Search NASA⌕ Search

SEARCH · Search NASA

Results for “operator exponential”

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 325 records · Page 18

Effects of cosine tapering window on quantum phase estimation

Here, we provide a modification to the quantum phase estimation algorithm (QPEA) [Abrams and Lloyd, Phys. Rev. Lett. 83, 5162 (1999); Cleve et al., Proc. R. Soc. A 454, 339 (1998); Nielsen and Chuang, Quantum computation and quantum information, 2002.] inspired by classical windowing methods for spectral density estimation. From this modification we obtain an upper bound in the cost that implies a cubic improvement with respect to the algorithm's error rate. Numerical evaluation of the costs also demonstrates an improvement. Moreover, with similar techniques, we detail an iterative projective measurement method for ground state preparation that gives an exponential improvement over previous bounds using QPEA. Numerical tests that confirm the expected scaling behavior are also obtained. For these numerical tests we have used a lattice Thirring model as testing ground. Using well-known perturbation theory results, we also show how to more appropriately estimate the cost scaling with respect to state error instead of evolution operator error.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Granular Media-Based Tunable Passive Vibration Suppressor

and vibration suppression device is composed of statically compressed chains of spherical particles. The device superimposes a combination of dissipative damping and dispersive effects. The dissipative damping resulting from the elastic wave attenuation properties of the bulk material selected for the granular media is independent of particle geometry and periodicity, and can be accordingly designed based on the dissipative (or viscoelastic) properties of the material. For instance, a viscoelastic polymer might be selected where broadband damping is desired. In contrast, the dispersive effects result from the periodic arrangement and geometry of particles composing a linear granular chain. A uniform (monatomic) chain of statically compressed spherical particles will have a low-pass filter effect, with a cutoff frequency tunable as a function of particle mass, elastic modulus, Poisson fs ratio, radius, and static compression. Elastic waves with frequency content above this cutoff frequency will exhibit an exponential decay in amplitude as a function of propagation distance. System design targeting a specific application is conducted using a combination of theoretical, computational, and experimental techniques to appropriately select the particle radii, material (and thus elastic modulus and Poisson fs ratio), and static compression to satisfy estimated requirements derived for shock and/or vibration protection needs under particular operational conditions. The selection of a chain of polymer spheres with an elastic modulus .3 provided the appropriate dispersive filtering effect for that exercise; however, different operational scenarios may require the use of other polymers, metals, ceramics, or a combination thereof, configured as an array of spherical particles. The device is a linear array of spherical particles compressed in a container with a mechanism for attachment to the shock and/or vibration source, and a mechanism for attachment to the article requiring isolation (Figure 1). This configuration is referred to as a single-axis vibration suppressor. This invention also includes further designs for the integration of the single-axis vibration suppressor into a six-degree-of-freedom hexapod "Stewart"mounting configuration (Figure 2). By integrating each singleaxis vibration suppressor into a hexapod formation, a payload will be protected in all six degrees of freedom from shock and/or vibration. Additionally, to further enable the application of this device to multiple operational scenarios, particularly in the case of high loads, the vibration suppressor devices can be used in parallel in any array configuration.

Dillon, Robert P.↗

Hamiltonian simulation in the low-energy subspace

Abstract We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian H . This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the low-energy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective low-energy norm of H . We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove exponentially decaying upper bounds on the leakage to high-energy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality.

97 MATHEMATICS AND COMPUTING↗

Meta-Study of Particulate Detection Losses on Radioactive Air Sample Filters

Several mathematical relationships between air sample filter mass loading and the correlated analytical self-absorption factor were developed using data from other published research in this meta-study. Gross-alpha and -beta applications are addressed for this research. As filter media becomes loaded with particulate matter, there is potential for measurement losses due to self-absorption by mass loading. Components contributing to absorption include particulate dust, radioactive particulates, and filter material. Standards indicate a correction factor should be used when the penetration of radioactive material into the collection media or self-absorption of radiation by the material collected would reduce the detection rate by more than 5%. Previously, losses due to self-absorption have been reported up to 100% over a range up to ~10 mg∙cm -2 mass loading. These absorption losses then can be used to determine a correction factor for sample results. For low mass loadings (e.g., ≤0.1 mg∙cm -2 ) corrections factors in the 0.85 - 1 range have been recommended and used, while at higher mass loadings nearer to 10 mg∙cm -2 correction factors closer to 0 (representing near 100% losses) are used. Based on data from published studies, the different methods for relating percent loss due to self-absorption to mass loading include linear, exponential, quadratic, and trinomial derived functions. Where applicable, both forced zero and non-forced zero results were evaluated. From the derived functions evaluated, the trinomial function provided the best fit. Once the sample filter mass loading is known, the trinomial function can be applied to estimate losses and the corresponding self-absorption factor. When applied to routine operating conditions for radiological facility stacks monitored at the Pacific Northwest National Laboratory for an average sample filter mass loading of 0.09 ± 0.12 (2σ) mg∙cm -2 (excluding negative values and outliers) and a range from 0 - 0.24 mg∙cm -2 , the estimated trinomial function nominal self-absorption losses are less than 5% at 0.09 mg∙cm -2 and less than 10% at 0.24 mg∙cm -2 . The trinomial function is one method that may be used to adjust the activity results of an air sample when the sample-specific mass loading is determined. The application of no correction factor when the ANSI/HPS N13.1-2021 guidance of a 5% threshold for loss is not reached with typical stack sample mass loadings may be reasonable in high-efficiency particulate air filtered systems. For simplicity, it would be conservative in assigning the self-absorption correction factor at the 5% threshold (i.e., 0.95) for general uses but in cases of heavy mass loading to calculate the factor.

air sampling↗

Investigation of Heat Transfer From

The convective heat transfer from the surface of an ellipsoidal forebody of fineness ratio 3 and 20-inch maximum diameter was investigated in clear air for both stationary and rotating operation over a range of conditions including air speeds up to 240 knots, rotational speeds up to 1200 rpm, and angles of attack of 0 deg, 3 deg, and 6 deg. The results are presented in the form of heat-transfer coefficients and the correlation of Nusselt and Reynolds numbers. Both a uniform surface temperature and a uniform input heater density distribution were used. The experimental results agree well with theoretical predictions for uniform surface temperature distribution. Complete agreement was not obtained with uniform input heat density in the laminar-flow region because of conduction effects. No significant effects of rotation were obtained over the range of airstream and rotational speeds investigated. Operation at angle of attack had only minor effects on the local heat transfer. Transition from laminar to turbulent heat transfer occurred over a wide range of Reynolds numbers. The location of transition depended primarily on surface roughness and pressure and temperature gradients. Limited transient heating data indicate that the variation of surface temperature with time followed closely an exponential relation.

Lewis, James P.↗

Service Life Extension of the Propulsion System of Long-Term Manned Orbital Stations

One of the critical non-replaceable systems of a long-term manned orbital station is the propulsion system. Since the propulsion system operates beginning with the launch of station elements into orbit, its service life determines the service life of the station overall. Weighing almost a million pounds, the International Space Station (ISS) is about four times as large as the Russian space station Mir and about five times as large as the U.S. Skylab. Constructed over a span of more than a decade with the help of over 100 space flights, elements and modules of the ISS provide more research space than any spacecraft ever built. Originally envisaged for a service life of fifteen years, this Earth orbiting laboratory has been in orbit since 1998. Some elements that have been launched later in the assembly sequence were not yet built when the first elements were placed in orbit. Hence, some of the early modules that were launched at the inception of the program were already nearing the end of their design life when the ISS was finally ready and operational. To maximize the return on global investments on ISS, it is essential for the valuable research on ISS to continue as long as the station can be sustained safely in orbit. This paper describes the work performed to extend the service life of the ISS propulsion system. A system comprises of many components with varying failure rates. Reliability of a system is the probability that it will perform its intended function under encountered operating conditions, for a specified period of time. As we are interested in finding out how reliable a system would be in the future, reliability expressed as a function of time provides valuable insight. In a hypothetical bathtub shaped failure rate curve, the failure rate, defined as the number of failures per unit time that a currently healthy component will suffer in a given future time interval, decreases during infant-mortality period, stays nearly constant during the service life and increases at the end when the design service life ends and wear-out phase begins. However, the component failure rates do not remain constant over the entire cycle life. The failure rate depends on various factors such as design complexity, current age of the component, operating conditions, severity of environmental stress factors, etc. Development, qualification and acceptance test processes provide rigorous screening of components to weed out imperfections that might otherwise cause infant mortality failures. If sufficient samples are tested to failure, the failure time versus failure quantity can be analyzed statistically to develop a failure probability distribution function (PDF), a statistical model of the probability of failure versus time. Driven by cost and schedule constraints however, spacecraft components are generally not tested in large numbers. Uncertainties in failure rate and remaining life estimates increase when fewer units are tested. To account for this, spacecraft operators prefer to limit useful operations to a period shorter than the maximum demonstrated service life of the weakest component. Running each component to its failure to determine the maximum possible service life of a system can become overly expensive and impractical. Spacecraft operators therefore, specify the required service life and an acceptable factor of safety (FOS). The designers use these requirements to limit the life test duration. Midway through the design life, when benefits justify additional investments, supplementary life test may be performed to demonstrate the capability to safely extend the service life of the system. An innovative approach is required to evaluate the entire system, without having to go through an elaborate test program of propulsion system elements. Evaluating every component through a brute force test program would be a cost prohibitive and time consuming endeavor. ISS propulsion system components were designed and built decades ago. There are no representative ground test articles for some of the components. A 'test everything' approach would require manufacturing new test articles. The paper outlines some of the techniques used for selective testing, by way of cherry picking candidate components based on failure mode effects analysis, system level impacts, hazard analysis, etc. The type of testing required for extending the service life depends on the design and criticality of the component, failure modes and failure mechanisms, life cycle margin provided by the original certification, operational and environmental stresses encountered, etc. When specific failure mechanism being considered and the underlying relationship of that mode to the stresses provided in the test can be correlated by supporting analysis, time and effort required for conducting life extension testing can be significantly reduced. Exposure to corrosive propellants over long periods of time, for instance, lead to specific failure mechanisms in several components used in the propulsion system. Using Arrhenius model, which is tied to chemically dependent failure mechanisms such as corrosion or chemical reactions, it is possible to subject carefully selected test articles to accelerated life test. Arrhenius model reflects the proportional relationship between time to failure of a component and the exponential of the inverse of absolute temperature acting on the component. The acceleration factor is used to perform tests at higher stresses that allow direct correlation between the times to failure at a high test temperature to the temperatures to be expected in actual use. As long as the temperatures are such that new failure mechanisms are not introduced, this becomes a very useful method for testing to failure a relatively small sample of items for a much shorter amount of time. In this article, based on the example of the propulsion system of the first ISS module Zarya, theoretical approaches and practical activities of extending the service life of the propulsion system are reviewed with the goal of determining the maximum duration of its safe operation.

Kamath, Ulhas↗

Logarithmic spiral grids for image processing

A picture digitization grid based on logarithmic spirals rather than Cartesian coordinates is presented. Expressing this curvilinear grid as a conformal exponential mapping reveals useful image processing properties. The mapping induces a computational simplification that suggests parallel architectures in which most geometric transformations are effected by data shifting in memory rather than arithmetic on coordinates. These include fast, parallel noise-free rotation, scaling, and some projective transformations of pixel defined images. Conformality of the mapping preserves local picture-processing operations such as edge detection.

Weiman, C. F. R.↗

Quick-Mixing Studies Under Reacting Conditions

The low-NO(x) emitting potential of rich-burn/quick-mix/lean-burn )RQL) combustion makes it an attractive option for engines of future stratospheric aircraft. Because NO(x) formation is exponentially dependent on temperature, the success of the RQL combustor depends on minimizing high temperature stoichiometric pocket formation in the quick-mixing section. An experiment was designed and built, and tests were performed to characterize reaction and mixing properties of jets issuing from round orifices into a hot, fuel-rich crossflow confined in a cylindrical duct. The reactor operates on propane and presents a uniform, non-swirling mixture to the mixing modules. Modules consisting of round orifice configurations of 8, 9, 10, 12, 14, and 18 holes were evaluated at a momentum-flux ratio of 57 and jet-to-mainstream mass-flaw ratio of 2.5. Temperatures and concentrations of O2, CO2, CO, HC, and NO(x) were obtained upstream, down-stream, and within the orifice plane to determine jet penetration as well as reaction processes. Jet penetration was a function of the number of orifices and affected the mixing in the reacting system. Of the six configurations tested, the 14-hole module produced jet penetration close to the module half-radius and yielded the best mixing and most complete combustion at a plane one duct diameter from the orifice leading edge. The results reveal that substantial reaction and heat release occur in the jet mixing zone when the entering effluent is hot and rich, and that the experiment as designed will serve to explore satisfactorily jet mixing behavior under realistic reacting conditions in future studies.

Leong, May Y.↗

Application of Reconfigurable Computing Technology to Multi-KiloHertz Micro-Laser Altimeter (MMLA) Data Processing

The Multi-KiloHertz Micro-Laser Altimeter (MMLA) is an aircraft based instrument developed by NASA Goddard Space Flight Center with several potential spaceflight applications. This presentation describes how reconfigurable computing technology was employed to perform MMLA signal extraction in real-time under realistic operating constraints. The MMLA is a "single-photon-counting" airborne laser altimeter that is used to measure land surface features such as topography and vegetation canopy height. This instrument has to date flown a number of times aboard the NASA P3 aircraft acquiring data at a number of sites in the Mid-Atlantic region. This instrument pulses a relatively low-powered laser at a very high rate (10 kHz) and then measures the time-of-flight of discrete returns from the target surface. The instrument then bins these measurements into a two-dimensional array (vertical height vs. horizontal ground track) and selects the most likely signal path through the array. Return data that does not correspond to the selected signal path are classified as noise returns and are then discarded. The MMLA signal extraction algorithm is very compute intensive in that a score must be computed for every possible path through the two dimensional array in order to select the most likely signal path. Given a typical array size with 50 x 6, up to 33 arrays must be processed per second. And for each of these arrays, roughly 12,000 individual paths must be scored. Furthermore, the number of paths increases exponentially with the horizontal size of the array, and linearly with the vertical size. Yet, increasing the horizontal and vertical sizes of the array offer science advantages such as improved range, resolution, and noise rejection. Due to the volume of return data and the compute intensive signal extraction algorithm, the existing PC-based MMLA data system has been unable to perform signal extraction in real-time unless the array is limited in size to one column, This limits the ability of the MMLA to operate in environments with sparse signal returns and a high number of noise return. However, under an IR&D project, an FPGA-based, reconfigurable computing data system has been developed that has been demonstrated to perform real-time signal extraction under realistic operating constraints. This reconfigurable data system is based on the commercially available Firebird Board from Annapolis Microsystems. This PCI board consists of a Xilinx Virtex 2000E FPGA along with 36 MB of SRAM arranged in five separately addressable banks. This board is housed in a rackmount PC with dual 850MHz Pentium processors running the Windows 2000 operating system. This data system performs all signal extraction in hardware on the Firebird, but also runs the existing "software based" signal extraction in tandem for comparison purposes. Using a relatively small amount of the Virtex XCV2000E resources, the reconfigurable data system has demonstrated to improve performance improvement over the existing software based data system by an order of magnitude. Performance could be further improved by employing parallelism. Ground testing and a preliminary engineering test flight aboard the NASA P3 has been performed, during which the reconfigurable data system has been demonstrated to match the results of the existing data system.

Powell, Wesley↗

Diagnosing Barren Plateaus with Tools from Quantum Optimal Control

Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is barren plateaus, where certain circumstances lead to exponentially vanishing gradients. It is common folklore that problem-inspired ansatzes avoid barren plateaus, but in fact, very little is known about their gradient scaling. In this work we employ tools from quantum optimal control to develop a framework that can diagnose the presence or absence of barren plateaus for problem-inspired ansatzes. Such ansatzes include the Quantum Alternating Operator Ansatz (QAOA), the Hamiltonian Variational Ansatz (HVA), and others. With our framework, we prove that avoiding barren plateaus for these ansatzes is not always guaranteed. Specifically, we show that the gradient scaling of the VQA depends on the degree of controllability of the system, and hence can be diagnosed through the dynamical Lie algebra $\mathfrak{g}$ obtained from the generators of the ansatz. We analyze the existence of barren plateaus in QAOA and HVA ansatzes, and we highlight the role of the input state, as different initial states can lead to the presence or absence of barren plateaus. Taken together, our results provide a framework for trainability-aware ansatz design strategies that do not come at the cost of extra quantum resources. Moreover, we prove no-go results for obtaining ground states with variational ansatzes for controllable system such as spin glasses. Our work establishes a link between the existence of barren plateaus and the scaling of the dimension of $\mathfrak{g}$.

97 MATHEMATICS AND COMPUTING↗

Mitigating Interfacial Mismatch between Lithium Metal and Garnet-Type Solid Electrolyte by Depositing Metal Nitride Lithiophilic Interlayer

Solid-state lithium batteries are generally considered as the next-generation battery technology that benefits from inherent nonflammable solid electrolytes and safe harnessing of high-capacity lithium metal. Among various solid-electrolyte candidates, cubic garnet-type Li 7 La 3 Zr 2 O 12 ceramics hold superiority due to their high ionic conductivity (10 –3 to 10 –4 S cm -1 ) and good chemical stability against lithium metal. However, practical deployment of solid-state batteries based on such garnet-type materials has been constrained by poor interfacing between lithium and garnet that displays high impedance and uneven current distribution. Herein, we propose a facile and effective strategy to significantly reduce this interfacial mismatch by modifying the surface of such garnet-type solid electrolyte with a thin layer of silicon nitride (Si 3 N 4 ). This interfacial layer ensures an intimate contact with lithium due to its lithiophilic nature and formation of an intermediate lithium–metal alloy. The interfacial resistance experiences an exponential drop from 1197 to 84.5 Ω cm 2 . Lithium symmetrical cells with Si 3 N 4 -modified garnet exhibited low overpotential and long-term stable plating/stripping cycles at room temperature compared to bare garnet. Furthermore, a hybrid solid-state battery with Si 3 N 4 -modified garnet sandwiched between lithium metal anode and LiFePO 4 cathode was demonstrated to operate with high cycling efficiency, excellent rate capability, and good electrochemical stability. This work represents a significant advancement toward use of garnet solid electrolytes in lithium metal batteries for the next-generation energy storage devices.

25 ENERGY STORAGE↗

Insulator edge voltage gradient effects in spacecraft charging phenomena

Insulating surfaces on geosynchronous satellites were charged by geomagnetic substorms to a point where discharges occur. The electromagnetic pulses from these discharges couple into satellite electronic systems disrupting operations are examined. Laboratory tests conducted on insulator charging have indicated that discharges appear to be initiated at insulator edges where voltage gradients can exist. An experimental investigation was conducted to measure edge voltage gradients on silvered Teflon samples as they are charged by monoenergetic electron beams. It was found that the surface voltage at insulator edges can be approximated by an exponential expression based on an electron current density balance.

Stevens, N. J.↗

Insulator edge voltage gradient effects in spacecraft charging phenomena

Insulating surfaces on geosynchronous satellites have been charged by geomagnetic substorms to a point where discharges occur. The electromagnetic pulses from these discharges couple into satellite electronic systems disrupting operations. Laboratory tests conducted on insulator charging have indicated that discharges appear to be initiated at insulator edges where voltage gradients can exist. An experimental investigation has been conducted to measure edge voltage gradients on silvered Teflon samples as they are charged by monoenergetic electron beams. It has been found that the surface voltage at insulator edges can be approximated by an exponential expression based on an electron current density balance. Using this expression at known breakdown conditions results in a discharge voltage gradient down the insulator edge to ground of about 150,000 V/cm.

Stevens, N. J.↗

Micromachined electron tunneling infrared sensors

The development of an improved Golay cell is reported. This new sensor is constructed entirely from micromachined silicon components. A silicon oxynitride (SiO(x)N(y)) membrane is deflected by the thermal expansion of a small volume of trapped gas. To detect the motion of the membrane, an electron tunneling transducer is used. This sensor detects electrons which tunnel through the classically forbidden barrier between a tip and a surface; the electron current is exponentially dependent on the separation between the tip and the surface. The sensitivity of tunneling transducers constructed was typically better than 10(exp -3) A/square root of Hz. Through use of the electron tunneling transducer, the scaling laws which have prevented the miniaturization of the Golay cell are avoided. This detector potentially offers low cost fabrication, compatibility with silicon readout electronics, and operation without cooling. Most importantly, this detector may offer better sensitivity than any other uncooled infrared sensor, with the exception of the original Golay cell.

Kenny, T. W.↗

Use of Diffusion Bonded Cu Strap and Integrated MLI for Thermal Control of 100 K IR Detector on L’Ralph Instrument

Passive cooling of cryogenic instruments is one of the most challenging aspects of spaceflight thermal control systems. They are highly sensitive to parasitic heat leaks from their warmer environment, especially the spacecraft components. The L’Ralph instrument on the Lucy mission is an example of such a system, with its LEISA detector requiring passive cooling to temperatures below 112 K. MLI performance can be measured in terms of estar, and analysts apply bias between a high and low estar value. This approach works well for conventional MLI at room temperature, however, it can be dangerous when a mission goes through a wide range of temperatures during its lifetime, with estar values increasing exponentially as temperatures get colder. Various estar correlations are presented as well as how L’Ralph is approaching the MLI problem with the use of IMLI. IMLI uses discrete spacers to isolate each layer, and doesn’t require intermediate layers such as dacron netting. This results in estar performance that can be more precisely estimated, and yields valuesaround 0.004 at the 112K operating temperature. L’Ralph is using IMLI on the backside of the radiator, which permits a more effective use of increased radiator area, by minimizing the area dependent heat leak impact from the instrument backloading. The detector is thermally coupled to the radiator via a diffusion bonded Cu strap. The diffusion bonding process chemically bonds the Cu foil ends in order to maximize heat transfer effectiveness across the multiple foils used. Employing a pressure compensation design via the use of Ti blocks and a clamp at the strap ends ensures that as temperatures go colder, pre-load is maintained in order to minimize resistance at the strap ends. The use of both of these technologies, and how they work together are crucial to the success of the L’Ralph thermal control system.

Thermal↗

Simulating large one-dimensional neutral-atom quantum systems

While abstract models of quantum computation assume a closed system of two-level states, practical quantum devices inevitably couple to the environment in some way, creating sources of noise. Understanding the tolerance to noise of specific quantum algorithms run on specific devices is important for determining the feasibility of quantum computing in the current noisy intermediate-scale quantum era. Of particular interest is understanding the noise sensitivity of these devices as more qubits are added to the system. Classical simulations are a useful tool to understand the effects of this noise, but direct classical simulations of open quantum systems are burdened by an exponentially growing cost in the number of qubits and a large local Hilbert space dimension. For onedimensional, shallow circuits, using tensor networks can replace this exponential cost with a linear one and simulate far wider systems than what would normally be available. In this paper, we describe a tensor network simulation of a neutral atom quantum system under the presence of noise, while introducing a purity-preserving truncation technique that compromises between the simplicity of the matrix product state and the positivity of the matrix product density operator. We apply this simulation to a near-optimized iteration of the quantum approximate optimization algorithm on a transverse field Ising model in order to investigate the influence of large system sizes on the performance of the algorithm. We find that while circuits with a large number of qubits fail more often under noise that depletes the qubit population, their outputs on a successful measurement are just as robust under Rydberg atom dissipation or qubit dephasing as smaller systems. However, such circuits might not perform as well under coherent multiqubit errors such as Rydberg atom crosstalk. We also find that the optimized parameters are especially robust to noise, suggesting that a noisier quantum system can be used to find the optimal parameters before switching to a cleaner system for measurements of observables.

Allen, James↗

An approach to multivariable control of manipulators

The paper presents simple schemes for multivariable control of multiple-joint robot manipulators in joint and Cartesian coordinates. The joint control scheme consists of two independent multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative (PD2) terms - implying feedforward from the desired position, velocity and acceleration. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-integral-derivative (PID) type and is designed to achieve pole placement. This controller reduces any initial tracking error to zero as desired and also ensures that robust steady-state tracking of step-plus-exponential trajectories is achieved by the joint angles. Simple and explicit expressions of computation of the feedforward and feedback gains are obtained based on the linearized model of robot dynamics. This leads to computationally efficient schemes for either on-line gain computation or off-line gain scheduling to account for variations in the linearized robot model due to changes in the operating point. The joint control scheme is extended to direct control of the end-effector motion in Cartesian space. Simulation results are given for illustration.

Seraji, H.↗

Shuttle Risk Progression: Use of the Shuttle Probabilistic Risk Assessment (PRA) to Show Reliability Growth

It is important to the Space Shuttle Program (SSP), as well as future manned spaceflight programs, to understand the early mission risk and progression of risk as the program gains insights into the integrated vehicle through flight. The risk progression is important to the SSP as part of the documentation of lessons learned. The risk progression is important to future programs to understand reliability growth and the first flight risk. This analysis uses the knowledge gained from 30 years of operational flights and the current Shuttle PRA to calculate the risk of Loss of Crew and Vehicle (LOCV) at significant milestones beginning with the first flight. Key flights were evaluated based upon historical events and significant re-designs. The results indicated that the Shuttle risk tends to follow a step function as opposed to following a traditional reliability growth pattern where risk exponentially improves with each flight. In addition, it shows that risk can increase due to trading safety margin for increased performance or due to external events. Due to the risk drivers not being addressed, the risk did not improve appreciably during the first 25 flights. It was only after significant events occurred such as Challenger and Columbia, where the risk drivers were apparent, that risk was significantly improved. In addition, this paper will show that the SSP has reduced the risk of LOCV by almost an order of magnitude. It is easy to look back afte r 30 years and point to risks that are now obvious, however; the key is to use this knowledge to benefit other programs which are in their infancy stages. One lesson learned from the SSP is understanding risk drivers are essential in order to considerably reduce risk. This will enable the new program to focus time and resources on identifying and reducing the significant risks. A comprehensive PRA, similar to that of the Shuttle PRA, is an effective tool quantifying risk drivers if support from all of the stakeholders is given.

Hamlin, Teri L.↗