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NASA NTRSDate not supplied

Spatial and Temporal Deconfliction of Trajectories in the Presence of Uncertainties

Demonstration of conflict-free movement for multi-agent teams in challenging scenarios is crucial in developing trust and trustworthiness in an autonomous transport system. Tolerance verification queries are explored as a mechanism to enforce spatial and temporal deconfliction for a cooperating team of Unmanned Aerial Systems (UAS) with prescribed heterogeneous path-following performance. Obstacles in the environment are modelled as set of polyhedra, whereas each vehicle’s trajectory is represented as a sequence of polynomial curves with C2 continuity, expressed in a Bernstein basis. Each vehicle is modelled as a point mass and a safety distance, informed by the geometry of the UAS and the worst-case path-following error. This defines a tube around the trajectories where each UAS is most likely to fly through. In addition, obstacles in the environment have an associated safety buffer around them to account for the uncertainty in their location and geometric description. The tolerance verification queries explored in this paper combine the safety distance information from each UAS and environmental hazard to compute trajectories that are contained within the safe configuration space. Tolerance verification is also compared with other proximity queries to determine the suitability of each method along the different steps of the trajectory generation algorithm. This paper analyzes the fitness and performance of three proximity queries – collision, tolerance verification, and distance computations – between polyhedral and polynomial curves to ensure deconfliction between obstacles and vehicles, but also between polynomial curves to guarantee safe separation among cooperating UAS.

trajectory generation↗

NASA NTRS2020

Design and Implementation of a Scenario Development Process for a 2040 Trajectory-Based Operations Simulation

The National Aeronautics and Space Administration (NASA) is supporting research to transition from a legacy, air traffic management (ATM) system to Trajectory-Based Operations (TBO) environment targeting the 2035-2045 timeframe by creating simulation scenarios for current and future studies. TBO in the National Airspace System (NAS) focuses on modernizing the current operating paradigm to increase efficiency, predictability, resilience, and flexibility while migrating toward greater operational autonomy across the airspace. These simulation scenarios offer a wide dissemination and use of system-level constraints and aircraft state/intent data, routine use of data communications to request complex trajectory modifications and to receive clearances, and aircraft that are flying on 4-D trajectories with flexibility when desired, but structure where required. This report describes the end-to-end development of scenarios for the NASA Langley Research Center simulation environment to represent a 2040 Trajectory-Based Operations airspace for air transport operations research.

Trajectory-Based Operations↗

NASA NTRSDate not supplied

Uncertainty Quantification of Expected Time-of-Arrival in UAV Flight Trajectory

One of the foremost requirements for accurate in-flight safety monitoring of autonomous unmanned aerial vehicles (UAVs) is tracking of their flight trajectory. Existing UAVs leverage autonomous flight functionalities based on trajectory generation algorithms developed in robotic applications such as polynomial or spline curves in order to facilitate kinematic smoothness, minimum vibrations and fuel efficiency. However in practice, the actual path may be subjected to unexpected local weather conditions, unexpected obstacles along the path or abrupt traffic changes in the low-altitude airspace resulting in large errors of the predicted time-of-arrival at way-points. In this study, an approach to quantify and propagate uncertainty in 4D trajectories is proposed. The paper presents a simple error interval propagation method based on the expected cruise speed of the UAV and its associated uncertainty. The uncertainty is then propagated in time to estimate reasonable confidence intervals on the times-of-arrival of the vehicle at each way-point as well as along the entire flight-path. The uncertainty propagation is demonstrated on a state-of-the-art trajectory generation algorithm based on non-uniform rational B-spline (NURBS) curves. Further, the effect of a stationary wind field is incorporated in the uncertainty propagation approach. The proposed method is implemented on synthetic and real data obtained from flight experiments with a small UAV.

Uncertainty Quantification↗

NASA NTRS2022

Low-Earth Orbit Trajectory Optimization in the Presence of Atmospheric Uncertainty

The previous 20 to 25 years have seen a tremendous increase in space exploration, and with that an increase in the level of logistics planning needed to ensure mission success. For spacecraft that are designed to be periodically re-supplied, a key logistics consumable is propellant, as it constitutes the greatest up-mass on re-supply vehicles. A trajectory design strategy is therefore desired that minimizes propellant usage in order to ease the demand for propellant re-supply missions. This thesis develops such a strategy in three stages, and uses the International Space Station (ISS) as its testbed, as no other LEO spacecraft is more challenging from a space logistics standpoint. First, the ISS trajectory planning problem is formulated as a constrained burn optimization problem assuming a deterministic atmosphere. The cost function is total ∆v, with constraints imposed on longitude of ascending viii node (LAN) and semi-major axis (SMA) altitude. Analytic derivatives are constructed for both the cost and constraints, which are necessary given the 6-week to 2-year time frames being considered. A gradient-based optimizer is then utilized to find locally-optimal solutions to real-world ISS trajectory planning problems. Second, atmospheric uncertainty is addressed by constructing a probabilistic model of space weather data using Gaussian Processes (GPs). Bayesian inference is performed using the GP model to generate mean and covariance estimates for space weather predictions, whose pedigree is assessed against test data. The predictions are then mapped into atmospheric density via the analytic Jacchia-Roberts density model, and the effect of space weather uncertainty on orbital lifetime is examined. Third, an ISS burn execution uncertainty model is developed. This model, along with the space weather uncertainty model, are deployed in a linear covariance analysis to ascertain their combined effect on LAN and SMA altitude dispersions. The deterministic constraints from the original problem are re-formulated as stochastic constraints, where now the constraint uncertainty interval is required to fall within specified bounds. An updated optimization framework is constructed using the original ∆v cost function along with the stochastic constraints to solve the trajectory optimization problem under atmospheric uncertainty. Finally, the complete architecture is summarized for deployment in an operational setting.

Trajectory Optimization↗

NASA NTRS2023

A Common Trajectory Language for New Airspace Domains

Revolutionary new aviation services are currently in development, including small package delivery and short-range urban passenger transportation. These new services need a language to represent and deconflict trajectories, and a common language will simplify coordination between the new airspace domains as well as traditional airspace. A Trajectory Specification Language (TSL) was previously proposed for traditional air traffic, and it can also serve as a common language for the new aviation domains and services. The TSL specifies a reference trajectory in 4D space along with spatial tolerances that determine a bounding volume at any given time in flight. The tolerances are defined in terms of the route-oriented cross-track, along-track, and vertical axes, and they are allowed to vary with distance along the route. This bounding model can guarantee safe separation between flights as long as they are in conformance with their assigned trajectories. The advantages of this model over the previously proposed Operational Intent Volumes (OIVs) in terms of airspace usage efficiency are explained.

air traffic control, aircraft trajectory, language↗

NASA NTRSDate not supplied

A History of Orion Mission Design, Copernicus Software Development, and the Artemis I Trajectory

This paper describes the history of the on-orbit trajectory design and optimization for the Orion spacecraft at NASA JSC, from the initial design through the execution of the Artemis I test flight. In parallel, the Copernicus trajectory optimization tool was also being developed and was the main tool used for Orion trajectory design during this period. Finally, the paper gives an overview of the Artemis I trajectory that was flown during the Artemis I mission from November 16 - December 11, 2022.

Orion↗

NASA NTRSDate not supplied

Onboard Autonomous Trajectory Planning for Mars Power Descent

In recent years, there has been an increasing interest in space-qualified processors such as multi-core central processing units and graphics processing units that can withstand the adverse effects of space radiation. These processors can allow parallel programming to perform tasks that typically demand high computational power. One can study guidance schemes that can take advantage of these currently developing processors and provide more robust guidance. Software for Multi-model Autonomous Real-time Trajectories (SMART) guidance can identify robust trajectories by running an onboard Monte Carlo analysis. SMART guidance can take advantage of knowledge updates obtained from the onboard sensors, allowing it to consider the off-nominal cases that it would not typically encounter during the offline trajectory analysis. This work uses the SMART guidance for the powered divert at Mars simulation in Program to Optimize and Simulated Trajectories- II.

Autonomous Planning↗

DOE OSTI2023

Revealing Excited‐State Trajectories on Potential Energy Surfaces with Atomic Resolution in Real Time

Abstract Photoexcited molecular trajectories on potential energy surfaces (PESs) prior to thermalization are intimately connected to the photochemical reaction outcome. The excited‐state trajectories of a diplatinum complex featuring photo‐activated metal–metal σ ‐bond formation and associated Pt−Pt stretching motions were detected in real time using femtosecond wide‐angle X‐ray solution scattering. The observed motions correspond well with coherent vibrational wavepacket motions detected by femtosecond optical transient absorption. Two key coordinates for intersystem crossing have been identified, the Pt−Pt bond length and the orientation of the ligands coordinated with the platinum centers, along which the excited‐state trajectories can be projected onto the calculated PESs of the excited states. This investigation has gleaned novel insight into electronic transitions occurring on the time scales of vibrational motions measured in real time, revealing ultrafast nonadiabatic or non‐equilibrium processes along excited‐state trajectories involving multiple excited‐state PESs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Revealing Excited‐State Trajectories on Potential Energy Surfaces with Atomic Resolution in Real Time

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Silica nanocluster binding rate coefficients from molecular dynamics trajectory calculations

Oxide nanoparticle growth from vapor phase precursors occurs in high temperature aerosol reactors first via the formation of nanoclusters, which are nanometer-scale condensed-phase species composed of 10 1 -10 2 atoms. The binding rate for nanoclusters, defined as the rate at which two nanoclusters collide with and stick to one another, is hence of interest in predicting nanoparticle size distribution functions in an aerosol. We have utilized molecular dynamics (MD) trajectory calculations to determine the homogeneous (equal-sized) and heterogeneous (disparate-sized) binding rate coefficients of SiO2 (silica) nanoclusters composed of 18, 144, and 333 atoms. MD trajectory calculations incorporated all-atom models of nanoclusters using a combined Born–Huggins–Mayer-Lennard-Jones potential model, which accounts for both short range interactions and electrostatic interactions. MD calculations were utilized to determine the binding probability as a function of both initial relative velocity and impact parameter; integration of the binding probability across impact parameter and relative velocity space yields the binding rate coefficient. MD trajectory calculations reveal that the most common type of encounters between nanoclusters leading to binding are grazing collisions, i.e. instances where collision would not occur without induced dipole potential influences. The resulting binding rate coefficients are found to be extremely weakly dependent on system temperature, which is in contrast to the use of rate coefficient models which are the product of a hard-sphere collision rate coefficient and a constant enhancement factor (leading to a rate coefficient proportional to the square root of temperature). Enhancement factors defined from MD trajectory calculations fall in the range of 3–9 as system temperature decreases from 1500 K to 300 K. Furthermore, such large values suggest that potential interactions need to be considered when modeling oxide nanocluster growth in the gas phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

CryoTRANS: predicting high-resolution maps of rare conformations from self-supervised trajectories in cryo-EM

Cryogenic electron microscopy (cryo-EM) has revolutionized structural biology, enabling efficient determination of structures at near-atomic resolutions. However, a common challenge arises from the severe imbalance among various conformations of vitrified particles, leading to low-resolution reconstructions in rare conformations due to a lack of particle images in these quasi-stable states. We introduce CryoTRANS, a method that predicts high-resolution maps of rare conformations by constructing a self-supervised pseudo-trajectory between density maps of varying resolutions. This trajectory is represented by an ordinary differential equation parameterized by a deep neural network, ensuring retention of detailed structures from high-resolution density maps. By leveraging a single high-resolution density map, CryoTRANS significantly improves the reconstruction of rare conformations and has been validated on four real-world datasets: alpha-2-macroglobulin, actin-binding protein complexes, SARS-CoV-2 spike glycoprotein, and the 70S ribosome. CryoTRANS can also predict high-resolution structures in cryogenic electron tomography maps using a high-resolution cryo-EM map.Cryogenic electron microscopy (cryo-EM) has revolutionized structural biology, enabling efficient determination of structures at near-atomic resolutions. However, a common challenge arises from the severe imbalance among various conformations of vitrified particles, leading to low-resolution reconstructions in rare conformations due to a lack of particle images in these quasi-stable states. We introduce CryoTRANS, a method that predicts high-resolution maps of rare conformations by constructing a self-supervised pseudo-trajectory between density maps of varying resolutions. This trajectory is represented by an ordinary differential equation parameterized by a deep neural network, ensuring retention of detailed structures from high-resolution density maps. By leveraging a single high-resolution density map, CryoTRANS significantly improves the reconstruction of rare conformations and has been validated on four real-world datasets: alpha-2-macroglobulin, actin-binding protein complexes, SARS-CoV-2 spike glycoprotein, and the 70S ribosome. CryoTRANS can also predict high-resolution structures in cryogenic electron tomography maps using a high-resolution cryo-EM map.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Material coherence from trajectories via Burau eigenanalysis of braids

In this paper, we provide a numerical tool to study a material’s coherence from a set of 2D Lagrangian trajectories sampling a dynamical system, i.e., from the motion of passive tracers. We show that eigenvectors of the Burau representation of a topological braid derived from the trajectories have levelsets corresponding to components of the Nielsen–Thurston decomposition of the dynamical system. One can thus detect and identify clusters of space–time trajectories corresponding to coherent regions of the dynamical system by solving an eigenvalue problem. Unlike previous methods, the scalable computational complexity of our braid-based approach allows the analysis of large amounts of trajectories.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

An implicit solution for Asay foil trajectories generated by separable, sustained-production ejecta source models

We present a simple implicit solution for the time-dependent trajectory of a thin Asay foil ejecta diagnostic for the general case where the impinging ejecta cloud is generated by a source function characterized by an arbitrary (sustained) time dependence and a time-independent (stationary) particle velocity distribution. In the limit that the source function time dependence becomes a delta function, this solution—which is amenable to rapid numerical calculations of arbitrary accuracy—exactly recovers a previously published solution for the special case of instantaneous ejecta production. We also derive simple expressions for the free-surface arrival (catch-up) time as well as the true ejecta areal mass accumulation on the accelerating foil and place bounds on the level of error incurred when applying instant-production mass solutions to a sustained-production trajectory. We demonstrate these solutions with example calculations for hypothetical source functions spanning a wide range of ejecta production durations, velocity distributions, and temporal behaviors. These calculations demonstrate how the foil trajectory is often insensitive to the temporal dependence of the source function, instead being dominated by the velocity distribution. We quantify this insensitivity using a “compatibility score” metric. Under certain conditions, one may capitalize upon this insensitivity to obtain a good approximation of the second integral of the velocity distribution from the observed foil trajectory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Importance Sampling Model-Based Diffusion for Trajectory Optimization

Trajectory optimization for robotic systems remains a challenging problem. This is especially true for robotic systems featuring nonlinear dynamics and many degrees of freedom. Data-based or model-free diffusion has recently been popularized in the fields of artificial intelligence and trajectory optimization. Model-Based Diffusion provides a data-free method of trajectory optimization, trained at runtime on a system dynamics model, suitable for high-dimensional models. This paper examines how importance sampling can enhance the performance of Model-Based Diffusion for trajectory optimization. Here, we quantify the benefits of importance sampling across three long horizon planning tasks. These results show as much as a 13x improvement in sample efficiency depending on environment and optimization parameters.

Golembeski, Seth [Georgia Institute of Technology,↗

DOE OSTI2023

Massive Trajectory Data Based on Patterns of Life

Individual human location trajectory and check-in data have been the driving force for human mobility research in recent years. However, existing human mobility datasets are very limited in size and representativeness. For example, one of the largest and most commonly used datasets of individual human location trajectories, GeoLife, captures fewer than two hundred individuals. To help fill this gap, this Data and Resources paper leverages an existing data generator based on fine-grained simulation of individual human patterns of life to produce large-scale trajectory, check-in, and social network data. In this simulation, individual human agents commute between their home and work locations, visit restaurants to eat, and visit recreational sites to meet friends. We provide large datasets of months of simulated trajectories for two example regions in the United States: San Francisco and New Orleans. In addition to making the datasets available, we also provide instructions on how the simulation can be used to re-generate data, thus allowing researchers to generate the data locally without downloading prohibitively large files.

Amiri, Hossein↗

DOE OSTI2022

Review—“Knees” in Lithium-Ion Battery Aging Trajectories

Lithium-ion batteries can last many years but sometimes exhibit rapid, nonlinear degradation that severely limits battery lifetime. In this work, we review prior work on “knees” in lithium-ion battery aging trajectories. We first review definitions for knees and three classes of “internal state trajectories” (termed snowball, hidden, and threshold trajectories) that can cause a knee. We then discuss six knee “pathways”, including lithium plating, electrode saturation, resistance growth, electrolyte and additive depletion, percolation-limited connectivity, and mechanical deformation—some of which have internal state trajectories with signals that are electrochemically undetectable. Additionally, we also identify key design and usage sensitivities for knees. Finally, we discuss challenges and opportunities for knee modeling and prediction. Our findings illustrate the complexity and subtlety of lithium-ion battery degradation and can aid both academic and industrial efforts to improve battery lifetime.

25 ENERGY STORAGE↗

DOE OSTI2021

Large-Scale Trajectory Analysis via Feature Vectors

The explosion of both sensors and GPS-enabled devices has resulted in position/time data being the next big frontier for data analytics. However, many of the problems associated with large numbers of trajectories do not necessarily have an analog with many of the historic big-data applications such as text and image analysis. Modern trajectory analytics exploits much of the cutting-edge research in machine-learning, statistics, computational geometry and other disciplines. We will show that for doing trajectory analytics at scale, it is necessary to fundamentally change the way the information is represented through a feature-vector approach. We then demonstrate the ability to solve large trajectory analytics problems using this representation.

58 GEOSCIENCES↗