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NASA NTRS1989

A spatial operator algebra for manipulator modeling and control

A recently developed spatial operator algebra, useful for modeling, control, and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanizaton of specific algorithms is greatly simplified. The analytical formulation of the operator algebra, as well as its implementation in the Ada programming language are discussed.

Rodriguez, G.↗

DOE OSTI2024

Effective interactions of the open bosonic string via field theory

Abstract We describe a method to extract an effective Lagrangian description for open bosonic strings, at zero transcendentality. The method relies on a particular formulation of its scattering amplitudes derived from color-kinematics duality. More precisely, starting from a (DF) 2 + YM quantum field theory, we integrate out all the massive degrees of freedom to generate an expansion in the inverse string tensionα′. We explicitly compute the Lagrangian terms through$$ \mathcal{O} $$ O (α′ 4 ), and target the sector of operators proportional toF 4 to all orders inα′.

Physics↗

NASA NTRS1991

A spatial operator algebra for manipulator modeling and control

A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.

Rodriguez, G.↗

NASA NTRS2011

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

Gherlone, Marco↗

DOE OSTI2026

Computing neutrino cross sections from Euclidian responses

Energy integrated neutrino cross sections are integrals of nuclear responses weighted with kinematic prefactors. We decompose the prefactors into a limited set of functions of energy transfer and show the relevant integrals are the moments of the responses, and integrals weighted with $1/(a+ω)^n$ with $n\leq 2$. These can be directly obtained from the Euclidean response, avoiding the need for inversion of the Laplace transform. As a proof of concept we study the procedure with toy-model responses for the quasielastic peak. We show that the different contributions can be straightforwardly organized in terms of relative importance, and how flux-averaged cross sections can be obtained. Using a realistic model for the response and numerical uncertainty we show that it is feasible to obtain the required integrals from the Euclidean response, with large uncertainties only for the third moment. Due to kinematic restrictions, the integrals contain contributions from the unphysical region for neutrino scattering, coming from high-momentum nucleons. We show that (in the absence of two-body currents) robust corrections for this contamination are obtained from the single-nucleon momentum distribution. These results present an opportunity to compute certain neutrino cross sections with ab-initio methods with controlled uncertainties.

Nikolakopoulos, A. [Washington U., Seattle]↗

DOE OSTI2026

Computing neutrino cross sections from Euclidian responses

Nikolakopoulos, A. [Washington U., Seattle]↗

DOE OSTI2020

Comparison of improved TMD and CGC frameworks in forward quark dijet production

For studying small- x gluon saturation in forward dijet production in high-energy dilute-dense collisions, the improved TMD (ITMD) factorization formula was recently proposed. In the Color Glass Condensate (CGC) framework, it represents the leading term of an expansion in inverse powers of the hard scale. It contains the leading-twist TMD factorization formula relevant for small gluon’s transverse momentum k t , but also incorporates an all-order resummation of kinematical twists, resulting in a proper matching to high-energy factorization at large k t . In this paper, we evaluate the accuracy of the ITMD formula quantitatively, for the case of quark dijet production in high-energy proton-proton( p + p ) and proton-nucleus ( p + A ) collisions at LHC energies. We do so by comparing the quark-antiquark azimuthal angle Δ ϕ distribution to that obtained with the CGC formula. For a dijet with each quark momentum p t much larger than the target saturation scale, Q s , the ITMD formula is a good approximation to the CGC formula in a wide range of azimuthal angle. It becomes less accurate as the jet p t ’s are lowered, as expected, due to the presence of genuine higher-twists contributions in the CGC framework, which represent multi-body scattering effects absent in the ITMD formula. We find that, as the hard jet momenta are lowered, the accuracy of ITMD start by deteriorating at small angles, in the high-energy-factorization regime, while in the TMD regime near Δ ϕ = π , very low values of p t are needed to see differences between the CGC and the ITMD formula. In addition, the genuine twists corrections to ITMD become visible for higher values of p t in p + A collisions, compared to p + p collisions, signaling that they are enhanced by the target saturation scale.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1987

Variable structure control of globally feedback-decoupled deformable vehicle maneuvers

The use of Cayley-Rodrigues attitude parameters as kinematic variables is shown to yield a globally linearized and decoupled model of the equations of motion of a deformable body, where the structural deformation state appears only in the coefficients of the inverse transformation. It is shown how commanded multiaxial attitude maneuvers can be encoded as switching surfaces for a variable-structure control implementation of the corresponding computed slew torques, automatically modulated in respnse only to detected angular rate error signs, for accurate tracking in the presence of separately damped or even uncontrolled (but stable) structural deformations.

Dwyer, T. A. W., III↗

NASA NTRS1990

Advanced control schemes and kinematic analysis for a kinematically redundant 7 DOF manipulator

The kinematic analysis and control of a kinematically redundant manipulator is addressed. The manipulator is the slave arm of a telerobot system recently built at Goddard Space Flight Center (GSFC) to serve as a testbed for investigating research issues in telerobotics. A forward kinematic transformation is developed in its most simplified form, suitable for real-time control applications, and the manipulator Jacobian is derived using the vector cross product method. Using the developed forward kinematic transformation and quaternion representation of orientation matrices, we perform computer simulation to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of Jacobian pseudo-inverse for various sampling times. The equivalence between Cartesian velocities and quaternion is also verified using computer simulation. Three control schemes are proposed and discussed for controlling the motion of the slave arm end-effector.

Nguyen, Charles C.↗

NASA NTRS1991

Kinematic analysis of generalized adaptive trusses

Adaptive trusses offer the greatest stiffness and strength for a given weight of any articulated structure or mechanism. Because of this, there are many potential extraterrestrial applications of these variable-geometry trusses, including serpentine manipulators, payload isolation, tracking, pointing and docking mechanisms, and gimbals. All of these applications will require the ability to precisely control the kinematic parameters of the mechanism, including position, velocity, and acceleration. This paper explores the fundamental nature of adaptive trusses by examining the basic truss elements or unit cells. A general method for analyzing forward and inverse motion of all the basic truss units is presented, followed by a more efficient formulation for the octahedral unit cell. Finally, general closed-form techniques are presented for finding velocity, acceleration, and all higher derivatives of truss motion.

Tidwell, Paul H.↗

DOE OSTI2024

UV massive resonance from IR double copy consistency

From the perspective of effective field theory (EFT), Wilson coefficients of the low energy theory are determined by integrating out modes of the full ultraviolet (UV) theory. The spectrum can be in principle resummed if one has access to all available infrared (IR) coefficients at low energies. In this work we show that there exists a general class of consistent massive resonance double-copy (CMRDC) models where UV massive residues are reconstructed through double-copy consistency conditions between the IR Wilson coefficients of the full EFT expansion. Through a color-dual bootstrap, we find surprisingly that double-copy consistency alone introduces the kinematic factors of CMRDC models that soften high energy behavior by exponentiating color-dual contacts. This bootstrap suggests that our massive resonance paradigm is an inevitable consequence of the duality between color and kinematics, thereby providing a path towards emergent UV structure directly from the IR. We then demonstrate how CMRDC models can capture a spectrum of massive modes compatible with general multiplicity, and use Padé extrapolation to solve the inverse problem of identifying massive UV resonance from a small number of IR Wilson coefficients. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Imaging surface topography with coherent x-ray reflectivity: Theory, kinematics, and simulations

A theoretical formalism is described for understanding coherent x-ray reflectivity (CXR) from the surface of a semi-infinite crystal having a variable surface topography, described by the height profile ℎ(𝑥,𝑦). The surface topography is imaged as a complex “effective density,” obtained from the phasing and inversion of the coherent x-ray reflectivity data, measured through a rocking scan centered at a vertical momentum transfer 𝑄$^{0}_{𝑧}$ and a vertical range Δ⁢𝑄 𝑧 . The formalism predicts that the effective density has an amplitude with a maximum located at the surface height for each position within the surface plane. The phase of the effective density has a lateral variation that is controlled by the surface height and a vertical variation that reflects a combination of the interfacial structure and specific choice of measurement conditions. This understanding enables direct observation of nanometer-scale interfacial topography, i.e., ℎ⁡(𝑥,𝑦)⁢𝑐 𝑠 (where 𝑐 𝑠 is the vertical substrate lattice parameter) with Å-scale sensitivity to surface height. Numerical simulations illustrate and confirm the theoretical results. These results show how the interpretation of the interfacial density phase obtained by CXR data inversion (i.e., surface topography with respect to a flat surface) is conceptually similar to that previously known for Bragg coherent diffraction imaging (BCDI) measurements of isolated nanoparticles (i.e., lattice displacements with respect to an ideal crystal lattice). This suggests that CXR can be thought of as a form of dark field imaging with respect to the bright field BCDI approach. An implication of these results is that interfacial imaging may bypass some of the significant challenges associated with BCDI imaging of multiple particles having different orientations.

X-ray imaging↗

NASA NTRS1991

Spatial operator approach to under-actuated manipulator kinematics and dynamics

A study is made of the kinematics and dynamics of under-actuated manipulators. The presence of passive hinges causes the kinematics and dynamics of these manipulators to be considerably more complex when compared with fully actuated manipulators. Techniques from the spatial operator algebra are used to develop expressions for the generalized Jacobian, the mass matrix, and an efficient inverse dynamics computational algorithm.

Jain, A.↗

NASA NTRS1984

Kinematic control of robot with degenerate wrist

Kinematic resolved rate equations allow an operator with visual feedback to dynamically control a robot hand. When the robot wrist is degenerate, the computed joint angle rates exceed operational limits, and unwanted hand movements can result. The generalized matrix inverse solution can also produce unwanted responses. A method is introduced to control the robot hand in the region of the degenerate robot wrist. The method uses a coordinated movement of the first and third joints of the robot wrist to locate the second wrist joint axis for movement of the robot hand in the commanded direction. The method does not entail infinite joint angle rates.

Barker, L. K.↗

NASA NTRS2003

The Rondonia Lightning Detection Network: Network Description, Science Objectives, Data Processing Archival/Methodology, and Results

A four station Advanced Lightning Direction Finder (ALDF) network was established in the state of Rondonia in western Brazil in 1999 through a collaboration of U.S. and Brazilian participants from NASA, INPE, INMET, and various universities. The network utilizes ALDF IMPACT (Improved Accuracy from Combined Technology) sensors to provide cloud-to-ground lightning observations (i.e., stroke/flash locations, signal amplitude, and polarity) using both time-of- arrival and magnetic direction finding techniques. The observations are collected, processed and archived at a central site in Brasilia and at the NASA/Marshall Space Flight Center in Huntsville, Alabama. Initial, non-quality assured quick-look results are made available in near real-time over the Internet. The network, which is still operational, was deployed to provide ground truth data for the Lightning Imaging Sensor (LIS) on the Tropical Rainfall Measuring Mission (TRMM) satellite that was launched in November 1997. The measurements are also being used to investigate the relationship between the electrical, microphysical and kinematic properties of tropical convection. In addition, the long-time series observations produced by this network will help establish a regional lightning climatological database, supplementing other databases in Brazil that already exist or may soon be implemented. Analytic inversion algorithms developed at the NASA/Marshall Space Flight Center have been applied to the Rondonian ALDF lightning observations to obtain site error corrections and improved location retrievals. The data will also be corrected for the network detection efficiency. The processing methodology and the results from the analysis of four years of network operations will be presented.

Blakeslee, R. J.↗

NASA NTRS1999

The Rondonia Lightning Detection Network: Network Description, Science Objectives, Data Processing/Archival Methodology, and First Results

A four station Advanced Lightning Direction Finder (ALDF) network was recently established in the state of Rondonia in western Brazil through a collaboration of U.S. and Brazilian participants from NASA, INPE, INMET, and various universities. The network utilizes ALDF IMPACT (Improved Accuracy from Combined Technology) sensors to provide cloud-to-ground lightning observations (i.e., stroke/flash locations, signal amplitude, and polarity) using both time-of-arrival and magnetic direction finding techniques. The observations are collected, processed and archived at a central site in Brasilia and at the NASA/Marshall Space Flight Center (MSFC) in Huntsville, Alabama. Initial, non-quality assured quick-look results are made available in near real-time over the internet. The network will remain deployed for several years to provide ground truth data for the Lightning Imaging Sensor (LIS) on the Tropical Rainfall Measurement Mission (TRMM) satellite which was launched in November 1997. The measurements will also be used to investigate the relationship between the electrical, microphysical and kinematic properties of tropical convection. In addition, the long-term observations from this network will contribute in establishing a regional lightning climatological data base, supplementing other data bases in Brazil that already exist or may soon be implemented. Analytic inversion algorithms developed at NASA/MSFC are now being applied to the Rondonian ALDF lightning observations to obtain site error corrections and improved location retrievals. The processing methodology and the initial results from an analysis of the first 6 months of network operations will be presented.

Blakelee, Richard↗

NASA NTRS1999

The Rondonia Lightning Detection Network: Network Description, Science Objectives, Data Processing/Archival Methodology, and First Results

A four station Advanced Lightning Direction Finder (ALDF) network was recently established in the state of Rondonia in western Brazil through a collaboration of U.S. and Brazilian participants from NASA, INPE, INMET, and various universities. The network utilizes ALDF IMPACT (Improved Accuracy from Combined Technology) sensors to provide cloud-to-ground lightning observations (i.e., stroke/flash locations, signal amplitude, and polarity) using both time-of-arrival and magnetic direction finding techniques. The observations are collected, processed and archived at a central site in Brasilia and at the NASA/ Marshall Space Flight Center (MSFC) in Huntsville, Alabama. Initial, non-quality assured quick-look results are made available in near real-time over the internet. The network will remain deployed for several years to provide ground truth data for the Lightning Imaging Sensor (LIS) on the Tropical Rainfall Measuring Mission (TRMM) satellite which was launched in November 1997. The measurements will also be used to investigate the relationship between the electrical, microphysical and kinematic properties of tropical convection. In addition, the long-term observations from this network will contribute in establishing a regional lightning climatological data base, supplementing other data bases in Brazil that already exist or may soon be implemented. Analytic inversion algorithms developed at NASA/Marshall Space Flight Center (MSFC) are now being applied to the Rondonian ALDF lightning observations to obtain site error corrections and improved location retrievals. The processing methodology and the initial results from an analysis of the first 6 months of network operations will be presented.

Blakeslee, Rich↗

NASA NTRS1991

Development of advanced control schemes for telerobot manipulators

To study space applications of telerobotics, Goddard Space Flight Center (NASA) has recently built a testbed composed mainly of a pair of redundant slave arms having seven degrees of freedom and a master hand controller system. The mathematical developments required for the computerized simulation study and motion control of the slave arms are presented. The slave arm forward kinematic transformation is presented which is derived using the D-H notation and is then reduced to its most simplified form suitable for real-time control applications. The vector cross product method is then applied to obtain the slave arm Jacobian matrix. Using the developed forward kinematic transformation and quaternions representation of the slave arm end-effector orientation, computer simulation is conducted to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of the Jacobian pseudo-inverse for various sampling times. In addition, the equivalence between Cartesian velocities and quaternion is also verified using computer simulation. The motion control of the slave arm is examined. Three control schemes, the joint-space adaptive control scheme, the Cartesian adaptive control scheme, and the hybrid position/force control scheme are proposed for controlling the motion of the slave arm end-effector. Development of the Cartesian adaptive control scheme is presented and some preliminary results of the remaining control schemes are presented and discussed.

Nguyen, Charles C.↗