Space Trajectories and Applications Research

Research

Active Research Projects

Frameworks for Studying the Solar System and Chaos Theory

Conceptual Mission for the Study of Cislunar Space Weather and Lunar Occultations from Stable Orbits around Earth-Moon L4

Funding from NASA Florida Space Grant Consortium

Project Summary

The project aims to study the effects of solar activity and space weather in the Cislunar region by deploying a spacecraft around the Earth-Moon L4 Lagrangian point. This spacecraft will leverage Lunar occultations to observe the solar corona and map the magnetic field and solar energetic particle (SEP) distribution. By using the Moon as a natural occulter, the mission seeks to achieve high-resolution observations in multiple wavelength regimes, enabling better understanding of the solar corona's heating processes and the impact of solar activity on the lunar surface. This project also includes mission feasibility, how to efficiently arrive at the target orbit and designing the control framework as well as spacecraft subsystems.

Significance and Innovation

This mission stands out due to its innovative use of the Earth-Moon L4 Lagrangian point for stable orbit, allowing for consistent lunar occultations. Unlike ground-based or other space missions that rely on artificial occulters, using the Moon provides a natural and cost-effective solution, reducing diffraction and vignetting in the images. Previous missions like PROBA-3, which require precise formation flying of multiple spacecraft, are more complex and expensive. This mission's approach simplifies operations while offering unique observational advantages, such as higher angular resolution and access to new spectral windows like the near-ultraviolet (NUV).

Key Objectives

Observe Solar Corona: Conduct detailed observations of the solar corona to study its structure and dynamics, leveraging the Moon's natural occultation to block the Sun's light.
Map Magnetic Field and SEP Distribution: Utilize instruments on the spacecraft to map the magnetic field and SEP distribution in the Cislunar space, enhancing our understanding of space weather phenomena.
Lunar Occultations: Perform high-resolution lunar occultation measurements to achieve unprecedented angular resolution in the NUV spectrum, providing valuable data on stellar diameters and binary systems.
Support Earth-Moon Space Situational Awareness: Monitor lunar impact flashes and other phenomena to improve situational awareness in the Earth-Moon system, contributing to the broader understanding of space weather effects on lunar exploration and potential future habitats.

Collaborators:

Embry-Riddle Aeronautical University: Dr. Riccardo Bevilacqua
University of Central Florida: Dr. Stephen Eikenberry
Institut d'Estudis Espacials de Catalunya: Drs. Angels Aran, Jose Maria Gomez, Octavi Fors, Andrea Riccicci

Funding Source:

2024-2025: This work was made under the support of “Florida Space Grant Consortium” (FSGC) as funded by the National Aeronautics and Space Administration by Training Grant number 80NSSC20M0093.

Integrating Dynamical Systems Theory with Multi-Dimensional Analytical Tools to Better Organize Multi-Body Chaotic Regimes

Project Summary:

This project aims to develop fundamental theory for studying chaos in dynamical systems, also integrating multi-dimensional analytical tools. The goal is to identify potentially new solutions through the combination of Finite-Time Lyapunov Exponents (FTLE) and isolating blocks to understand the sensitivity of chaotic systems. The project also explores how these results can be extrapolated or linked with universal templates from Ghrist and knot theory, integrating new data analysis methods that increase the dimensions of analysis.

Significance and Innovation

Traditional methods in dynamical systems, such as Poincaré maps, are often limited to two-dimensional representations, which can constrain their ability to capture the full complexity of chaotic systems. This project distinguishes itself by utilizing Ghrist’s universal templates from knot theory, which provide a comprehensive framework for mapping all possible periodic orbits and their topological changes in higher dimensions. Additionally, by combining FTLE with isolating blocks, the project aims to offer a more detailed understanding of the sensitivity of chaotic trajectories, surpassing the limitations of traditional 2D tools. This approach also includes the use of augmented reality (AR) for a 4D interactive experience, making complex topological concepts more accessible and reducing cognitive load.

Key Objectives

Develop Fundamental Theory: Create new theoretical frameworks for understanding chaos in dynamical systems using multi-dimensional analytical and mathematical tools.
Combine FTLE and Isolating Blocks: Integrate FTLE with isolating blocks to analyze and understand the sensitivity of chaotic systems.
Explore Universal Templates and Knot Theory: Link the results with universal templates from Ghrist and knot theory to identify new solutions, enhance predictive capabilities and organize chaos.
Increase Dimensional Analysis: Implement new data analysis methods that expand the dimensions of analysis, facilitating deeper insights into complex dynamical systems.

Collaborators:

Purdue University: Dr. Kathleen Howell

Cislunar Space Situational Awareness (SSA), Policy and Applications

Cislunar Space-Based Tracking, Navigation and Surveillance Constellation Design

Project Summary:

This project focuses on developing a space-based tracking and navigation algorithms, and designing surveillance constellation for the Cislunar region to support the increasing number of missions and establish a constant lunar presence. The primary objectives are to investigate optimal placements for observers, implement efficient tracking algorithms, and develop low-complexity orbit prediction algorithms to enhance space situational awareness and mission support. Additionally, we identify key regions of interest within the Cislunar region, both on the Lunar surface and Cislunar space, as well as study current, past and future missions and SSA requirements.

Significance and Innovation

Traditional Earth-based observation systems face limitations due to significant distances, illumination conditions, and over-tasked deep-space sensors. This project addresses these challenges by studying hypothetical space-based observers within the Cislunar region. The proposed tracking algorithms and low-complexity orbit prediction methods offer innovative solutions for accurate and efficient monitoring of spacecraft. This approach contrasts with existing methodologies by providing continuous, reliable surveillance and navigation support specifically tailored for the Cislunar environment. The use of Short-Period Orbits (SPO) and novel interpolation algorithms further distinguishes this work by ensuring stable and accessible observation points. Control algorithms for tracking are also part of this project.

Key Objectives

Investigate Observer Placement: Determine the optimal locations for placing space-based observers to maximize coverage and support for Cislunar missions.
Develop Tracking Algorithms: Create efficient tracking algorithms capable of targeting and observing spacecraft with high accuracy.
Low-Complexity Orbit Prediction: Implement and validate low-complexity algorithms for predicting spacecraft orbits, reducing computational demands while maintaining precision.
Support Cislunar Infrastructure: Enhance communication, surveillance, and orbit determination capabilities to support the infrastructure required for a sustainable lunar presence.

Collaborators:

Embry-Riddle Aeronautical University: Sirani Perera
Purdue University: Dr. Carolin Frueh, Dr. David Arnas

Assessing the Impact of Spacecraft Fragmentation in the Cislunar Realm for Informed Policy Solutions for Traffic Management

Project Summary:

The project aims to evaluate the consequences of spacecraft fragmentation in the Cislunar space. This evaluation is critical for understanding the propagation of debris and its potential impact on space missions. By developing advanced analytical tools and creating comprehensive databases, this project seeks to model and simulate debris behavior in the Cislunar region. The insights gained will help shape policies and regulations to ensure safe and sustainable operations in this increasingly congested area.

Significance and Innovation

While existing studies have addressed debris analysis and its impact on spacecraft, significant gaps remain in the computation and propagation of debris in Cislunar space. This project builds upon previous research by introducing a novel approach to database generation, significantly reducing computation time and enhancing the accuracy of debris propagation models. Unlike traditional methods, this project focuses on the chaotic nature of debris behavior and applies these findings to inform space policy. By comparing various orbit families and analyzing the most hazardous scenarios, this research offers a more comprehensive understanding of fragmentation events and their implications for space traffic management.

Key Objectives

Developing Analytical Tools: Create advanced analytical tools to simulate debris propagation in the Cislunar realm, focusing on reducing computation time and increasing accuracy.
Database Generation: Establish detailed databases for different types of debris and their trajectories, enabling better prediction and management of debris clouds.
Policy Recommendations: Based on the analysis, provide informed recommendations for policy and regulatory measures to enhance space traffic management and ensure mission safety in Cislunar space.
Mission Safety: Identify the most hazardous scenarios and assess the impact of fragmentation events on nearby missions, providing data to support the development of safer mission planning and execution strategies.
Comparative Analysis: Conduct a comparative analysis of different periodic orbit families to determine the most critical areas for debris accumulation and potential collisions.

Collaborators:

Purdue University: Dr. Kathleen Howell
Space Policy Institute at George Washington University: Dr. Scott Pace

Rigid-Body Dynamics and Machine Learning for Control of Rendezvous and Precision Landing in the Cislunar Environment

Funding from 2024 CoE Research and Innovation Stimulus Program Space and Hypersonics

Project Summary:

This project focuses on the integration of SE(3) rigid body dynamics with LiDAR and optical technology and machine learning for control of rendezvous and precision landing in the Cislunar region. The objective is to develop advanced algorithms for spacecraft navigation and control that can handle the complexities of multi-body dynamics in full-ephemeris models. This includes the use of LiDAR for state estimation and machine learning techniques to enhance control methods, ensuring precise and reliable operations.

Significance and Innovation

NASA plans to operate a space station in lunar orbit through the Gateway project. Since several modules need to be docked for successful space station construction, it is important to develop a controller with robust characteristics in the cislunar region, which receives the gravity of the earth and the moon at the same time. This project defines the most effective reference frame for docking in the cislunar region and develops a controller that successfully performs rendezvous and docking under various constraint conditions. Traditional approaches to spacecraft navigation and control often rely on simplified dynamical models, which do not fully capture the complexities of the Cislunar environment. This project leverages SE(3) rigid body dynamics, which allows for a more accurate representation of both translational and rotational motions. The integration of LiDAR technology for real-time state estimation and the use of machine learning to optimize control inputs represent significant advancements over conventional methods. This combination provides a robust framework for dealing with the highly sensitive and chaotic nature of Cislunar space, enabling more precise and reliable mission execution.

Key Objectives

Develop SE(3) Rigid Body Dynamics: Formulate and implement SE(3) dynamics to accurately model the combined translational and rotational motion of spacecraft in the Cislunar region.
LiDAR Integration: Simulate and develop algorithms for using LiDAR point cloud data to predict spacecraft states, enhancing the accuracy of rendezvous and landing operations.
Machine Learning for Control: Implement adaptive and machine learning-based control methods, such as the ZEM-ZEV controller, to optimize control inputs under varying conditions.
Full-Ephemeris and Multi-Body Analysis: Study and apply different control methods within full-ephemeris and multi-body dynamical models to ensure robust and precise spacecraft navigation.
Optimal Trajectory Planning: Use global optimization algorithms to find the most efficient trajectories for missions, including transfers from near-rectilinear halo orbits (NRHO) to low-lunar orbits (LLO).

Collaborators:

Embry-Riddle Aeronautical University: Drs. Morad Nazari and Dongeun Seo
OSCorp: Dr. Axel Garcia
Princeton University: Dr. Ryne Beeson

Technology and Applications in Aerospace Engineering

Augmented Reality Digital Twin for Enhanced Space Mission Operations, Trajectory Design and Surveillance

Project Summary:

This project aims to revolutionize space mission operations by developing an Augmented Reality (AR) digital twin for enhanced trajectory design and surveillance. By creating a dynamic 3D representation of spacecraft and mission parameters, this initiative seeks to improve operational efficiency, decision-making, and collaboration among engineers.

Significance and Innovation

Traditional mission management tools often rely on 2D displays and lack real-time collaborative capabilities, which limits the understanding of complex spatial dynamics. This project differentiates itself by leveraging AR to offer a real-time, immersive 3D experience, enhancing the visualization and management of space missions. This project also emphasizes the importance of human factors, incorporating user-centered design principles to ensure the AR system meets the needs of mission operators.

Key Objectives

Develop AR Digital Twin Platform: Create a prototype AR platform that displays real-time data from a simulated spacecraft, enabling operators to access and visualize mission parameters.
Enhance Operational Efficiency: Utilize AR technology to streamline decision-making processes, reduce mission planning timelines, and improve overall mission efficiency.
Improve Collaboration: Facilitate real-time collaborative mission planning and problem-solving through shared visual representations and interactive features.
Validate and Compare: Conduct comparative studies to evaluate the AR system's performance against traditional tools, focusing on operational efficiency and collaborative decision-making.

Collaborators:

Embry-Riddle Aeronautical University: Dr. Barbara Chaparro
Auburn University: Dr. Davide Guzzetti

Funding Source:

2024-2025: This work was made under the support of “Florida Space Grant Consortium” (FSGC) as funded by the National Aeronautics and Space Administration by Training Grant number 80NSSC20M0093.

Detection and Multilateration of Uncrewed Aircraft using Convolutional Neural Networks (CNN)

Project Summary:

This project focuses on developing a system for detecting and multilaterating uncrewed aircraft (drones) using Convolutional Neural Networks (CNN). By leveraging audio data from embedded recording devices and applying CNNs for event detection, the project aims to provide a cost-effective alternative to traditional radar systems for drone detection and tracking. This system will use acoustic data to train a neural network to identify the presence of drones, enhancing security measures for sensitive sites.

Significance and Innovation

Traditional drone detection systems, such as radar and passive multilateration, are effective but often come with high costs. This project introduces a novel approach by using CNNs to process audio data, which significantly reduces the cost burden. Unlike image-based applications of CNNs, this project adapts convolutional techniques to audio data through the use of mel-spectrograms, transforming audio waveforms into visual representations that the neural network can process and considering feature extraction, allowing for efficient and accurate detection of drones based on their acoustic signatures. This approach offers a scalable and economically viable solution for drone detection, setting it apart from existing methodologies.

Key Objectives

Develop CNN-based Detection System: Create and train a convolutional neural network to detect uncrewed aircraft using audio data, converting acoustic signals into mel-spectrograms for processing.
Train and Validate Neural Network: Collect and use sound data from various drones to train and validate the CNN, ensuring high accuracy and low false-positive rates.
Implement Multilateration Techniques: Combine CNN detection with multilateration methods to accurately locate the position of detected drones based on the timing of acoustic signals.
Assess Performance and Scalability: Evaluate the system's performance in various environments, focusing on detection accuracy, computational efficiency, and scalability for larger systems and broader applications.

Collaborators:

Embry-Riddle Aeronautical University: Dr. Avinash Krishnan
HTT Consulting: Robert Moskowitz

GitHub Repositories for Open-Source Code and Databases

Assessing the Impact of Spacecraft Fragmentation in the Cislunar Realm for Informed Policy Solutions for Traffic Management

Data Availability: The codes and GUI developed for the database, as well as the analysis presented in this manuscript, are available as a free-source repository on GitHub. Information on how to use the code is included in the readme file in the same repository. Additionally, the pre-computed dataset used in this study has been uploaded to the Mendeley Data communal data repository, along with the files generated for the explosions analyzed in this study, which form the explosion database. The link to this database is also indicated in the readme file of the GitHub repository.

Previous Research Projects

Perturbed Lambert Problem Using the Theory of Functional Connections

The Theory of Functional Connections (TFC) is used to solve Lambert’s problem. The mathematical model involves a functional approximation of the solution using orthogonal polynomials and a non-linear least squares solution. The solver has the ability to include any perturbation, namely J2 perturbation, third-body perturbations, and Solar radiation pressure. The algorithm performs faster than other solvers, namely differential corrections, and is generally more robust with the exception of a singularity when the transfer arc is close to 180 degrees.

RSO Identification in Arbitrary Unresolved Space Imagery

Identifying Resident Space Objects (RSOs) in arbitrary space imagery with little prior information is a challenging, yet crucial next step in space domain awareness applications. This work proposes improvements to an existing RSO identification process for unresolved space images. The algorithm has three main phases: image processing, star elimination, and RSO association. Star elimination and RSO association use nearest neighbor association and tresholds on inertial frame-to-frame motion of observations to associate objects. Given a set of unresolved space images contiguous in time, the product of the algorithm presented is a set of measurements for orbit estimation.

Simulator Development for Coverage Planning of a 5G/loT Constellation

The challenges posed by new 5G-IoT (Internet-of-Things) satellite constellations in telecommunication are assessed. The focus is on the development of an efficient and autonomous management system for such constellations. We developed a management tool and a simulator capable of computing visibility events across multiple locations, including ground stations, user equipment, and target areas. The contact simulator has been upgraded to incorporate key features such as inter-satellite links, Kalman filter for orbit determination, and the implementation of link budgets. These advancements enable improved management and optimization of IoT satellite constellations in the evolving telecommunication landscape. The structure of the tool is restated with minor advancements in automation and efficiency.

The STAR group greatly appreciates funding from:

Posters

Posters 2024

Immersive trajectory design using augmented reality (REU Program)

Detection of Uncrewed Aircraft using CNN (REU Program)

Drone detection through acoustic signal processing

(best poster award in discovery day)

Posters 2023

Space Trajectories and Applications Research Group

Exposure Poster

Drone Detection Through Acoustic Signal Processing

Trajectory Design and Surveillance of the Cislunar Region Using Augmented Reality

Leveraging the Moon and Stable Libration Point Orbits around L4/L5 to Observe the Solar Corona

Orbit and Attitude Coupling in the Full Higher-Fidelity Ephemeris Model within the context of the Geometric Mechanics Framework

Creation of a Trajectory Framework that is Sustainable for a Continuous Exploration of Mars and its Moons

A review on hot-spot areas within the Cislunar region and an orbital framework for key regions

Resident Space Object Identification in Arbitrary Unresolved Space Images

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