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NASA NTRS1994

A meteorological interpretation of the Arctic Boundary Layer Expedition (ABLE) 3B flight series

The Arctic Boundary Layer Expedition (ABLE) 3B was conducted to determine the summertime tropospheric distribution, sources, and sinks of important trace gas and aerosol species over the wetlands and boreal forests of central and eastern Canada. Isentropic trajectories and analyzed midtropospheric circulation patterns were used to group flights according to the transport histories of polar, midlatitude, or tropical air masses which were sampled. These data were then divided into bands of potential temperature levels representing the low, middle, and maximum aircraft altitudes to assess the effects of both local and long distance transport and natural and man-made pollutants to the measured chemical species. Detailed case studies are provided to depict the complex three-dimensional airflow regimes that transported air with differing chemical signatures to the study area. Mission 6 details the large-scale movement of smoke in the generally prevailing west to northwesterly airflow that was observed on the majority of flights. Mission 1 analyzes the horizontal and vertical motions of maritime Pacific air in the upper troposphere that was routinely mixed downward to the aircraft altitude. Finally, mission 14 tracks the far northward excursion of tropical air that had been associated with a Pacific typhoon. The following three factors all had important influences on the collected chemical data sets: (1) local and distant stratospheric in puts into the upper and middle troposphere; (2) biomass-burning plumes from active fires in Alaska and Canada; (3) a band of 'low ozone' upper tropospheric air that was observed by airborne differential absorption lidar (DIAL) above the aircraft maximum altitude. Other modification factors observed on some flights included urban pollution from U.S. and Canadian cities, tropical air that had been associated with a Pacific typhoon, and precipitation scavenging by clouds and rain. Many flights were affected by several of the above factors which led to complex chemical signatures that will be discussed in other companion papers.

Shipham, Mark C.↗

NASA NTRS1993

Telerobot local-remote control architecture for space flight program applications

The JPL Supervisory Telerobotics (STELER) Laboratory has developed and demonstrated a unique local-remote robot control architecture which enables management of intermittent communication bus latencies and delays such as those expected for ground-remote operation of Space Station robotic systems via the Tracking and Data Relay Satellite System (TDRSS) communication platform. The current work at JPL in this area has focused on enhancing the technologies and transferring the control architecture to hardware and software environments which are more compatible with projected ground and space operational environments. At the local site, the operator updates the remote worksite model using stereo video and a model overlay/fitting algorithm which outputs the location and orientation of the object in free space. That information is relayed to the robot User Macro Interface (UMI) to enable programming of the robot control macros. This capability runs on a single Silicon Graphics Inc. machine. The operator can employ either manual teleoperation, shared control, or supervised autonomous control to manipulate the intended object. The remote site controller, called the Modular Telerobot Task Execution System (MOTES), runs in a multi-processor VME environment and performs the task sequencing, task execution, trajectory generation, closed loop force/torque control, task parameter monitoring, and reflex action. This paper describes the new STELER architecture implementation, and also documents the results of the recent autonomous docking task execution using the local site and MOTES.

Zimmerman, Wayne↗

NASA NTRS1991

Rapid near-optimal aerospace plane trajectory generation and guidance

Problems associated with onboard trajectory optimization, propulsion system cycle selection, and the synthesis of guidance laws are addressed for ascent to low earth orbit of an airbreathing, single-stage-to-orbit vehicle. A multicycle propulsion system is assumed that incorporates turbojet, ramjet, scramjet, and rocket engines. An energy state approximation is applied to a singularly perturbed, four-state dynamic model for flight of a point mass over a spherical nonrotating earth. An algorithm is then derived for generating both the fuel-optimal climb profile and the guidance commands required to follow that profile. In particular, analytic switching conditions are derived that, under appropriate assumptions, efficiently govern optimal transition from one propulsion cycle to another. The algorithm proves to be computationally efficient and suitable for real-time implementation. The paper concludes with the presentation of representative numerical results that illustrate the nature of the fuel-optimal climb paths and the tracking performance of the guidance algorithm.

Corban, J. E.↗

NASA NTRS2006

On the Rates of Coronal Mass Ejections: Remote Solar and In Situ Observations

We compare the rates of coronal mass ejections (CMEs) as inferred from remote solar observations and interplanetary CMEs (ICMEs) as inferred from in situ observations at both 1 AU and Ulyssses from 1996 through 2004. We also distinguish between those ICMEs that contain a magnetic cloud (MC) and those that do not. While the rates of CMEs and ICMEs track each other well at solar minimum, they diverge significantly in early 1998, during the ascending phase of the solar cycle, with the remote solar observations yielding approximately 20 times more events than are seen at 1 AU. This divergence persists through 2004. A similar divergence occurs between MCs and non-MC ICMEs. We argue that these divergences are due to the birth of midlatitude active regions, which are the sites of a distinct population of CMEs, only partially intercepted by Earth, and we present a simple geometric argument showing that the CME and ICME rates are consistent with one another. We also acknowledge contributions from (1) an increased rate of high-latitude CMEs and (2) focusing effects from the global solar field. While our analysis, coupled with numerical modeling results, generally supports the interpretation that whether one observes a MC within an ICME is sensitive to the trajectory of the spacecraft through the ICME (i.e., an observational selection effect), one result directly contradicts it. Specifically, we find no systematic offset between the latitudinal origin of ICMEs that contain MCs at 1 AU in the ecliptic plane and that of those that do not.

Riley, Pete↗

NASA NTRS2015

HSRL-2 Observations of Aerosol Variability During an Aerosol Build-up Event in Houston and Comparisons With WRF-Chem

The NASA Langley airborne multi-wavelength High Spectral Resolution Lidar (HSRL-2) provides vertical distribution of aerosol optical properties as curtains of aerosol extinction, backscatter and depolarization along the flight track, plus intensive properties that are used to infer aerosol type and external mixing of types. Deployed aboard the NASA Langley King Air on the DISCOVER-AQ field mission in Houston in September 2013, HSRL-2 flew a pattern that included 18 ground sites, repeated four times a day, coordinated with a suite of airborne in situ measurements. The horizontally and vertically resolved curtains of HSRL-2 measurements give an unparalleled view of the spatial and temporal variability of aerosol, which provide broad context for interpreting other measurements and models. Detailed comparisons of aerosol extinction are made with the WRF-Chem chemical transport model along the HSRL-2 flight path. The period from Sept. 11-14 is notable for a large aerosol build-up and persistent smoke layers. We investigate the aerosol properties using the vertically resolved HSRL-2 measurements and aerosol typing analysis plus WRFChem model tracers and back trajectories, and modeling of humidification effects.

Burton, Sharon P.↗

NASA NTRS1998

Minimization of Retinal Slip Cannot Explain Human Smooth-Pursuit Eye Movements

Existing models assume that pursuit attempts a direct minimization of retinal image motion or "slip" (e.g. Robinson et al., 1986; Krauzlis & Weisberger, 1989). Using occluded line-figure stimuli, we have previously shown that humans can accurately pursue stimuli for which perfect tracking does not zero retinal slip (Neurologic ARCO). These findings are inconsistent with the standard control strategy of matching eye motion to a target-motion signal reconstructed by adding retinal slip and eye motion, but consistent with a visual front-end which estimates target motion via a global spatio-temporal integration for pursuit and perception. Another possible explanation is that pursuit simply attempts to minimize slip perpendicular to the segments (and neglects parallel "sliding" motion). To resolve this, 4 observers (3 naive) were asked to pursue the center of 2 types of stimuli with identical velocity-space descriptions and matched motion energy. The line-figure "diamond" stimulus was viewed through 2 invisible 3 deg-wide vertical apertures (38 cd/m2 equal to background) such that only the sinusoidal motion of 4 oblique line segments (44 cd/m2 was visible. The "cross" was identical except that the segments exchanged positions. Two trajectories (8's and infinity's) with 4 possible initial directions were randomly interleaved (1.25 cycles, 2.5s period, Ax = Ay = 1.4 deg). In 91% of trials, the diamond appeared rigid. Correspondingly, pursuit was vigorous (mean Again: 0.74) with a V/H aspect ratio approx. 1 (mean: 0.9). Despite a valid rigid solution, the cross however appeared rigid in 8% of trials. Correspondingly, pursuit was weaker (mean Hgain: 0.38) with an incorrect aspect ratio (mean: 1.5). If pursuit were just minimizing perpendicular slip, performance would be the same in both conditions.

Stone, Leland S.↗

NASA NTRSDate not supplied

Characterization of Large Drop Velocity in the NASA Icing Research Tunnel

This paper presents experimental work conducted in the Icing Research Tunnel at NASA Glenn Research Center to characterize the velocity of large drops in the test section. Some icing spray clouds with large drops were generated with Mod1 nozzles at low nozzle air pressure of 2 to 4 psig for various tunnel air speeds. Drop diameters and drop velocities were measured via high-resolution imaging with a Particle Imaging Particle Tracking Velocimetry probe developed by Artium Technologies. The probe was mounted at four different locations aligned with the centerline of the test section from near the end of the contraction to the constant height test section part of the tunnel. CFD analyses were performed. It showed that the probe head geometry affects the local air flow in the measurement area of the probe between the prongs and in front of the probe. Initial analysis of the air velocity data during the test also indicated that the probe mounting stand has blockage effect on the local tunnel air velocity measurement by a pitot-static probe affixed on the mounting plate next to the stand. Those findings were later verified in the Icing Research Tunnel using a new pitot-static probe design with a linear motion system to measure the local tunnel air velocity with and without the probe. As a result, additional drop trajectory simulations were performed with the airflow moving towards the probe head with a Langmuir-D 7-bin distribution cloud containing large drops. The simulation results helped identify a critical drop-size threshold of 300 μm above which the velocities of larger drops are negligibly affected by the adverse pressure gradient generated by the probe head due to their large drop inertia. From the dimensional analysis of the drop velocity measurement data obtained, it showed that at the tunnel test section reference location a generalized empirical correlation was developed for the non-dimensional drop velocity as a function of the non-dimensional corrected drop diameter independent of the actual spraybar pressure settings and the tunnel air speeds. The generalized curve-fit correlation showed that the drop velocity was universally asymptotic to about 86 percent of the corresponding tunnel air speed at the test section reference location for the largest drop diameter captured by the probe. Further evaluation of this correlation is recommended to assess its applicability for Supercooled Large Drop icing scaling applications in the Icing Research Tunnel.

SLD↗

NASA NTRSDate not supplied

Linear Covariance Techniques to Analyze a Multi-Vehicle, Multi-GN&C System with Applications to Rendezvous in a Near Rectilinear Halo Orbit

Typically for a rendezvous and docking scenario, only a single vehicle is considered the active vehicle. As a result, the target vehicle’s GN&C system is typically not a factor in the integrated performance analysis as it assumes a passive role. However, for upcoming NASA Artemis missions the active vehicle is both the chaser and target spacecraft. In addition, both vehicles are cooperating with one another, sharing telemetry data, and relying on data extracted from the GN&C system of the other. The process also includes a team of ground support personnel in mission control are tracking and monitoring each spacecraft uplinking state estimates and targeting solutions to support mission operations and enhance the onboard flight system performance. Being able to quickly analyze the impact of both vehicles with two different GN&C systems that also interact with the ground that does its own navigation and targeting uploads is critical. This paper outlines how to perform this rapid analysis using linear covariance techniques and applies them to a rendezvous scenario initiated in low lunar orbit and completed in a Near Rectilinear Halo Orbit (NRHO) representative of the NASA Artemis III mission.

Linear Covariance Analysis↗

NASA NTRS1986

An exact solution for orbit view-periods from a station on a tri-axial ellipsoidal planet

This paper presents the concise exact solution for predicting view-periods to be observed from a masked or unmasked tracking station on a tri-axial ellipsoidal surface. The new exact approach expresses the azimuth and elevation angles of a spacecraft in terms of the station-centered geodetic topocentric coordinates in an elegantly concise manner. A simple and efficient algorithm is developed to avoid costly repetitive computations in searching for neighborhoods near the rise and set times of each satellite orbit for each station. Only one search for each orbit is necessary for each station. Sample results indicate that the use of an assumed spherical earth instead of an 'actual' tri-axial ellipsoidal earth could introduce an error up to a few minutes in a view-period prediction for circular orbits of low or medium altitude. For an elliptical orbit of high eccentricity and long period, the maximum error could be even larger. The analytic treatment and the efficient algorithm are designed for geocentric orbits, but they should be applicable to interplanetary trajectories by an appropriate coordinates transformation at each view-period calculation. This analysis can be accomplished only by not using the classical orbital elements.

Tang, C. C. H.↗

DOE OSTI2019

On the Convergence of the Inexact Running Krasnosel'skii-Mann Method

This letter leverages a framework based on averaged operators to tackle the problem of tracking fixed points associated with maps that evolve over time. In particular, this letter considers the Krasnosel'skii-Mann (KM) method in a settings where: 1) the underlying map may change at each step of the algorithm, thus leading to a 'running' implementation of the KM method, and 2) an imperfect information of the map may be available. An imperfect knowledge of the maps can capture cases where processors feature a finite precision or quantization errors, or the case where (part of) the map is obtained from measurements. The analytical results are applicable to inexact running algorithms for solving optimization problems, whenever the algorithmic steps can be written in the form of (a composition of) averaged operators; examples are provided for inexact running gradient methods and the forward-backward splitting method. Convergence of the average fixed-point residual is investigated for the non-expansive case; linear convergence to a unique fixed-point trajectory is showen in the case of inexact running algorithms emerging from contractive operators.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1993

Dynamics and control of coherent structures in the turbulent wall layer: An overview

We expand the velocity field in the vicinity of the wall in empirical eigenfunctions obtained from experiment. Truncating our system and using Galerkin projection, we obtain a closed set of non-linear ordinary differential equations with ten degrees of freedom. We find a rich dynamical behavior, including in particular a heteroclinic attracting orbit giving rise to intermittency. The intermittent jump from one attracting point to the other resembles in many respects the bursts observed in experiments. Specifically, the time between jumps and the duration of the jumps, is approximately that observed in a burst; the jump begins with the formation of a narrowed and intensified updraft, like the ejection phase of a burst, and is followed by a gentle, diffuse downdraft like the sweep phase of a burst. The magnitude of the Reynolds stress spike produced during a burst is limited by our truncation. The behavior is quite robust, much of it being due to the symmetries present (Aubry's group has examined dimensions up to 128 with persistence of the global behavior). We have examined eigenvalues and coefficients obtained from experiment, and from exact simulation, which differ in magnitude. Similar behavior is obtained in both cases; in the latter case, the heteroclinic orbits connect limit cycles instead of fixed points, corresponding to cross-stream waving of the streamwise rolls. The bifurcation diagram remains structurally similar, but somewhat distorted. The role of the pressure term is made clear - it triggers the intermittent jumps, which otherwise would occur at longer and longer intervals, as the system trajectory is attracted closer and closer to the heteroclinic cycle. The pressure term results in the jumps occurring at essentially random times, and the magnitude of the signal determines the average timing. Stretching of the wall region shows that the model is consistent with observations of polymer drag reduction. Change of the third order coefficients, corresponding to acceleration or deceleration of the mean flow, changes the heteroclinic cycles from attracting to repelling, increasing or decreasing the stability, in agreement with observations. The existence of fixed points is an artifact introduced by the projection; however, a decoupled model still displays the rich dynamics. Numerous assumptions made in Aubry et al. (1988) can now be proved exactly. Feeding back eigenfuncitons with the proper phase can delay the bursting, (the heteroclinic jump to the other fixed point), decreasing the drag. It is also possible to speed up the bursting, increasing mixing to control separation. Our approach is optimal for short time tracking in control.

Berkooz, Gal↗

NASA NTRS2022

Robust Vision-based Multi-spacecraft Guidance Navigation and Control using CNN-based Pose Estimation

In this paper, we present an end-to-end simulation framework for tracking an uncooperative Target spacecraft in Low Earth Orbit using a CubeSat-class Ego spacecraft outfitted with a camera. Currently, capturing high-fidelity realistic images in space for this scenario is difficult and exorbitantly expensive. Therefore, we developed a framework to simulate the spacecraft orbits in Basilisk software and generate high-fidelity realistic images of spacecraft in Unreal Engine, including the effects from Sun, Earth, Moon and stars. The Ego spacecraft uses cameras to capture images of the uncooperative Target and estimates its position and attitude using a CNN based 6DOF pose estimation pipeline, eliminating need for large SWAP-C(Size, Weight, Power and Cost) sensors like LIDAR or reliance on inter-spacecraft communication, This CNN, which is motivated by ESA’s Pose Estimation challenge of 2019, is trained using simulated data from our end-to-end simulation framework. We compare the performance of two distinct CNNbased algorithms for pose estimation along a nominal trajectory. In presence of non-Gaussian modeling uncertainties, the statedependent estimation error is characterized with a quadratic upper-bound. The quadratically-bounded error can be used by a robust controller to maneuver

Rahmani, Amir↗

NASA NTRS1993

In-situ radio-metric tracking to support navigation for interplanetary missions with multiple spacecraft

Doppler and ranging measurements between spacecraft can be obtained only when the ratio of the total received signal power to noise power density (P(sub t/N(sub 0)) at the receiving spacecraft is sufficiently large that reliable signal detection can be achieved within a reasonable time period. In this paper, the requirements on P(sub t)/N(sub 0) for reliable carrier signal detection is calculated as a function of various system parameters, including characteristics of the spacecraft computing hardware and a priori uncertainty in spacecraft-spacecraft relative velocity and acceleration. Also calculated is the P(sub t)/N(sub 0) requirement for relaible detection of a ranging signal, consistting of a carrier with pseudo-noise phase modulation. Once the P(sub t)/N(sub 0) requirement is determined, then for a given set of assumed spacecraft telecommunication characteristics (transmitted signal power, antenna gains, receiver noise temperatures) it is possible to calculate the maximum range at which a carrier signal or ranging signal may be acquired. A brief error covariance analysis has been conducted to illustrate the utility of in situ Doppler and ranging measurements for Mars approach navigation. The results indicate that navigation accuracies of a few kilometers can be achieved with either data type. The analysis also illustrates dependency of the achievable accuracy on the approach trajectory velocity.

Kahn, Robert D.↗

NASA NTRS2003

Software for Allocating Resources in the Deep Space Network

TIGRAS 2.0 is a computer program designed to satisfy a need for improved means for analyzing the tracking demands of interplanetary space-flight missions upon the set of ground antenna resources of the Deep Space Network (DSN) and for allocating those resources. Written in Microsoft Visual C++, TIGRAS 2.0 provides a single rich graphical analysis environment for use by diverse DSN personnel, by connecting to various data sources (relational databases or files) based on the stages of the analyses being performed. Notable among the algorithms implemented by TIGRAS 2.0 are a DSN antenna-load-forecasting algorithm and a conflict-aware DSN schedule-generating algorithm. Computers running TIGRAS 2.0 can also be connected using SOAP/XML to a Web services server that provides analysis services via the World Wide Web. TIGRAS 2.0 supports multiple windows and multiple panes in each window for users to view and use information, all in the same environment, to eliminate repeated switching among various application programs and Web pages. TIGRAS 2.0 enables the use of multiple windows for various requirements, trajectory-based time intervals during which spacecraft are viewable, ground resources, forecasts, and schedules. Each window includes a time navigation pane, a selection pane, a graphical display pane, a list pane, and a statistics pane.

Wang, Yeou-Fang↗

NASA NTRSDate not supplied

BioSentinel: NASA’s First Deep Space Biological Mission

Since Apollo 17 in 1972, NASA has sent no humans or other biological organisms outside of Earth’s protective magnetosphere. NASA’s current Artemis program plans to put astronauts back on the Moon and eventually land human missions on Mars. One of the major challenges to long-duration crewed travel and habitation in deep space is an in-depth understanding of the biological effects of space radiation, often convoluted by the impact of reduced gravity. Such missions will require significant countermeasures, likely both technological and biomedical, to protect organisms from chronic radiation exposure. Small satellite missions like CubeSats can inform these countermeasures by investigating model organisms in relevant space environments. The BioSentinel mission is comprised of four segments developed at NASA Ames Research Center: a 6U CubeSat (1U = 10-cm cube), an ISS payload launched in December 2021 and two ground units, one for the mission’s CubeSat and one for the ISS payload. The last three segments have been operational since January 2022 and serve as experimental controls. BioSentinel’s 6U CubeSat is planned to launch as a secondary payload on the Artemis-1 rocket. It will be deployed on a lunar fly-by trajectory and into a heliocentric orbit. BioSentinel will be the first interplanetary satellite to study the biological response to space radiation outside Low Earth Orbit (LEO) in almost 50 years. BioSentinel is a complete, autonomous spacecraft capable of conducting experiments in deep space. Its 4U BioSensor payload is a fully automated and adaptable platform that can perform biological measurements with a range of microorganisms in multiple space environments, including the ISS, free flyers, and other platforms like the Lunar Gateway and lander vehicles. Once it reaches its orbit, BioSentinel’s CubeSat will measure the DNA damage response to ambient radiation in a model organism, the budding yeast Saccharomyces cerevisiae, which will be compared to information provided by an onboard radiation sensor and to data obtained in LEO (on ISS) and on Earth. Once in interplanetary space, fluidic cards containing desiccated yeast will be activated by growth medium addition at different time points throughout the mission. Growth and metabolic activity will be tracked continuously via optical measurements. This paper describes BioSentinel’s objectives, science, data management, and preliminary results from the ISS and ISS ground control segments.

BioSentinel↗

NASA NTRSDate not supplied

BioSentinel: NASA’s First Deep Space Biological Mission

BioSentinel↗

DOE OSTI2019

Modelling Curvilinear Beamline Effects on Beam- and Spin-Dynamics in the Fermilab Muon g-2 Storage Ring.

A model of the Fermilab Muon g-2 Experiment storage ring is developed with the BMAD simulation library for beam- and spin-dynamics studies. Particular focus is given to the electrostatic quadrupoles, the plates of which follow the curvature of the particle design trajectory of the magnetically uniform storage ring. To model these, standard electric multipoles and a novel method based on cylindrical harmonics are investigated and found to accurately match the electric field maps produced for the bulk and fringe regions of the curved quadrupoles respectively, despite these methods being specifically for straight beamlines. The toroidal multipole description is then developed, to include curvature and longitudinal field variations (to model the fringe field regions). Various combinations of the different descriptions (including use of the field maps) are used for the bulk and fringe fields of the quadrupoles, and the toroidal multipoles are found to provide the best agreement with the measured tunes of the storage ring. Two integrators are also developed, based on the method of Wu, Forest and Robin. The first of these describes motion in a uniform magnetic dipole field with arbitrary electric field, and produces results comparable to those of the adaptive-step fourth-order Runge–Kutta integrator implemented in BMAD, suitable for tracking over thousands of turns. The second is a generalisation of the first to arbitrary magnetic vector potentials superimposed on that of the uniform dipole, with arbitrary electric fields, and was also found to agree with the Runge–Kutta integrator. Simulations of antimuon storage for 2000 turns of the storage ring were performed, where losses were studied along with the evolution of beam polarisation. The storage losses, important for reducing the systematic error in the measurement of the muon g-2, were found to be largely due to collimator shape. The correlation between momentum and spin precession frequency reflect the effects expected from the electric field correction in the T-BMT equation, on the order of 10 -6 . Particle injection was also studied, for various injection angles, quadrupole strengths and strengths of injection kick, and in the cases where experimental data was provided, the model was found to be consistent with the experiment.

43 PARTICLE ACCELERATORS↗

NASA NTRS1991

System monitoring and diagnosis with qualitative models

A substantial foundation of tools for model-based reasoning with incomplete knowledge was developed: QSIM (a qualitative simulation program) and its extensions for qualitative simulation; Q2, Q3 and their successors for quantitative reasoning on a qualitative framework; and the CC (component-connection) and QPC (Qualitative Process Theory) model compilers for building QSIM QDE (qualitative differential equation) models starting from different ontological assumptions. Other model-compilers for QDE's, e.g., using bond graphs or compartmental models, have been developed elsewhere. These model-building tools will support automatic construction of qualitative models from physical specifications, and further research into selection of appropriate modeling viewpoints. For monitoring and diagnosis, plausible hypotheses are unified against observations to strengthen or refute the predicted behaviors. In MIMIC (Model Integration via Mesh Interpolation Coefficients), multiple hypothesized models of the system are tracked in parallel in order to reduce the 'missing model' problem. Each model begins as a qualitative model, and is unified with a priori quantitative knowledge and with the stream of incoming observational data. When the model/data unification yields a contradiction, the model is refuted. When there is no contradiction, the predictions of the model are progressively strengthened, for use in procedure planning and differential diagnosis. Only under a qualitative level of description can a finite set of models guarantee the complete coverage necessary for this performance. The results of this research are presented in several publications. Abstracts of these published papers are presented along with abtracts of papers representing work that was synergistic with the NASA grant but funded otherwise. These 28 papers include but are not limited to: 'Combined qualitative and numerical simulation with Q3'; 'Comparative analysis and qualitative integral representations'; 'Model-based monitoring of dynamic systems'; 'Numerical behavior envelopes for qualitative models'; 'Higher-order derivative constraints in qualitative simulation'; and 'Non-intersection of trajectories in qualitative phase space: a global constraint for qualitative simulation.'

Kuipers, Benjamin↗