Search NASA⌕ Search

SEARCH · Search NASA

Results for “inequality”

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 145 records · Page 8

A global approach to kinematic path planning to robots with holonomic and nonholonomic constraints

Robots in applications may be subject to holonomic or nonholonomic constraints. Examples of holonomic constraints include a manipulator constrained through the contact with the environment, e.g., inserting a part, turning a crank, etc., and multiple manipulators constrained through a common payload. Examples of nonholonomic constraints include no-slip constraints on mobile robot wheels, local normal rotation constraints for soft finger and rolling contacts in grasping, and conservation of angular momentum of in-orbit space robots. The above examples all involve equality constraints; in applications, there are usually additional inequality constraints such as robot joint limits, self collision and environment collision avoidance constraints, steering angle constraints in mobile robots, etc. The problem of finding a kinematically feasible path that satisfies a given set of holonomic and nonholonomic constraints, of both equality and inequality types is addressed. The path planning problem is first posed as a finite time nonlinear control problem. This problem is subsequently transformed to a static root finding problem in an augmented space which can then be iteratively solved. The algorithm has shown promising results in planning feasible paths for redundant arms satisfying Cartesian path following and goal endpoint specifications, and mobile vehicles with multiple trailers. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima.

Divelbiss, Adam↗

Numerical methods for multibody systems

This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.

Glowinski, Roland↗

Analytical investigations in aircraft and spacecraft trajectory optimization and optimal guidance

A collection of analytical studies is presented related to unconstrained and constrained aircraft (a/c) energy-state modeling and to spacecraft (s/c) motion under continuous thrust. With regard to a/c unconstrained energy-state modeling, the physical origin of the singular perturbation parameter that accounts for the observed 2-time-scale behavior of a/c during energy climbs is identified and explained. With regard to the constrained energy-state modeling, optimal control problems are studied involving active state-variable inequality constraints. Departing from the practical deficiencies of the control programs for such problems that result from the traditional formulations, a complete reformulation is proposed for these problems which, in contrast to the old formulation, will presumably lead to practically useful controllers that can track an inequality constraint boundary asymptotically, and even in the presence of 2-sided perturbations about it. Finally, with regard to s/c motion under continuous thrust, a thrust program is proposed for which the equations of 2-dimensional motion of a space vehicle in orbit, viewed as a point mass, afford an exact analytic solution. The thrust program arises under the assumption of tangential thrust from the costate system corresponding to minimum-fuel, power-limited, coplanar transfers between two arbitrary conics. The thrust program can be used not only with power-limited propulsion systems, but also with any propulsion system capable of generating continuous thrust of controllable magnitude, and, for propulsion types and classes of transfers for which it is sufficiently optimal the results of this report suggest a method of maneuvering during planetocentric or heliocentric orbital operations, requiring a minimum amount of computation; thus uniquely suitable for real-time feedback guidance implementations.

Markopoulos, Nikos↗

A Geometrical Approach to Bell's Theorem

Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

Rubincam, David Parry↗

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Barth, Timothy↗

On-Board Generation of Three-Dimensional Constrained Entry Trajectories

A methodology for very fast design of 3DOF entry trajectories subject to all common inequality and equality constraints is developed. The approach make novel use of the well known quasi-equilibrium glide phenomenon in lifting entry as a center piece for conveniently enforcing the inequality constraints which are otherwise difficulty to handle. The algorithm is able to generate a complete feasible 3DOF entry trajectory, given the entry conditions, values of constraint parameters, and final conditions in about 2 seconds on a PC. Numerical simulations with the X-33 vehicle model for various entry missions to land at Kennedy Space Center will be presented.

Shen, Zuojun↗

Changes in ratio of soluble sugars and free amino nitrogen in the apical meristem during floral transition of tobacco

Under a modification of the nutrient diversion hypothesis, we propose that an inequality in carbohydrate and nitrogen translocation to the apical meristem may be a controlling factor in floral transition. Experiments were conducted in controlled-environment chambers to determine the associations between microscopic characteristics of the transition from vegetative to floral stages of the apical meristem of flue-cured tobacco and to assimilate concentrations in the plant and apical meristem. Low temperature, nitrogen withdrawal, and restriction of nitrogen uptake were used as treatment variables. In all of these stress treatments, flowering occurred at a lesser number of leaves than in control treatments. Low temperature stress accelerated the time of transition to the floral stage as compared with a high temperature control; however, nitrogen stress did not accelerate the time of transition. All stress treatments affected the levels of nitrogen and carbohydrate in whole plants. Most notable was an increase in the percentage of starch and a decrease in the percentage of total soluble carbohydrate induced by the stress treatments. These data indicate that tobacco plants under stress accumulate excess carbohydrate in the form of starch. An apparent inequality in the relative concentrations of carbohydrate and nitrogen in the apical meristem was observed in all treatments at the time of floral transition and is in support of the nutrient diversion hypothesis.

NASA Discipline Number 61-10↗

Kalman Filter Constraint Tuning for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.

Simon, Dan↗

Constrained Kalman Filtering Via Density Function Truncation for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops an analytic method of incorporating state variable inequality constraints in the Kalman filter. The resultant filter truncates the PDF (probability density function) of the Kalman filter estimate at the known constraints and then computes the constrained filter estimate as the mean of the truncated PDF. The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is demonstrated via simulation results obtained from a turbofan engine model. The turbofan engine model contains 3 state variables, 11 measurements, and 10 component health parameters. It is also shown that the truncated Kalman filter may be a more accurate way of incorporating inequality constraints than other constrained filters (e.g., the projection approach to constrained filtering).

Simon, Dan↗

DEVELOP Poster: Louisville Urban Development

Greenness and land surface temperature (LST) have been extensively correlated to urban public health. Chronic diseases such as diabetes, asthma, and cardiovascular illnesses have been linked to regions of high LST and areas lacking urban green spaces. One of our partners, the University of Louisville Envirome Institute, champions the importance of urban green spaces. Their research has pioneered efforts in increasing the area and accessibility of urban parks and greenspaces as a way to improve public health and combat environmental inequality. Louisville, Kentucky, is currently working to plant and manage urban trees. Our team used NASA Landsat 8 Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS) imagery to calculate the Normalized Difference Vegetation Index (NDVI) in Louisville at the census tract level and automated the process for use in other cities. The New York University School of Medicine’s City Health Dashboard displays public health metrics across 500 US cities and will use our methods to complete the NDVI analysis for all of these locations plus an additional 293 cities they are adding to their dashboard in the near future. Our NDVI and LST calculations will allow cites across the US to make informed decisions about reducing environmental inequality by focusing on areas with low NDVI and high LST.

Urban Development↗

Spatial Variation of Fine Particulate Matter Levels in Nairobi Before and During the COVID-19 Curfew: Implications for Environmental Justice

The temporary decrease of fine particulate matter (PM(sub 2.5)) concentrations in many parts of the world due to the COVID-19 lockdown spurred discussions on urban air pollution and health. However there has been little focus on sub-Saharan Africa, as few African cities have air quality monitors and if they do, these data are often not publicly available. Spatial differentials of changes in PM(sub 2.5) concentrations as a result of COVID also remain largely unstudied. To address this gap, we use a serendipitous mobile air quality monitoring deployment of eight Sensirion SPS 30 sensors on motorbikes in the city of Nairobi starting on 16 March 2020, before a COVID-19 curfew was imposed on 25 March and continuing until 5 May 2020. We developed a random-forest model to estimate PM(sub 2.5) surfaces for the entire city of Nairobi before and during the COVID-19 curfew. The highest PM(sub 2.5) concentrations during both periods were observed in the poor neighborhoods of Kariobangi, Mathare, Umoja, and Dandora, located to the east of the city center. Changes in PM(sub 2.5) were heterogeneous over space. PM(sub 2.5) concentrations increased during the curfew in rapidly urbanizing, the lower-middle-class neighborhoods of Kahawa, Kasarani, and Ruaraka, likely because residents switched from LPG to biomass fuels due to loss of income. Our results indicate that COVID-19 and policies to address it may have exacerbated existing air pollution inequalities in the city of Nairobi. The quantitative results are preliminary, due to sampling limitations and measurement uncertainties, as the available data came exclusively from low-cost sensors. This research serves to highlight that spatial data that is essential for understanding structural inequalities reflected in uneven air pollution burdens and differential impacts of events like the COVID pandemic. With the help of carefully deployed low cost sensors with improved spatial sampling and at least one reference-quality monitor for calibration, we can collect data that is critical for developing targeted interventions that address environmental injustice in the African context.

Environmental justice↗

Demonstration of a Compact Franson Interferometer for Highly Non-degenerate Time-energy Entangled Photons

We present results from a time-energy entanglement Bell inequality violation measurement of two highly non-degenerate photons using a compact Franson interferometer. The entangled photons are generated via the spontaneous parametric downconversion of a 532 nm pump photon into time-energy and polarization degrees of freedom hyper-entangled 810 nm and 1550 nm photons. The source is a type II periodically poled potassium titanyl phosphate (KTP) crystal with a fiber-coupled input and free-space output. These wavelengths are of particular interest as they lie at the intersection of free-space quantum communication and terrestrial entanglement distribution due to 810 nm undergoing little atmospheric absorption, making it a candidate for satellite to ground quantum links. Furthermore, 1550 nm is capable of directly interfacing with existing telecommunications infrastructure. We report an initial violation of Bell's inequality by more than 3 standard deviations and describe efforts to improve upon this while maintaining stable operation in a low size, weight, and power (SWaP) package.

A J Fallon↗

Wichita Climate II: Quantifying and Mapping Urban Heat to Inform Equitable and Sustainable Urban Planning Initiatives in Wichita, Kansas

Wichita, Kansas is experiencing a host of climate threats, particularly extreme heat manifested through Urban Heat Islands (UHI). Heat is unevenly distributed within cities due to factors such as income inequality, historical discriminatory practices like redlining, and divestment in neighborhoods of color. This leads to less vegetation and more heat-absorbing infrastructure in specific communities. Moreover, adverse effects of heat, including heat-related morbidity and mortality, disproportionately impact populations that experience vulnerability through social inequities and structural discrimination. Heat vulnerability is a combination of the factors of heat exposure, sensitivity, and adaptive capacity, and can be harnessed to guide urban heat interventions. This DEVELOP project partnered with the City of Wichita to understand the spatial distribution and drivers of UHIs and heat vulnerability indicators. The team modeled outcomes of tree cover interventions using Landsat 8’s Thermal Infrared Sensor (TIRS) and Operational Land Imager (OLI), Landsat 9 TIRS-2 and OLI-2, and the International Space Station’s Ecosystem Spaceborne Thermal Radiometer Experiment on the International Space Station (ECOSTRESS) sensor, along with the Integrated Valuation of Ecosystem Services and Tradeoffs (InVEST) Urban Cooling model. The team also leveraged statistical analysis by implementing principal component analysis to develop a heat vulnerability index (HVI) specific to Wichita. Ultimately, the project’s outputs will inform the City of Wichita’s Climate Adaptation and Mitigation Plan, identify priority areas for heat mitigation initiatives, and be used in public-facing communications to educate communities on the impacts of urban heat.

Environmental Justice↗

Extreme copositive quadratic forms. II.

Five-variable extreme copositive quadratic forms, presenting previously unknown forms for application to inequality theory and block design analysis

QUADRATIC EQUATION↗

Spacecraft inertia estimation via constrained least squares

This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

inertia estimation↗

Fuzzy Model-based Pitch Stabilization and Wing Vibration Suppression of Flexible Wing Aircraft.

This paper presents a fuzzy nonlinear controller to regulate the longitudinal dynamics of an aircraft and suppress the bending and torsional vibrations of its flexible wings. The fuzzy controller utilizes full-state feedback with input constraint. First, the Takagi-Sugeno fuzzy linear model is developed which approximates the coupled aeroelastic aircraft model. Then, based on the fuzzy linear model, a fuzzy controller is developed to utilize a full-state feedback and stabilize the system while it satisfies the control input constraint. Linear matrix inequality (LMI) techniques are employed to solve the fuzzy control problem. Finally, the performance of the proposed controller is demonstrated on the NASA Generic Transport Model (GTM).

Stability and Control↗

Switching State-Feedback LPV Control with Uncertain Scheduling Parameters

This paper presents a new method to design Robust Switching State-Feedback Gain-Scheduling (RSSFGS) controllers for Linear Parameter Varying (LPV) systems with uncertain scheduling parameters. The domain of scheduling parameters are divided into several overlapped subregions to undergo hysteresis switching among a family of simultaneously designed LPV controllers over the corresponding subregion with the guaranteed H-infinity performance. The synthesis conditions are given in terms of Parameterized Linear Matrix Inequalities that guarantee both stability and performance at each subregion and associated switching surfaces. The switching stability is ensured by descent parameter-dependent Lyapunov function on switching surfaces. By solving the optimization problem, RSSFGS controller can be obtained for each subregion. A numerical example is given to illustrate the effectiveness of the proposed approach over the non-switching controllers.

Switching LPV control↗

Social Bias in AI and its Implications

Previous studies have documented many different types of biases that exist in artificial intelligence (AI) and machine learning (ML) systems. We reviewed the literature on AI and ML bias with a focus on social implications and found that bias in AI and ML can potentially have harmful social impacts on individuals and/or groups of people. By affecting people differently according to characteristics such as race, gender, or sexual orientation, AI and ML systems may lead to harm by exacerbating social inequities. We recount examples of issues that have occurred in systems that use technology that might be used at NASA and elsewhere so that similar issues might be identified and mitigated in future systems. We also provide interested parties with a gateway into existing work on social bias in AI and ML systems.

artificial intelligence (AI)↗