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At least 145 records · Page 8

Determining Appropriate Risk Remediation Thresholds from Empirical Conjunction Data Using Survival Probability Methods

Satellites sometimes maneuver before conjunctions to remediate the risk of an on-orbit collision. Many missions use probability of collision (P_c) thresholds to decide when such maneuvers should be performed. These thresholds tend to be conservative because of policies that require satellites survive their lifetimes without collision with high confidence (e.g., 99.9%). This study presents a semi-empirical method to estimate remediation P_c thresholds that satisfy such lifetime risk requirements. The formulation combines survival probability analysis with empirical conjunction histories to estimate remediation thresholds as a function of satellite size, remaining on-orbit duration, lifetime collision probability limit, collision consequence, and other parameters.

Risk Remediation↗

Comet and Asteroid Hazard to the Terrestrial Planets

We made computer simulations of orbital evolution for intervals of at least 5-10 Myr of N=2000 Jupiter-crossing objects (JCOs) with initial orbits close to those of real comets with period P less than 10 yr, 500 objects with orbits close to that of Comet 10P, and the asteroids initially located at the 3:1 and 5:2 resonances with Jupiter at initial eccentricity e(sub 0)=0.15 and initial inclination i(sub 0)=10(sup 0). The gravitational influence of all planets, except for Mercury and Pluto, was taken into account (without dissipative factors). We calculated the probabilities of collisions of bodies with the terrestrial planets, using orbital elements obtained with a step equal to 500 yr, and then summarized the results for all bodies, obtaining, the total probability Psigma of collisions with a planet and the total time interval Tsigma during which perihelion distance q of bodies was less than a semimajor axis of the planet. The values of p(sub r) =10(exp 6)Psigma/N and T(sub r)=T/1000 yr (where T=Tsigma/N) are presented in a table together with the ratio r of the total time interval when orbits were of Apollo type (at a greater than 1 AU, q less than 1.017 AU, e less than 0.999) to that of Amor type (1.017 less than q less than 1.33 AU), r(sub 2) is the same as r but for Apollo objects with e less than 0.9. For asteroids we present only results obtained by direct integration, as a symplectic method can give large errors for these resonances.

Ipatov, S. I.↗

Constitutive Relation in Transitional Granular Flows

To study the constitutive behavior of granular materials, the presence of gravity is detrimental. Although empirical relations have been obtained for engineering designs to control granular flows on Earth, it is not known how well these Earthbound relations can be used in another gravity field. Fundamental understanding must be derived to reliably design for granular flows in space exploration. There are two extremes of granular flows of which significant amount of knowledge is available. One deals with a dense and quasi-static situation where the deformation rate nearly vanishes. The other deals with dilute and rapidly fluctuating grain velocities where particle inertia dominates. This project, funded by the NASA Microgravity Fluid Physics Program, aims to study this transitional regime via physical experiments and computer simulations. A conceptual model has been established as described below. There are two natural time scales in a granular flow. One is the travel time between two consecutive collisions and the other is the duration of a collision contact. At a very low shear-rate, the shear-induced particle velocity is low. Hence the travel time between collisions is longer than the contact time between colliding particles. Binary collisions prevail. As the shear-rate increases, the traveling time between collisions reduces and the probability of multiple collisions goes up. These particle groups disperse shortly after and new groups form. When shear-rate is further increased, clusters grow in size due to an increasing chance for free particles to join before groups have the time to disperse. The maximum cluster size may depend on the global concentration and material properties. As the solid concentration approaches zero, the cluster size goes to one particle diameter. The maximum possible cluster size under any condition is the container size, provided that the shear flow is inside a container. The critical shear-rates that dictate the initiation of the multiple contacts, and the size and lifetime of the collision clusters, are functions of the concentration also. A 'regime' theory has been proposed by Babic et al. This theory suggested that both the solid concentration, C, and the non-dimensional shear-rate, B, are important in determining the regimes of the granular constitutive law. Additional information is included in the original extended abstract.

Shen, Hayley H.↗

Multivariate Normality of Cartesian-Framed Covariances: Evaluation and Operational Significance

Collision avoidance relies on representative Cartesian uncertainty volumes in order to calculate probabilities of collision. Among the potential shortcomings of a covariance matrix representation of state errors, the most worrisome is the coordinate mismatch between the Cartesian framework in which these matrices are distributed and the curvilinear path that satellite orbits actually follow. The present study compares curvilinear-based and Cartesian covariance representations for ~50,000 conjunctions to determine the frequency in which significant deviations from Gaussianity are observed, then compares the 2-D Pc result from the Cartesian covariance to a Monte Carlo Pc conducted in element space to assess operational significance.

Lechtenberg, Travis F.↗

Multivariate Normality of Cartesian Frame Covariances: Evaluation and Operational Significance

Collision avoidance relies on representative Cartesian uncertainty volumes in order to calculate probabilities of collision. Among the potential shortcomings of a covariance matrix representation of state errors, the most worrisome is the coordinate mismatch between the Cartesian framework in which these matrices are distributed and the curvilinear path that satellite orbits actually follow. The present study compares curvilinear-based and Cartesian covariance representations for ~50,000 conjunctions to determine the frequency in which significant deviations from Gaussianity are observed, then compares the 2-D Pc result from the Cartesian covariance to a Monte Carlo Pc conducted in element space to assess operational significance.

Lechtenberg, Travis F.↗

Statistical Analysis of Deflation in Covariance and Resultant Pc Values for AQUA, AURA and TERRA

This presentation will display statistical analysis performed for raw conjunction CDMs received for the EOS Aqua, Aura and Terra satellites within the period of February 2015 through July 2016. The analysis performed indicates a discernable deflation in covariance calculated at the JSpOC after the utilization of the dynamic drag consider parameter was implemented operationally in May 2015. As a result, the overall diminution in the conjunction plane intersection of the primary and secondary objects appears to be leading to reduced probability of collision (Pc) values for these conjunction events. This presentation also displays evidence for this theory with analysis of Pc trending plots using data calculated by the SpaceNav CRMS system.

raw conjunction↗

Migration of Trans-Neptunian Objects to a Near-Earth Space

Our estimates of the migration of trans-Neptunian objects (TNOs) to a near-Earth space are based on the results of investigations of orbital evolution of TNOs and Jupiter-crossing objects (JCOs). The orbital evolution of TNOs was considered in many papers. Recently we investigated the evolution for intervals of at least 5-10 Myr of 2500 JCOs under the gravitational influence of all planets, except for Mercury and Pluto (without dissipative factors). In the first series we considered N=2000 orbits near the orbits of 30 real Jupiter-family comets with period P(sub alpha)less than 10 yr, and in the second series we took N=500 orbits close to the orbit of Comet 10P Tempel 2 (alpha=3.1 AU, e=0.53, i=12 deg). We calculated the probabilities of collisions of objects with the terrestrial planets, using orbital elements obtained with a step equal to 500 yr, and then summarized the results for all time intervals and all bodies, obtaining the total probability P(sub sigma) of collisions with a planet and the total time interval T(sub sigma) during which perihelion distance q of bodies was less than a semimajor axis of the planet.

Ipatov, S. I.↗

Orbital Evolution of Jupiter-Family Comets

We investigated the evolution for periods of at least 5-10 Myr of 2500 Jupiter-crossing objects (JCOs) under the gravitational influence of all planets, except for Mercury and Pluto (without dissipative factors). In the first series we considered N=2000 orbits near the orbits of 30 real Jupiter-family comets with period less than 10 yr, and in the second series we took 500 orbits close to the orbit of Comet 10P Tempel 2. We calculated the probabilities of collisions of objects with the terrestrial planets, using orbital elements obtained with a step equal to 500 yr and then summarized the results for all time intervals and all bodies, obtaining the total probability P(sub sigma) of collisions with a planet and the total time interval T(sub sigma) during which perihelion distance of bodies was less than a semimajor axis of the planet. The values of P = 10(exp 6)P(sub sigma)/N and T = T(sub sigma)/1000 yr are presented in Table together with the ratio r of the total time interval when orbits were of Apollo type (at e less than 0.999) to that of Amor type.

Ipatov, S. I.↗

An Investigation Into Transecting Satellites in Future Space Traffic Management Scenarios

The number of satellites expected to populate the near-Earth space environment is set to dramatically increase in the coming decade as new large constellations are approved and deployed. Current strategies for placing new batches of these satellites on orbit often involve launching into an initial orbit, and then performing apogee raising maneuvers to reach a target altitude. Similarly, end-of-life planning for these constellation satellites can consist of de-orbit burns that lower perigee to permit disposal via re-entry. Both the raising and de-orbiting maneuvers can result in the individual satellites traveling in high-eccentricity orbits that have the potential to transect other spacecraft trajectories. While individual large constellations may be able to coexist in separate altitude and inclination bands, having thousands of satellites moving between these bands as new satellites are replaced and old ones are removed could pose additional collision risks. Similar concerns have been raised regarding the impact that large numbers of university-class CubeSats might have in terms of their overall collision risk, especially as these satellites typically do not have propulsion systems for active maneuvering. To assess the impact that transecting satellites might have to future space traffic management strategies, this study explored a variety of future realistic scenarios using a high-fidelity simulation tool. The model can simulate the orbit of tens of thousands of resident space objects (RSOs) simultaneously, to include active satellites, debris, rocket bodies, or even future hypothetical scenarios, using a realistic force model that incorporates non-spherical gravity, atmospheric drag, solar radiation pressure, and more. As the model is run forward in time, various statistics and meta-data are gathered on any predicted conjunction event, providing insight into the nature and frequency of potential collisions, e.g., what size are the two satellites, who operates the satellites, are they active or passive objects, etc. Additional customization is available in terms of how probability of collision is computed, and how the probability ellipsoids and screening volumes are determined. The simulation tool also allows for rule-based maneuvers for active satellites, e.g, given an advance conjunction “warning,” one or both of the satellites can maneuver to a safe distance. A wide range of maneuvers can be implemented using impulsive or low-thrust methods, and the latencies can also be varied, e.g., using maneuver lead times of 48 hours, 24 hours, or 12 hours. Validation of the simulation results is performed against current and historical datasets available, to include comparisons to prior conjunction data messages (CDMs), object properties (mass, volume, etc.), and two-line-element records from both public and internal sources. Using the simulation environment, an assessment on the general risks that transecting satellites might pose for hypothetical future space object environments will be presented. This will involve the simulation of approximately 50,000 new large constellation satellites, in addition to the existing catalog of approximately 20,000 known resident space objects (RSOs), over propagation periods of one month to one year. A description of the simulation methodologies, scenarios evaluated, and validation methods will also be presented, as well as a preliminary assessment of the effectiveness of several candidate maneuver strategies that have the potential to reduce collision risk between active satellites.

Brian Gunter↗

Three CA-Related Covariance Issues and Their Solutions

This presentation addresses three issues that arise in the use of DoD-produced satellite state estimate covariances in the conjunction assessment process: the realism of the provided covariances, how to address correlated error between two satellites' covariance matrices, and how to proceed when a furnished covariance is non-positive-definite. To address the first, DoD has implemented a set of two "consider parameters" with which to alter/expand the covariance to account for atmospheric density forecast error and satellite frontal area uncertainty, the two largest sources of unmodeled position prediction error for LEO orbits; these values are governed by a satellite's orbital parameters and ballistic coefficient histories, as well as the current and predicted space weather situation. This approach substantially improves the realism of the covariance by accounting for expected prediction errors that are not part of the fit process that generates the covariance. The second issue of covariance correlation is a complicated one, but the main shared error source—global atmospheric density error that is common to both satellites can be characterized and, through sensitivity vectors, quantified at the conjunction's time of closest approach and removed from the joint covariance, which is used in the CA probability of collision (Pc) calculation. Finally, while according to the orbit determination theory a non-positive-definite (NPD) covariance is not possible, numerical truncation and covariance interpolation can conspire to produce NPD results, which render the covariance unusable for certain CA risk assessment calculations, such as Monte Carlo Pc determination. Three similar techniques are profiled and the simplest of them recommended as a reasonable remediation technique when NPD covariances are encountered by CA practitioners.

Dynamic Consider Parameter↗

Quantifying Shortcomings in the 2-D Pc Calculation

The probability of collision, Pc, between two Earth-orbiting satellites can often, but not always, be approximated adequately using the "2D-Pc" formulation. The objective is to find a set of "boundary conditions" that ensure the 2D-Pc approximation be sufficiently accurate, so that it may be determined when computationally-intensive Brute Force Monte Carlo1 (BFMC) Pc estimates are required. We critically examine the assumptions used in the formulation of the 2D-Pc approximation and then formulate 2D-Pc boundary condition tests to check if these assumptions are satisfied adequately.

Analysis↗

Trending in Pc Measurements via a Bayesian Zero-Inflated Mixed Model

Two satellites predicted to come within close proximity of one another, usually a high-value satellite and a piece of space debris moving the active satellite is a means of reducing collision risk but reduces satellite lifetime, perturbs satellite mission, and introduces its own risks. So important to get a good statement of the risk of collision in order to determine whether a maneuver is truly necessary. Two aspects of this Calculation of the Probability of Collision (Pc) based on the most recent set of position velocity and uncertainty data for both satellites. Examination of the changes in the Pc value as the event develops. Events should follow a canonical development (Pc vs time to closest approach (TCA)). Helpful to be able to guess where the present data point fits in the canonical development in order to guide operational response.

Conjuction Assessment↗

An Investigation Into Transecting Satellites in Future Space Traffic Management Scenarios

The number of satellites expected to populate the near-Earth space environment is set to dramatically increase in the coming decade as new large constellations are approved and deployed. Current strategies for deploying new batches of these satellites often involve launching into an initial orbit, and then performing apogee raising maneuvers to reach a target altitude. Similarly, end-of-life planning for these constellation satellites can consist of de-orbit burns that lower perigee to permit disposal via re-entry. Both the raising and de-orbiting maneuvers can result in the individual satellites traveling in transecting orbits that have the potential to cross other spacecraft trajectories. While individual large constellations may be able to coexist in separate altitude and inclination bands, having thousands of satellites moving between these bands as new satellites are added and old satellites are removed could pose additional collision risks. Similar concerns have been raised regarding the impact that large numbers of university-class CubeSats might have in terms of their overall collision risk, especially as these satellites typically do not have propulsion systems for active maneuvering. To assess the impact that transecting satellites might have on future space traffic management strategies, this study explored a variety of realistic future scenarios using a high-fidelity simulation tool. The model can simulate the orbit of tens of thousands of resident space objects (RSOs) simultaneously, to include active satellites, debris, rocket bodies, or even future hypothetical satellite constellations, using a realistic force model that incorporates non-spherical gravity, atmospheric drag, and solar radiation pressure, as well as station-keeping. The simulation can be customized to accommodate different methods of calculating the probability of collision, as well as the process for determining probability ellipsoids and screening volumes. This makes it possible to replicate, and compare, different processes used by different spacecraft operators and space situational awareness (SSA) providers. As the model is run forward in time, each conjunction event is recorded, allowing for the analysis of statistics and meta-data related to these events, providing insight into the nature and frequency of potential collisions, such as whether are they active or passive objects, what size are the two objects, and who owns the objects (if known). This information makes it possible to characterize how changes to the status quo affect the number and type of conjunctions that occur, as well as the distributional effects on various types of satellite operators. To assess the general risks that transecting satellites might pose for hypothetical future space object environments, approximately 60,000 new large constellation satellites were considered, in addition to the existing catalog of approximately 7800 known resident space objects (RSOs), over a simulation period of one year. The results indicate that the future space environment will introduce a non-linear increase in conjunction events as the number of RSOs also increase. This will require adjustments to spacecraft fuel budgets in order to conduct the avoidance maneuvers necessary to minimize collision risk, both for existing and new satellites. This increase is due in large part to the higher density of RSOs and the overlap between some constellation orbits. Current catalog objects were shown to require three times more ∆V for collision avoidance (CA) maneuvers in the simulated future environment, and some constellation spacecraft were estimated to devote the majority of their annual ∆V to CA. The impact of small satellites was found to be proportional for the current space environment, and actually decreased in terms of percentage for the future scenario, suggesting that small satellites do not pose an outsized collision risk. Lastly, transecting satellites were found to contribute thousands of additional conjunctions outside of their operational orbit, and may require up to an additional 5% in CA maneuver fuel allocation.

conjunction assessment↗

Investigating and implementing enhancements to the simulation of short-term collision hazards

A software tool, the Relative Collision Matrix (RCM), has been developed to provide a quick-look representation of the shortterm collision hazard to space systems from a fragmentation event in Earth orbit. The software performs multiple fragmentation simulations of space objects to quantify the probability of collision for a satellite or a constellation of satellites nearby. Previously, the results were displayed in a color matrix format which showed the relative hazard of each constellation. The RCM can be used for scientific research and operational assessments even though it was designed for test and evaluation applications. Because of its successful use as an analytical tool, the capabilities of RCM are being extended by enhancing the orbital hazard analysis routines, developing ballistic trajectory hazard analysis routines, and expanding the breakup modeling. Improvements are also being made to the RCM's usability and presentation quality by developing a graphical user interface and by providing graphical animated and nonanimated output.

Huth, Jeffrey S.↗

Real-time hierarchically distributed processing network interaction simulation

The Telerobot Testbed is a hierarchically distributed processing system which is linked together through a standard, commercial Ethernet. Standard Ethernet systems are primarily designed to manage non-real-time information transfer. Therefore, collisions on the net (i.e., two or more sources attempting to send data at the same time) are managed by randomly rescheduling one of the sources to retransmit at a later time interval. Although acceptable for transmitting noncritical data such as mail, this particular feature is unacceptable for real-time hierarchical command and control systems such as the Telerobot. Data transfer and scheduling simulations, such as token ring, offer solutions to collision management, but do not appropriately characterize real-time data transfer/interactions for robotic systems. Therefore, models like these do not provide a viable simulation environment for understanding real-time network loading. A real-time network loading model is being developed which allows processor-to-processor interactions to be simulated, collisions (and respective probabilities) to be logged, collision-prone areas to be identified, and network control variable adjustments to be reentered as a means of examining and reducing collision-prone regimes that occur in the process of simulating a complete task sequence.

Zimmerman, W. F.↗

Operational Implementation of a Pc Uncertainty Construct for Conjunction Assessment Risk Analysis

Earlier this year the NASA Conjunction Assessment and Risk Analysis (CARA) project presented the theoretical and algorithmic aspects of a method to include the uncertainties in the calculation inputs when computing the probability of collision (Pc) between two space objects, principally uncertainties in the covariances and the hard-body radius. The output of this calculation approach is to produce rather than a single Pc value an entire probability density function that will represent the range of possible Pc values given the uncertainties in the inputs and bring CA risk analysis methodologies more in line with modern risk management theory. The present study provides results from the exercise of this method against an extended dataset of satellite conjunctions in order to determine the effect of its use on the evaluation of conjunction assessment (CA) event risk posture. The effects are found to be considerable: a good number of events are downgraded from or upgraded to a serious risk designation on the basis of consideration of the Pc uncertainty. The findings counsel the integration of the developed methods into NASA CA operations.

assessment↗

3D Representation of UAV-obstacle Collision Risk Under Off-nominal Conditions

Safe operations of autonomous unmanned aerial vehicles (UAVs) in low-altitude airspace with beyond visual line-of-sight (BVLOS) flights demand robust risk monitoring of airspace as well as of people and property on ground. One of the safety critical factors for UAV flights is the risk of collision with static and dynamic obstacles in proximity to its flight path. This paper presents a detailed formulation of risk of obstacle collision incorporating the effects of off-nominal conditions introduced by component failures, degraded controllability and environmental disturbances such as wind gusts. The risk is represented in terms of a matrix with rows corresponding to the likelihood of occurrence of collision and columns representing severity of collision to the vehicle and surrounding structures. Risk likelihood is generated using a Bayesian Belief Network (BBN) that compiles knowledge from related Failure Modes and Effects Analysis (FMEAs) and Subject Matter Experts (SMEs) to determine the probability of collision based on on-board sensor measurements indicative of vehicle health and controllability. Risk severity is computed utilizing a point-mass 3D kinematic model of the vehicle in presence of wind. The proposed risk factor is demonstrated on real flight data from experimental flights of an octocopter at NASA Langley Research Center in presence of simulated obstacles and wind conditions. Effect of varying wind conditions, level of controllability and obstacle measurement noise on the risk factor is demonstrated. The proposed approach enables risk-informed decision making for timely mitigation of current and future unsafe events in autonomous systems.

risk analysis↗

NASA CARA Tools

The NASA Conjunction Assessment Risk Analysis (CARA) team has created and posted to GitHub a set of MATLAB software tools for collision assessment (CA) analysis. The software is provided to the public under a NASA Open-Source Software Agreement and is maintained/updated by the CARA Analysis team. Capabilities provided within the toolset include algorithms in assessing probability of collision (Pc), collision consequence, covariance realism, Orbit Determination (OD) quality assessment, and single covariance max Pc. Additionally, a set of utilities are provided for astrodynamics topics closely related to CA, such as: Conjunction Data Message (CDM) parsing, covariance transformations, coordinate system transformations, etc. The repository is regularly updated on a monthly basis and new functionality will be added as algorithms are approved for public release. This presentation will provide a brief introduction to the toolset, highlight some of the key components which can be used in operations, and will present information on algorithms that are in the release pipeline and can be expected soon. This software will enable operators to independently perform CA calculations using the same core algorithms that CARA uses in operations.

L. Baars↗