constraints into an equivalent tree-topology system, and thus allows one to take advantage of the host of techniques available to the latter class of systems. This technology is highly suitable for the class of multibody systems where the closure-constraints are local, i.e., where they are confined to small groupings of bodies within the system. Important examples of such local closure-constraints are constraints associated with four-bar linkages, geared motors, differential suspensions, etc. One can eliminate these closure-constraints and convert the system into a tree-topology system by embedding the constraints directly into the system dynamics and effectively replacing the body groupings with virtual aggregate bodies. Once eliminated, one can apply the well-known results and algorithms for tree-topology systems to solve the dynamics of such closed-chain system.

Woo, Simon S.↗
NASA NTRS1984

A solution of Mx(double dot) + Cx(dot) + Kx = 0 applicable to the design of active dampers

A solution is presented for the equations of motion for the damped linear oscillator, Mx(double dot) + Cx(dot) + Kx = 0. The algorithm solves a transformed set of equations in terms of the modal variables of the undamped system and, at the same time, solves the adjoint equation of the transformed problem. The adjoint solution is normalized to give the inverse of the solution matrix of the transformed problem. The normalized inverse is useful in design for direct computation of sensitivity derivatives of damping ratios with respect to damping rates. The algorithm is programmed to reduce storage requirements by a factor of three-fourths compared to standard complex eigenvalue subroutines. A numerical example is included.

Thurston, G. A.↗
NASA NTRS1989

Digital restoration of multichannel images

The Wiener solution of a multichannel restoration scheme is presented. Using matrix diagonalization and block-Toeplitz to block-circulant approximation, the inversion of the multichannel, linear space-invariant imaging system becomes feasible by utilizing a fast iterative matrix inversion procedure. The restoration uses both the within-channel (spatial) and between-channel (spectral) correlation; hence, the restored result is a better estimate than that produced by independent channel restoration. Simulations are also presented.

Galatsanos, Nikolas P.↗
NASA NTRS1972

Optimal inputs for system identification

Identification criteria are presented for linear dynamic systems with and without process noise. With process noise, the state equations are replaced by the Kalman filter equations. If the identification performance index is expanded in a Taylor's series with respect to the parameters to be identified, then maximizing the weighting factor of the quadratic term with respect to the inputs will insure that an identification algorithm will converge more rapidly and to a more accurate result than with nonoptimal inputs. The expectation of this weighting factor is the Fisher information matrix, and its inverse is a lower bound for the covariance of the parameters. Direct and indirect methods of calculating the information matrix are presented for systems with and without process noise.

Reid, D. B.↗
NASA NTRS1982

Determination of eigenvalues of dynamical systems by symbolic computation

A symbolic computation technique for determining the eigenvalues of dynamical systems is described wherein algebraic operations, symbolic differentiation, matrix formulation and inversion, etc., can be performed on a digital computer equipped with a formula-manipulation compiler. An example is included that demonstrates the facility with which the system dynamics matrix and the control distribution matrix from the state space formulation of the equations of motion can be processed to obtain eigenvalue loci as a function of a system parameter. The example chosen to demonstrate the technique is a fourth-order system representing the longitudinal response of a DC 8 aircraft to elevator inputs. This simplified system has two dominant modes, one of which is lightly damped and the other well damped. The loci may be used to determine the value of the controlling parameter that satisfied design requirements. The results were obtained using the MACSYMA symbolic manipulation system.

Howard, J. C.↗
NASA NTRS1990

Spatial operator approach to flexible manipulator inverse and forward dynamics

This study extends to flexible multibody manipulators the recent results of the author on the use of spatially recursive filtering and smoothing techniques for robot arm dynamics. The configuration analyzed is that of a mechanical system of flexible bodies joined together by articulated joints. The inverse and forward dynamics problems are solved using the techniques of spatially recursive Kalman filtering and smoothing. The algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. The identities are easily derived using a spatial operator algebra developed by the author.

Rodriguez, G.↗