Research

Project Summary:

This project aims to understand and systematically categorize chaotic motion in the cislunar region. We leverage Ghrist’s universal template from knot theory to express cislunar trajectories via symbolic dynamics that are intuitive for humans to interpret. To connect these symbolic descriptions to machine-usable state information, we compute Lagrangian Coherent Structures (LCS) using isolating blocks and FTLE maps. Because LCS inhabit three or more dimensions, we investigate AR-based visualization and modern dimension-reduction techniques to make high-dimensional structure legible and actionable. 

Significance and Innovation

Traditional tools for cislunar design (e.g., differential correction and Poincaré maps) excel locally but struggle to provide a global view of chaotic behavior. Our integrated framework targets system-level understanding and classification across the full trajectory space. By combining symbolic dynamics, LCS, and high-dimensional analytics (with AR visualization), we not only understand and classify chaotic motion in the cislunar regime, but also compute control policies to transition between symbolically classified trajectory families, enabling intuitive orbit design and transfer planning. 

Key Objectives

1. Develop Fundamental Theory: Create new multi-dimensional analytical tools to characterize chaos in dynamical systems.

2. Combine FTLE with Isolating Blocks: Integrate FTLE with isolating blocks to analyze and understand the sensitivity of chaotic systems.

3. Leverage Universal Templates & Knot Theory: Use Ghrist’s universal template to understand and categorize chaotic behavior in the cislunar region.

4. Scale Up Dimensional Analysis: Advance methods for analyzing and visualizing higher-dimensional structures, including AR-assisted exploration and dimension-reduction workflows.

Collaborators:

• Purdue University: Dr. Kathleen C. Howell 

Funding Source:

• 2024-2025: This work was made under the support of “National Science Foundation ” (NSF), Grant number 2501408.

Funding from NASA Florida Space Grant Consortium

Project Summary:

With NASA’s renewed emphasis on lunar and eventual Mars exploration, the demand for interoperable, compact, and precise orbital tracking in cislunar space has become mission-critical. Existing standards reveal key limitations: TLEs, though efficient, break down under multi-body dynamics, while OEMs, despite their accuracy, impose prohibitive data volumes. This work proposes the Compact Cislunar Orbital Representation (CCOR), designed to balance TLE-level efficiency with OEM-level fidelity. The outcome is a foundational prototype for a universal standard enabling real-time, multi-actor navigation and sustainable mission architectures in the cislunar domain. 

Significance and Innovation

Existing orbital formats either fail to capture the complexity of cislunar dynamics or demand excessive data volumes that limit scalability across missions. This project introduces the Compact Cislunar Orbital Representation (CCOR) as a balanced alternative, embedding perturbation-aware dynamics into a compact, transferable format. By bridging the efficiency of TLEs with the fidelity of OEMs, CCOR enables precise yet lightweight tracking tailored for multi-actor operations in the cislunar domain. This innovation establishes the foundation for a universal standard that directly supports sustainable exploration architectures and international coordination.

Key Objectives

1. Mission Profile Survey: Analyze representative cislunar orbits (NRHO, DRO, LLO, Lunar insertion) to define CCOR requirements and identify limitations of current formats like TLEs. 

2. Representation Strategy Development: Explore candidate encoding methods (Fourier/polynomial fits, CR3BP-based, modified orbital elements, GEqOEs) to capture multi-body dynamics compactly and accurately. 

3. Prototype Implementation: Build a software prototype of the CCOR format with encode/decode capability, validation against GMAT/SPICE, and propagation over relevant timescales. 

Funding Source:

• 2025-2026: This work was made under the support of “Florida Space Grant Consortium” (FSGC)

Project Summary:

This project focuses on developing space-based tracking and navigation algorithms as well as designing surveillance constellation for the Cislunar region to support the increasing number of missions aimed to establish a constant lunar presence. The primary objectives are to investigate optimal placements for observers, implement initial orbit determination algorithms, and retain custody of objects through accurate tracking 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 of cislunar space faces 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. This approach provides continuous, reliable surveillance and navigation support specifically tailored for commonly traversed regions of cislunar space. The use of Short-Period Orbits (SPO) and development of a thorough analysis of candidate housing orbits further distinguishes this work by ensuring stable trajectories and a generalizable analysis to other regions of interest and constellation orbits​. 

Key Objectives

1. Investigate Observer Placement: Determine the optimal locations for placing space-based observers to maximize coverage and support for Cislunar missions.

2. Develop Tracking Algorithms: Create efficient tracking algorithms capable of targeting and observing spacecraft with high accuracy.

3. 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

Project Summary:

This work investigates the dynamics of spacecraft fragmentation and debris propagation within the cislunar environment and aims to synthesize policy frameworks to identify operational risks. Unlike Earth-centric orbital regimes, the Earth-Moon space is governed by multi-body dynamics, rendering current space law insufficient in mitigating debris. This research develops computational methods to simulate debris evolution, first in the circular restricted three-body problem (CR3BP) and then transitioned to higher fidelity models. These models leverage insight from Hill's lunar theory to gain an in-depth understanding of higher order dynamics without necessitating the computational resources of a higher-fidelity ephemeris model. The intent is that the in-plane quasi-Hill restricted four-body problem (IQHR4BP) or the out-of-plane quasi-Hill restricted four-body problem (OQHR4BP) may be utilized as an analogue to the extensive studies of debris propagation in LEO using SGP4, a model that includes many relevant perturbations in this regime. These technical findings map high-risk clustering zones and evaluate risk along critical mission trajectories; they will be used to propose risk-informed zoning and capacity limits for sustainable traffic management in the cislunar region. 

Significance and Innovation

While space debris in LEO and GEO has received substantial regulatory attention, the cislunar region remains underexplored in both engineering and legal domains. This work innovates on multiple fronts, leveraging high-fidelity astrodynamics and satellite breakup models to simulate debris in multi-body gravitational environments. It defines new clustering metrics (e.g., dwell time, relative dispersion) that quantify debris hazard and persistence, which is vital for mission planning in key cislunar transit corridors. It synthesizes legal analysis with technical outputs to expose regulatory blind spots, notably in attribution, mitigation compliance, and space traffic management (STM) governance. Finally, it introduces the idea of debris "zoning" to advocate capacity thresholds grounded in fragment behavior. This cross-disciplinary research represents a novel framework for defining enforceable safety standards in future lunar operations. 

Key Objectives

1. Policy and Legal Review: Evaluate the adequacy of existing treaties (e.g., OST, Liability Convention) and soft-law instruments (e.g., COPUOS LTS Guidelines) in managing cislunar debris. Identify legal blind spots around attribution, fault, and enforcement. 

2. Advanced Simulation Tools: Develop simulations of debris behavior in the Earth-Moon system using the CR3BP preliminarily, then the IQHR4BP or OQHR4BP for higher-fidelity simulations. These tools will identify long-term clustering, impact risks, and regime transitions across various initial conditions. 

3. High-Risk Regime Characterization: Systematically identify and classify orbital regimes with elevated debris retention, clustering, or encounter risks. Generate spatial and temporal maps of debris distribution, clustering likelihood, and high-risk zones based on Monte Carlo realizations. These maps will support evidence-based zoning recommendations and inform operational safety protocols. 

4. Zoning and Threshold Recommendations: Propose enforceable cislunar "zoning" based on model-identified high-risk regions. Introduce the idea of risk density as a guiding metric for capacity planning. 

5. Space Traffic and Risk Governance: Offer policy recommendations for new international instruments, including dynamic licensing regimes and shared risk thresholds adapted to the nonlinear cislunar environment. Propose necessary STM infrastructure to ensure these instruments are enforceable. 

Collaborators:

• Purdue University: Dr. Kathleen Howell

• Space Policy Institute at George Washington University: Dr. Scott Pace

• George Washington University: Colleen Hartman 

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

1. 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.

2. LiDAR Integration: Simulate and develop algorithms for using LiDAR point cloud data to predict spacecraft states, enhancing the accuracy of rendezvous and landing operations.

3. 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.

4. 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.

5. 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

Project Summary:

This research aims to develop a hybrid semantic segmentation-guided pose estimation pipeline for LiDAR-based spacecraft proximity operations in the cislunar domain. Leveraging simulated LiDAR data and deep learning neural networks, PointNet++ models are employed to identify and segment rigid components of spacecraft (e.g., main bus, docking ports) while rejecting non-rigid or articulating parts (e.g., rotating solar arrays). Post-segmentation, a feature-centric registration process is applied to extract precise pose estimates by aligning rigid features.

Significance and Innovation

A central challenge in spacecraft pose estimation is the presence of non-rigid or articulating components, such as solar panels and antennas, which violate the rigid-body assumptions required by classical registration algorithms. These features often dominate LiDAR point clouds, leading to degraded performance or complete failure when traditional Iterative Closest Point (ICP)-based methods are applied. To address this challenge, this work introduces a hybrid segmentation-guided registration framework that combines the strengths of deep learning and classical geometry. A PointNet++ model is employed to semantically segment LiDAR point clouds, discarding non-rigid features while isolating rigid, mission-relevant structures such as the spacecraft bus or docking port. These filtered point clouds are then used to guide a feature-centric ICP registration, yielding more accurate and robust pose estimates. This advancement ensures that registration remains reliable even in the presence of articulating structures, while maintaining computational efficiency suitable for real-time, onboard operation.

Key Objectives

1. Train the model: Train and evaluate a PointNet++-based segmentation model that effectively classifies spacecraft components.

2. Develop the estimation pipeline: Integrate the deep learning segmentation results with classical point cloud registration to compute accurate pose estimates.

3. Quantify System Robustness Across Simulations: Test system performance across varying conditions while evaluating sensitivity to segmentation errors and introducing uncertainty to characterize confidence.

Project Summary:

This project develops an end-to-end framework for autonomous rendezvous and proximity operations (RPO) and precision landing in the cislunar environment. The relative motion model is built on the circular restricted full three-body problem (CRF3BP) with coupled attitude–orbit dynamics on the special Euclidean Lie group SE(3). For control, we employ a neural network based control Lyapunov barrier function (NN-CLBF) approach that drives the system to desired states while enforcing safety via barrier constraints, with formal robustness to modeling uncertainties and sensor errors/noise. Relative state estimation draws on both LiDAR point cloud registration and convolutional neural network (CNN) based computer vision pipelines capable of pose estimation from single images.

Significance and Innovation

This framework provides an end-to-end solution for cislunar RPO and precision landing. The CRF3BP model captures the coupled translational–rotational dynamics. A neural-network–based CLBF controller delivers formal stability and safety guarantees even in the presence of modeling errors and sensor noise. On the perception side, we investigate both LiDAR and camera modalities: LiDAR point cloud registration yields lighting-invariant relative pose estimates, while CNN-based single-image pose estimation recovers relative pose from a single camera frame and remains viable under tight compute budgets.

Key Objectives

1. CRF3BP on SE(3): Derive and validate an SE(3) based relative motion model that captures coupled translation–rotation dynamics for cislunar RPO and landing.

2. NN-CLBF Control: Design and verify neural network assisted CLBF controllers that guarantee convergence and enforce safety via control-barrier constraints, robust to modeling errors and sensor noise.

3. LiDAR Registration: Obtain lighting-invariant relative pose estimates from point clouds using robust registration; characterize accuracy, latency, and failure modes.

4. Computer Vision: Develop CNN-based single-image pose estimation and integrate it with state estimation for long-to-close-range operations under tight compute budgets.

5. System Integration & Evaluation: Close the loop across perception → estimation → control; evaluate end-to-end performance in representative cislunar scenarios using mission-relevant metrics (e.g., constraint violations, pose/velocity error, Δv, compute latency).

Collaborators:

• OSCorp: Dr. Axel Garcia

• Translunar ESI

Project Summary:

In collaboration with NASA Langley Research Center, this project develops an augmented-reality (AR) simulation pipeline that replays and analyzes real lunar-landing mission data. The system not only reconstructs lander state (position, velocity, and attitude) with high fidelity but also ingests LiDAR point cloud data collected by onboard sensors, rendering it in AR for interactive inspection and analysis. 

Significance and Innovation

By simulating actual landing-mission data in an AR environment, the system doubles as a training platform for early-career engineers and students and as a tool for end-to-end mission analysis. In addition, analysis of the LiDAR point cloud stream makes it possible to identify landing-phase error sources and constraints—such as sensor biases or dropouts and limitations caused by lunar dust—informing more robust sensing, filtering, and contingency planning for future missions.

Key Objectives

1. AR Simulation Development: Build a flight-data-driven AR simulation environment for lunar landing scenarios.

2. LiDAR Data Analysis: Ingest and analyze LiDAR point clouds produced during prior landing missions.

3. High-Fidelity Evaluation: Enable higher-fidelity simulations for prospective lunar EDL/DDL concepts, including sensor-performance studies and edge-case evaluation.

Collaborators:

• NASA Langley Research Center 

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

1. 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.

2. Enhance Operational Efficiency: Utilize AR technology to streamline decision-making processes, reduce mission planning timelines, and improve overall mission efficiency.

3. Improve Collaboration: Facilitate real-time collaborative mission planning and problem-solving through shared visual representations and interactive features.

4. 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.