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NASA NTRS2017

Computationally Efficient Motion Planning Algorithms for Agile Autonomous Vehicles in Cluttered Environments

Fast, real-time motion planning of an agile, autonomous vehicle in a cluttered environment, with many geometrically-fixed obstacles, is a very complex problem, especially because of the vehicle dynamics constraints and resource constrained computational capabilities onboard the vehicle. In this paper, we present computationally-efficient versions of our novel motion planning algorithm called the Spherical Expansion and Sequential Convex Programming (SE–SCP) algorithm. The SE–SCP algorithm first uses a spherical-expansion-based randomized sampling algorithm to explore the workspace. Oncea path is found from the start position to the goal position, the algorithm computes a locally optimal trajectory, within its homotopy class for a desired cost function, by solving a sequence of convex optimization problems. Thus, the SE–SCP algorithm is anytime locally optimal and the trajectory is globally optimal if the number of samples tends to infinity. In this paper, we further enhance the computational efficiency of the SE–SCP algorithm using uni-directional and bi-directional rewiring techniques. We also present a detailed proof of the local optimality characteristics of the new SE–SCP algorithms for aspecial case of vehicle dynamics. Simulation examples involving quadrotor and spacecraft help demonstrate the effectiveness of our new algorithms.

Bandyopadhyay, Saptarshi↗
NASA NTRS1986

Observational constraints on bending the wide-angle tailed radio galaxy 1919+479

A wide range of new observations of the wide-angle tailed radio galaxy 1919+479 and its environs are presented. Multifrequency and multiconfiguration VLA observations are described, ranging in resolution from 0.7 arcsec to 40 arcsec. Distributions of source structures at different scale sizes, spectral indices, and polarizations are presented. Wide-field photographic and CCD imaging data are presented along with a review of the measured galaxy redshifts in the field. A newly reprocessed Einstein IPC X-ray image of the cluster is shown, and the X-ray emission's relationship to the radio morphology is described. The radio, optical, and X-ray data are used to constrain the cD galaxy dynamics and models for bending the radio structure. In particular, the possible role of jet collisions with clouds in the intracluster medium is considered. The applicability of cloud collision models to wide-angle tails in general is considered.

Burns, J. O.↗
NASA NTRS1992

Plio-Pleistocene time evolution of the 100-ky cycle in marine paleoclimate records

To constrain theories for the dynamical evolution of global ice mass through the late Neogene, it is important to determine whether major changes in the record were gradual or rapid. Of particular interest is the evolution of the near 100-ky ice age cycle in the middle Pleistocene. We have applied a new technique based on multiple taper spectrum analysis which allows us to model the time evolution of quasi-periodic signals. This technique uses both phase and amplitude information, and enables us to address the question of abrupt versus gradual onset of the 100-ky periodicity in the middle Pleistocene.

Park, Jeffrey↗
NASA NTRS1994

Measurement of Residual Flexibility for Substructures Having Prominent Flexible Interfaces

Verification of a dynamic model of a constrained structure requires a modal survey test of the physical structure and subsequent modification of the model to obtain the best agreement possible with test data. Constrained-boundary or fixed-base testing has historically been the most common approach for verifying constrained mathematical models, since the boundary conditions of the test article are designed to match the actual constraints in service. However, there are difficulties involved with fixed-base testing, in some cases making the approach impractical. It is not possible to conduct a truly fixed-base test due to coupling between the test article and the fixture. In addition, it is often difficult to accurately simulate the actual boundary constraints, and the cost of designing and constructing the fixture may be prohibitive. For use when fixed-base testing proves impractical or undesirable, alternate free-boundary test methods have been investigated, including the residual flexibility technique. The residual flexibility approach has been treated analytically in considerable detail and has had limited frequency response measurements for the method. This concern is well-justified for a number of reasons. First, residual flexibilities are very small numbers, typically on the order of 1.0E-6 in/lb for translational diagonal terms, and orders of magnitude smaller for off-diagonal values. This poses difficulty in obtaining accurate and noise-free measurements, especially for points removed from the excitation source. A second difficulty encountered in residual measurements lies in obtaining a clean residual function in the process of subtracting synthesized modal data from a measured response function. Inaccuracies occur since modes are not subtracted exactly, but only to the accuracy of the curve fits for each mode; these errors are compounded with increasing distance from the excitation point. In this paper, the residual flexibility method is applied to a simple structure in both test and analysis. Measured and predicted residual functions are compared, and regions of poor data in the measured curves are described. It is found that for accurate residual measurements, frequency response functions having prominent stiffness lines in the acceleration/force format are needed. The lack of such stiffness lines increases measurement errors. Interface drive point frequency respose functions for shuttle orbiter payloads exhibit dominant stiffness lines, making the residual test approach a good candidate for payload modal tests when constrained tests are inappropriate. Difficulties in extracting a residual flexibility value from noisy test data are discussed. It is shown that use of a weighted second order least-squares curve fit of the measured residual function allows identification of residual flexibility that compares very well with predictions for the simple structure. This approach also provides an estimate of second order residual mass effects.

Tinker, Michael L.↗
NASA NTRS1994

Utilitarian models of the solar nebula

Models of the primitive solar nebula based on a combination of theory, observations of T Tauri stars, and global conservation laws are presented. The models describe the motions of nebular gas, mixing of interstellar material during the formation of the nebula, and evolution of thermal structure in terms of several characteristic parameters. The parameters describe key aspects of the protosolar cloud (its rotation rate and collapse rate) and the nebula (its mass relative to the Sun, decay time, and density distribution). For most applications, the models are heuristic rather than predicted. Their purpose is to provide a realistic context for the interpretation of solar system data, and to distinquish those nebular characteristics that can be specified with confidence, independently of the assumtions of particular models, form those that are poorly constrained. It is demonstrated that nebular gas typically experienced large radial excursions during the evolution of the nebula and that both inward and outward mean radial velocities on the order of meters per second occured in the terrestrial planet region, with inward velocities predominant for most ofthe evolution. However, the time history of disk size, surface density, and radial velocities are sensitive to the total angular momentun of the protosolar cloud, which cannot be constrained by purely theoretical considerations.It is shown that a certain amount of 'formational' mixing of interstellar material was an inevitable consequenc of nebular mass and angular momentum transport during protostellar collapse, regardless of the specific transport mechanisms invloved. Even if the protosolar cloud was initially homogeneous, this mixing was important because it had the effect of mingling presolar material that had experienced different degrees of thermal processing during collapse and passage through the accertion shock. Nebular thermal structure is less sensitive to poorly constrained parameters than is dynamical history. A simple criterion is derived for the condition that silicate grains are evaporated at midplane, and it is argued that this condition was probably fulfilled early in nebular history. Cooling of a hot nebula due tocoagulation of dust and consequent local reduction of optical depth is examined, and it is shown how such a process leads naturally to an enrichment of rock-forming elements in the gas phase.

Cassen, Patrick↗
NASA NTRS1999

Seasonal-to-Interannual Variability in Antarctic Sea-Ice Dynamics, and Its Impact on Surface Fluxes and Water Mass Production

Strong seasonal and interannual signals in Antarctic bottom-water outflow remain unexplained yet are highly correlated with anomalies in net sea-ice growth in coastal polynyas. The mechanisms responsible for driving salination and replenishment and rejuvenation of the dense shelf "source" waters likely also generate pulses of bottom water outflow. The objective of this research is to investigate time-scales of variability in the dynamics of sea-ice in the Southern Ocean in order to determine the primary sites for production of dense shelf waters. We are using a merged satellite/buoy sea-ice motion data set for the period 1978-present day to compute the dynamics of opening and closing of coastal polynyas over the continental shelf. The Ocean Circulation and Climate Advanced Model (OCCAM) ocean general circulation model with coupled sea-ice dynamics is presently forced using National Center for Environmental Prediction (NCEP) data to simulate fluxes and the salination impact of the ocean shelf regions. This work is relevant in the context of measuring the influence of polar sea-ice dynamics upon polar ocean characteristics, and thereby upon global thermohaline ocean circulation. Interannual variability in simulated net freezing rate in the Southern Weddell Sea is shown for the period 1986-1993. There is a pronounced maximum of ice production in 1988 and minimum in 1991 in response to anomalies in equatorward meridional wind velocity. This follows a similar approximate 8-year interannual cycle in Sea Surface Temperature (SST) and satellite-derived ice-edge anomalies reported elsewhere as the "Antarctic Circumpolar Wave." The amplitude of interannual fluctuations in annual net ice production are about 40% of the mean value, implying significant interannual variance in brine rejection and upper ocean heat loss. Southward anomalies in wind stress induce negative anomalies in open water production, which are observed in passive microwave satellite images. Thus, cycles of enhanced poleward wind stress reduce ice growth by compacting the ice along the coastline and closing open water in leads and polynyas. Model simulations confirm that years of low ice production, such as 1991, coincide with years of lower than normal bottom water outflow. Future plans include the assimilation of satellite ice concentrations and ice drift dynamics to more accurately constrain boundary conditions in the model.

Drinkwater, Mark R.↗
NASA NTRS2013

Explicit Low-Thrust Guidance for Reference Orbit Targeting

The problem of a low-thrust spacecraft controlled to a reference orbit is addressed in this paper. A simple and explicit low-thrust guidance scheme with constrained thrust magnitude is developed by combining the fundamental equations of motion for constrained systems from analytical dynamics with a Lyapunov-based method. Examples are given for a spacecraft controlled to a reference trajectory in the circular restricted three body problem.

low-thrust guidance↗
NASA NTRS1982

Constrained and unconstrained modes - Some modeling aspects of flexible spacecraft

Spacecraft that are partially rigid and partially flexible may be dynamically modeled in terms of either 'constrained' modes of vibration, for which the rigid part is held motionless, or the 'unconstrained' modes of the whole vehicle. A model 'completeness index' is defined for each expansion and used as a truncation criterion. Using as an example a large flexible platform with a rigid body at the center, it is shown that as the rigid portion of the vehicle becomes very small, a great many constrained modes are needed to achieve satisfactory model completeness. Otherwise, one finds an erroneous distribution of angular momentum among the modes. It is also shown that the importance of unconstrained modes is not necessarily ordered by frequency.

Hablani, H. B.↗
NASA NTRS2012

Direct Detection and Orbit Analysis of the Exoplanets HR 8799 bcd from Archival 2005 Keck/NIRC2 Data

We present previously unpublished July 2005 H-band coronagraphic data of the young, planet-hosting star HR 8799 from the newly-released Keck/NIRC2 archive. Despite poor observing conditions, we detect three of the planets (HR 8799 bcd), two of them (HR 8799 bc) without advanced image processing. Comparing these data with previously published 1998-2011 astrometry and that from re-reduced October 2010 Keck data constrains the orbits of the planets. Analyzing the planets' astrometry separately, HR 8799 d's orbit is likely inclined at least 25 deg from face-on and the others may be on in inclined orbits. For semimajor axis ratios consistent with a 4:2:1 mean-motion resonance our analysis yields precise values for HR 8799 bcd's orbital parameters and strictly constrains the planets' eccentricities to be less than 0.18-0.3. However, we find no acceptable orbital solutions with this resonance that place the planets in face-on orbits; HR 8799 d shows the largest deviation from such orbits. Moreover, few orbits make HR 8799 d coplanar with b and c, whereas dynamical stability analyses used to constrain the planets' masses typically assume coplanar and/or fare.on orbits. This paper illustrates the significant science gain enabled with the release of the NIRC2 archive.

Currie, Thayne↗
NASA NTRS2007

Influences of Local Sea-Surface Temperatures and Large-scale Dynamics on Monthly Precipitation Inferred from Two 10-year GCM-Simulations

Two parallel sets of 10-year long: January 1, 1982 to December 31, 1991, simulations were made with the finite volume General Circulation Model (fvGCM) in which the model integrations were forced with prescribed sea-surface temperature fields (SSTs) available as two separate SST-datasets. One dataset contained naturally varying monthly SSTs for the chosen period, and the oth& had the 12-monthly mean SSTs for the same period. Plots of evaporation, precipitation, and atmosphere-column moisture convergence, binned by l C SST intervals show that except for the tropics, the precipitation is more strongly constrained by large-scale dynamics as opposed to local SST. Binning data by SST naturally provided an ensemble average of data contributed from disparate locations with same SST; such averages could be expected to mitigate all location related influences. However, the plots revealed: i) evaporation, vertical velocity, and precipitation are very robust and remarkably similar for each of the two simulations and even for the data from 1987-ENSO-year simulation; ii) while the evaporation increased monotonically with SST up to about 27 C, the precipitation did not; iii) precipitation correlated much better with the column vertical velocity as opposed to SST suggesting that the influence of dynamical circulation including non-local SSTs is stronger than local-SSTs. The precipitation fields were doubly binned with respect to SST and boundary-layer mass and/or moisture convergence. The analysis discerned the rate of change of precipitation with local SST as a sum of partial derivative of precipitation with local SST plus partial derivative of precipitation with boundary layer moisture convergence multiplied by the rate of change of boundary-layer moisture convergence with SST (see Eqn. 3 of Section 4.5). This analysis is mathematically rigorous as well as provides a quantitative measure of the influence of local SST on the local precipitation. The results were recast to examine the dependence of local rainfall on local SSTs; it was discernible only in the tropics. Our methodology can be used for computing relationship between any forcing function and its effect(s) on a chosen field.

Sud, Y. C.↗
NASA NTRS2022

Electromagnetic Time and Wavelength Domain Predictions for Accreting Binary Black Holes

Accreting massive binary black holes in gaseous environments are keymulti-messenger sources for the LISA mission. We will present some ofthe latest predictions of the observational signatures of accreting binary black holes across the electromagnetic spectrum from the fieldand provide some of our own. In particular, we will provide a briefsummary of the progress made in our group to understand these systemstheoretically using high-performance simulations of generalrelativistic magnetohydrodynamics (MHD) and dynamic spacetimes.Simulating these systems realistically is challenging asradiation-coupled MHD must be considered over large dynamic ranges inspace and time. Constraining our view to the circumbinary disk regionfirst, we will show how the evolution duration, accretion disk size,mass ratio, and thermodynamics model affect the structure andvariability of the accretion flow. We particularly emphasize how theseparameters influence the over-density feature, or "lump", which orbitsthe binary near the edge of the cavity, since it is responsible formost of the electromagnetic emission's variability---a key signatureof a system being a binary. Extending to smaller length scales, wewill report on simulations following accretion all the down to theevent horizons so that we may begin to investigate how black hole spinaffects mini-disk dynamics, accretion rate, and jet power. We willalso report on our radiative transfer predictions for how black holespin alters the spectral energy distribution of these systems.Wrapping up, we will itemize the remaining key theoreticaltechnologies and directions needed to be accomplished to betterunderstand these sources, and assess strategies for searching for themin the coming decade.

Scott C Noble↗
NASA NTRS2013

Initial Assessment of a Variable-Camber Continuous Trailing-Edge Flap System on a Rigid Wing for Drag Reduction in Subsonic Cruise

In this paper, we describe an initial optimization study of a Variable-Camber Continuous Trailing-Edge Flap (VCCTEF) system. The VCCTEF provides a light-weight control system for aircraft with long flexible wings, providing efficient high-lift capability for takeoff and landing, and greater efficiency with reduced drag at cruising flight by considering the effects of aeroelastic wing deformations in the control law. The VCCTEF system is comprised of a large number of distributed and individually-actuatable control surfaces that are constrained in movement relative to neighboring surfaces, and are non-trivially coupled through structural aeroelastic dynamics. Minimzation of drag results in a constrained, coupled, non-linear optimization over a high-dimension search space. In this paper, we describe the modeling, analysis, and optimization of the VCCTEF system control inputs for minimum drag in cruise. The purpose of this initial study is to quantify the expected benefits of the system concept. The scope of this analysis is limited to consideration of a rigid wing without structural flexibility in a steady-state cruise condition at various fuel weights. For analysis, we developed an optimization engine that couples geometric synthesis with vortex-lattice analysis to automate the optimization procedure. In this paper, we present and describe the VCCTEF system concept, optimization approach and tools, run-time performance, and results of the optimization at 20%, 50%, and 80% fuel load. This initial limited-scope study finds the VCCTEF system can potentially gain nearly 10% reduction in cruise drag, provides greater drag savings at lower operating weight, and efficiency is negatively impacted by the severity of relative constraints between control surfaces.

trailing edge flaps↗
NASA NTRS1988

Passive damping for space truss structures

Theoretical and experimental studies of passive damping techniques in truss-type structures are presented, with emphasis on the use of viscoelastic damping in the parallel load path. The constraining member length is shown to be a convenient design variable for enhancing damping performance. Results are presented for integral damping members made of thin-wall aluminum tubes, concentric constraining members, and viscoelastic materials in a six-bay truss structure at low frequency and low dynamic strain conditions. Integral members with graphite/epoxy constraining members exhibited relatively low damping values due to the possible polymer interaction during the cocure stage.

Chen, Gun-Shing↗
NASA NTRS2017

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗
NASA NTRS2011

Constraining the Absolute Orientation of eta Carinae's Binary Orbit: A 3-D Dynamical Model for the Broad [Fe III] Emission

We present a three-dimensional (3-D) dynamical model for the broad [Fe III] emission observed in Eta Carinae using the Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS). This model is based on full 3-D Smoothed Particle Hydrodynamics (SPH) simulations of Eta Car's binary colliding winds. Radiative transfer codes are used to generate synthetic spectro-images of [Fe III] emission line structures at various observed orbital phases and STIS slit position angles (PAs). Through a parameter study that varies the orbital inclination i, the PA(theta) that the orbital plane projection of the line-of-sight makes with the apastron side of the semi-major axis, and the PA on the sky of the orbital axis, we are able, for the first time, to tightly constrain the absolute 3-D orientation of the binary orbit. To simultaneously reproduce the blue-shifted emission arcs observed at orbital phase 0.976, STIS slit PA = +38deg, and the temporal variations in emission seen at negative slit PAs, the binary needs to have an i approx. = 130deg to 145deg, Theta approx. = -15deg to +30deg, and an orbital axis projected on the sky at a P A approx. = 302deg to 327deg east of north. This represents a system with an orbital axis that is closely aligned with the inferred polar axis of the Homunculus nebula, in 3-D. The companion star, Eta(sub B), thus orbits clockwise on the sky and is on the observer's side of the system at apastron. This orientation has important implications for theories for the formation of the Homunculus and helps lay the groundwork for orbital modeling to determine the stellar masses.

Madura, T. I.↗
NASA NTRS1975

Tracking performance under time sharing conditions with a digit processing task: A feedback control theory analysis

A one dimensional compensatory tracking task and a digit processing reaction time task were combined in a three phase experiment designed to investigate tracking performance in time sharing. Adaptive techniques, elaborate feedback devices, and on line standardization procedures were used to adjust task difficulty to the ability of each individual subject and manipulate time sharing demands. Feedback control analysis techniques were employed in the description of tracking performance. The experimental results show that when the dynamics of a system are constrained, in such a manner that man machine system stability is no longer a major concern of the operator, he tends to adopt a first order control describing function, even with tracking systems of higher order. Attention diversion to a concurrent task leads to an increase in remnant level, or nonlinear power. This decrease in linearity is reflected both in the output magnitude spectra of the subjects, and in the linear fit of the amplitude ratio functions.

Gopher, D.↗
NASA NTRS1991

Friction damping of two-dimensional motion and its application in vibration control

This paper presents an approximate method for analyzing the two-dimensional friction contact problem so as to compute the dynamic response of a structure constrained by friction interfaces. The friction force at the joint is formulated based on the Coulomb model. The single-term harmonic balance scheme, together with the receptance approach of decoupling the effect of the friction force on the structure from those of the external forces has been utilized to obtain the steady state response. The computational efficiency and accuracy of the method are demonstrated by comparing the results with long-term time solutions.

Menq, C.-H.↗
NASA NTRS1991

Stratospheric processes: Observations and interpretation

Explaining the observed ozone trends discussed in an earlier update and predicting future trends requires an understanding of the stratospheric processes that affect ozone. Stratospheric processes occur on both large and small spatial scales and over both long and short periods of time. Because these diverse processes interact with each other, only in rare cases can individual processes be studied by direct observation. Generally the cause and effect relationships for ozone changes were established by comparisons between observations and model simulations. Increasingly, these comparisons rely on the developing, observed relationships among trace gases and dynamical quantities to initialize and constrain the simulations. The goal of this discussion of stratospheric processes is to describe the causes for the observed ozone trends as they are currently understood. At present, we understand with considerable confidence the stratospheric processes responsible for the Antarctic ozone hole but are only beginning to understand the causes of the ozone trends at middle latitudes. Even though the causes of the ozone trends at middle latitudes were not clearly determined, it is likely that they, just as those over Antarctica, involved chlorine and bromine chemistry that was enhanced by heterogeneous processes. This discussion generally presents only an update of the observations that have occurred for stratospheric processes since the last assessment (World Meteorological Organization (WMO), 1990), and is not a complete review of all the new information about stratospheric processes. It begins with an update of the previous assessment of polar stratospheres (WMO, 1990), followed by a discussion on the possible causes for the ozone trends at middle latitudes and on the effects of bromine and of volcanoes.

Brune, William H.↗