Tutorial Session

Overview:

The Global Exploration Roadmap has inspired international interest in a new era of human exploration of the solar system. Recent years have seen exponential growth in the launch of space objects and there is an increased interest in having a permanent cislunar presence through the Artemis program and various other governmental and private-sector efforts. A sophisticated understanding of motion of a spacecraft in multi-body environments such as the cislunar space is essential to transit across various regions in the cislunar space and to forecast and track objects for mission safety and collision avoidance. Over the past several decades, the perturbed two-body restrictive framework has been the foundational backbone for providing extensive modeling, analysis, and analytical solutions to study spacecraft motion in orbits around the Earth. However, beyond GEO (XGEO) the dynamical environment shifts, and the structure of fundamental behaviors can be radically different. The primary challenge that limits the transferability of tools and techniques from the LEO/GEO to XGEO regions is non-Keplerian dynamics, data sparsity from limited coverage and availability of sensors. In a large part, periodic orbits and their associated invariant manifolds dictate the design of transfer trajectories between the neighborhoods of the Earth and Moon. This tutotial session will provide a primer on the methods and mathematics for cislunar astrodynamics methods with a focus on state-of-the-art tools and techniques developed to investigate the behavior of transport mechanisms across this region. The design of transport highways connecting different cislunar regimes will be discussed. The talks will also provide details of transitioning low-fidelity solutions to higher-fidelity. Novel tools to propagate state uncertainty, search and track spacecraft in cislunar space will be discussed.  How the navigation error grows in different cislunar regimes and the performance of different state estimation algorithms in providing a statistically consistent estimate of spacecraft position and velocity will be discussed. At the end of the tutorial session, participants will be able to:

1. Explore the dynamical environment of cislunar space under multiple fidelities: equilibrium points, periodic orbits, quasi-periodic orbits using tools such as chaos indicators, invariant manifolds, and Poincare sections.
2. Learn to apply uncertainty propagation and filtering techniques to cislunar trajectories.
3. Develop methods for trajectory design and performing Guidance, Navigation, and Control for inside the cislunar environment.
4. Be exposed to implementation challenges such as computational complexity, non-Gaussian uncertainty, reduction of filter dimension, colored noise, and discretization.

Cislunar space is drawing increasingly sharp interest from the international space community warranting attention. This tutorial session will cater to both professionals from the defense community who develop plans, capabilities, expertise, and operational concepts for enhanced space domain awareness beyond GEO realm and commercial space players necessary for a sustainable human presence as part of the “Moon-to-Mars” paradigm. It will address challenges in spacecraft operations such as staying in a trajectory, transfers between different trajectories, Earth and Moon, different orbit types and their utility for exploration v/s surveillance and present the state-of-the-art in their development.

Format:

This tutorial session will be approximately 4 hours in duration. The workshop is structured into a single session comprising multiple key topics: Transport mechanisms in cislunar regime, trajectory planning, uncertainty quantification and propagation, and designing navigation and control strategies. The first major talk, Understanding Transport Mechanisms in Cislunar Space, will cover fundamental aspects of the circular restricted three-body problem (CR3BP), Lagrange points, periodic orbits, and manifolds, along with a transition to full ephemeris models. This will be followed by Chaoticity in Cislunar Space, which will focus on the nonlinear characteristics of cislunar dynamics, including methods such as the nonlinearity index and the application of the Conjugate Unscented Transform in the development of navigation filters and uncertainty propagation. The third talk, Navigating Cislunar Space will address key strategies for trajectory design, navigation, and control in cislunar space. The final talk will present some recent research in representing and characterization of trajectories in cislunar space using semi-analytic perturbation theories. The session will conclude with a discussion segment, allowing participants to engage with the speakers, ask questions, and explore practical implications of the presented topics.

Target Audience:

Practitioners looking for advanced techniques in trajectory planning, navigation, and uncertainty quantification for mission design and space situational awareness. Researchers looking for new ideas and the connection between theory and practice; students and early career professionals looking for better understanding of the foundation of multi-body cislunar operations and the development of Guidance and Navigation strategies; Defense space professionals focused on domain awareness beyond GEO and commercial space players pursuing lunar exploration will gain insights into operational challenges like station-keeping, transfers, and long-term sustainability;

Tentative Schedule and Speakers:

Speakers:

• Dr. Maruthi Akella (The University of Texas at Austin)
• Dr. Roshan Eapen (The Pennsylvania State University)
• Dr. Puneet Singla (The Pennsylvania State University)

Session Organization:

• Introduction and Opening Remarks (10 minutes)
• Understanding Transport Mechanisms in Cislunar Space (50 minutes)
• Chaoticity in Cislunar Space (50 minutes)
Break (10 minutes)
• Navigating Cislunar Space (50 minutes)
• Orbit Element Equivalents for Cislunar Space (50 minutes)
• Discussion and Audience Interactions (20 minutes)

Abstracts for Talks:

• Understanding Transport Mechanisms in Cislunar Space: (Speaker: Roshan Eapen)Transport mechanisms in the restricted three-body problem rely on the topology of dynamical structures created by gravitational interactions between a particle and the planets’ governing its motion. In a large part, periodic orbits and their associated invariant manifolds dictate the design of transfer trajectories between the neighborhoods of the two primaries. In this talk, the behavior of such dynamical structures is investigated using dynamical systems theory. This talk will identify transport opportunities to planar libration point orbits and promote the development of a catalog of transfers in cislunar space. A special focus on dynamical modeling of high-fidelity motion will also be discussed.
• Chaoticity in Cislunar Space (Speaker: Puneet Singla)This talk examines navigation error growth in cislunar space and evaluates the consistency of various linear and nonlinear uncertainty propagation algorithms. Error growth is quantified using the nonlinearity index and finite-time Lyapunov exponent, while consistency is assessed by comparing state probability density approximations. Insights will be provided on the long-term propagation of state errors and effects of measurement sparsityon the performance of precise orbit determination.
• Navigating Cislunar Space (Speaker: Maruthi Akella)This talk will leverage the advances in optimal control theory and numerical methods to design ballistic trajectories and periodic orbits in the cislunar space. The process of exporting these trajectories and orbits to high-fidelity motion models will be discussed. Insights into designing feedback control laws to ensure safe operations with performance guarantees will be provided.
• Orbit Element Equivalents for Cislunar Space (Speaker: Roshan Eapen, Puneet Singla & Maruthi Akella)This talk will introduce recent advances in multi-body dynamics to define local features to characterize trajectories in the neighborhood of a Lagrange points. These dynamical features though local in nature are equivalent to orbit elements in the Keplerian dynamics. The utility of these local elements in station-keeping, trajectory design and tracking space traffic in the cislunar space will be discussed. Semi-analytical means to predict spacecraft behavior will be also discussed.