Kathleen Howell

Purdue University West Lafayette | Purdue · School of Aeronautics and Astronautics

While the L2 halo orbits as constructed in the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) play an important role in future space exploration, the global behavior of the analogs within a Higher-Fidelity Ephemeris Model (HFEM) remains elusive. Leveraging a common numerical transition method from the CR3BP to the HFEM, the Earth-Moon L2...

A frequency-based hierarchy of dynamical models in cislunar space is introduced in recent literature, where multiple models between the Circular Restricted Three-Body Problem (CR3BP) and a Higher-Fidelity Ephemeris Model (HFEM) are investigated within a common rotating reference frame. The primary objective of the current investigation is a focus o...

In the cislunar environment, the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) is widely recognized as a valuable dynamical model, providing essential structures for the preliminary design process. However, for these trajectories to be practically applicable in flight, validation in a Higher-Fidelity Ephemeris Model (HFEM) is imperative...

This contribution focuses on the use of finite-time Lyapunov exponent (FTLE) maps to investigate spacecraft motion within the context of the circular restricted three-body problem as a conceptual model. The study explores the advantages and limitations of FTLE maps by examining spacecraft trajectories in the vicinity of the Jovian moons, Ganymede a...

Space situational awareness is a priority to enable the development of the cislunar region. The 30-degree cone with vertex at the Earth and opening towards the Moon is identified as a region requiring frequent visibility. Constellations of sidereal resonant orbits with a synodic resonance overlap in the Circular Restricted Three-Body Problem posses...

Principal stretching and restoring directions form sets of orthonormal vector bases that can be leveraged to describe and design spacecraft motion relative to a reference trajectory. This investigation characterizes relative states as linear combinations of these principal directions to introduce techniques for relative trajectory design formulatio...

To establish a comprehensive SSA architecture in cislunar space, space-based sensors that can traverse the expansive volume are currently an option being evaluated. With the availability of unique vantage points across the domain of cislunar space via sidereal resonant orbits, orbits that are additionally commensurate with the lunar synodic period...

Understanding the applicability of different dynamical models within cislunar space is a useful yet challenging problem. The current work constructs a hierarchy of dynamical models leveraging a common rotating reference frame that accommodates multiple dynamical models. In such a formulation, the Higher-Fidelity Ephemeris Model (HFEM) is approximat...

Increased interest in the development of cislunar space requires greater intuition for the operation of spacecraft in multi-body orbits. Many such orbits are linearly unstable , and an orbit maintenance strategy is required to secure a spacecraft near some desired reference motion. The development of effective stationkeeping approaches is facilitat...

Near-Earth Objects (NEOs) are asteroids, comets and meteoroids in heliocentric orbits with perihelion below 1.3 au. Similarly to the population of the Main Asteroid Belt, NEOs are primordial bodies and their study can improve our understanding of the origins of the Solar System. With a catalog of over 30~000 known asteroids and approximately 100 li...

This contribution focuses on the use of finite-time Lyapunov exponent (FTLE) maps to investigate spacecraft motion within the context of the circular restricted three-body problem. The authors expose some of the advantages and shortcomings of FTLE maps and illustrate their use by examining the motion in the vicinity of a moon; in particular, the Jo...

While the Circular Restricted Three-Body Problem (CR3BP) provides useful structures for various applications, transitioning the solutions from the CR3BP to a higher-fidelity ephemeris model while maintaining specific characteristics remains non-trivial. An analytical approach is leveraged to provide additional insight on the perturbations that are...

The NASA Gateway spacecraft is intended to frequently host visiting vehicles in support of the Artemis program and cislunar operations. Relative motion in libration point orbits such as the Gateway Near Rectilinear Halo Orbit (NRHO) is an area of ongoing research, and the rendezvous, proximity operations, and docking procedures in this challenging...

For a viable cislunar space infrastructure, the transfer trajectories between various types of host orbits require reasonable maneuver costs and flight times. Multiple transfer design frameworks are presented that leverage the hyperbolic invariant manifolds associated with quasi-periodic orbits to uncover transfers between periodic orbits with diff...

Structures in the Circular Restricted Three-Body Problem (CR3BP) are vital to enable multiple space mission concepts, yet delivering their counterparts in a Higher-Fidelity Ephemeris Model (HFEM) poses a non-trivial task. Achieving a seamless transition between the CR3BP and HFEM necessitates a thorough comprehension of the underlying dynamical fac...

The Earth-Moon L1, L2 halo orbit families support a variety of options for lunar surface activities as well as other developments in the cislunar region. The planned operational orbit for NASA's Gateway is the 9:2 L2 synodic resonant halo orbit. Furthermore, orbits from this family could serve as staging locations for future missions to near-Earth...

The paper investigates close range rendezvous, nearby orbital transfer, and collision avoidance maneuvers for a chaser spacecraft moving relative to a target in a 9:2 L2 Near-Rectilinear Halo Orbit (NRHO). A feature learning optimal control method (L-OCM) is proposed to solve optimal control problems corresponding to the maneuvers to minimize fuel...

Near Earth Objects (NEOs) are small Solar System bodies (such as asteroids, comets and meteoroids) in heliocentric orbits with perihelion below 1.3 astronomical units. With a catalog of over 30,000 known asteroids and approximately 100 listed short-period comets, the NEO population represents an inventory of exploration targets reachable with signi...

This contribution focuses on the design of low-energy transfers between planetary moons and presents an efficient technique to compute trajectories characterized by desirable behaviors in the vicinities of the departure and destination bodies. The method utilizes finite-time Lyapunov exponent maps in combination with the Moon-to-Moon Analytical Tra...

This contribution focuses on the design of low-energy transfers between planetary moons and presents an efficient technique to compute trajectories characterized by desirable behaviors in the vicinities of the departure and destination bodies. The method utilizes finite-time Lyapunov exponent maps in combination with the moon-to-moon analytical tra...

Currently, Koopman operator theory is being explored as a method for analysis in the Circular Restricted Three-Body Problem (CRTBP). The potential for use in the computation of periodic orbits as well as stationkeeping has increased the interest in its applications to other analysis problems within the CRTBP. However, due to the nature of the metho...

The Astrodynamics Software and Science Enabling Toolkit (ASSET) is a free and open-source software library enabling rapid spacecraft mission design and analysis. The software is a parallel, object-oriented C++ library, with a Python front-end for quick development, and ease-of-use. This paper outlines new enhancements added to ASSET since its initi...

Trajectories in support of emerging concepts for utilization of cislunar space, including space domain awareness, are of growing interest. However, Earth and Moon eclipses in the cislunar regime can induce significant challenges that hamper nominal spacecraft operations. As such, strategies to identify and predict the occurrence of, as well as to m...

While many dynamical structures in the Circular Restricted Three-Body Problem (CR3BP) serve as useful approximations to the motion of a spacecraft within a higher-fidelity ephemeris model (HFEM), a subset of the Earth-Moon L2 halo orbit family is known to display a more dispersed behavior in the HFEM. Leveraging a consistent numerical transition me...

Quasi-periodic orbits offer a broad range of flexibly and adapable destinations in multi-body systems. In this investigation, a computational framework for construction of heteroclinic connections between quasi-periodic orbits is summarized. Subsequently, families of heteroclinic connections are characterized and examples are provided in the Circul...

Halo orbits in the Circular Restricted Three Body Problem (CR3BP) serve as the reference motion for several current and planned missions in cislunar space. Many of these orbits are linearly unstable and, thus, require some form of an orbit maintenance strategy. Two existing orbit maintenance strategies for halo orbits are a phase-augmented x-axis c...

A novel, compact formalism of rigid body motion dynamics is presented in a general reference frame based on the geometric mechanics framework. This formalism, proposed on the special Euclidean space (SE(3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackag...

Space missions to Near Rectilinear Halo Orbits (NRHOs) in the Earth-Moon system are upcoming. A rendezvous technique in cislunar space is proposed in this investigation, one that leverages coupled orbit and attitude dynamics in the Circular Restricted Three-body Problem (CR3BP). An autonomous Guidance, Navigation and Control (GNC) technique is demo...

Low-energy transfers offer propellant-efficient paths to the Moon. This investigation introduces techniques for constructing low-energy lunar transfers with a focus on the trade-offs between time-of-flight and propellant requirements, if any. A type of low-energy transfer, denoted a Ballistic Lunar Transfer (BLT), leverages the gravitational influe...

Models representing four-body problems (4BPs) offer useful dynamical environ- ments to investigate the impact of the Sun on behavior near the Earth-Moon li- bration points. Four-body models include the Bicircular Restricted Four-Body Problem (BCR4BP) and the Quasi-Bicircular Four-Body Problem (QBC4BP). The BCR4BP is widely used to examine the dynam...

There is a growing interest in trajectories to support missions throughout cislunar space, specifically the region beyond GEO and through the vicinity of the Moon and the L1 and L2 libration points. Multiple satellites, potentially in formations or constellations, assist with the monitoring and surveillance of cislunar space for long-term sustainab...

Many future satellite applications in cislunar space require periodic transfers that shift away from some operational orbit but return. Numerous resonant orbit families in the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) possess a ratio of orbital period to lunar period that is sufficiently close to an integer ratio and can be exploite...

A novel, compact formalism of rigid body motion dynamics is presented in a general reference frame based on the geometric mechanics framework. This formalism, proposed on the special Euclidean space (SE(3)) of the Lie group, naturally accounts for the orbit/attitude coupling due to the gravitational moments and forces. It is demonstrated that the s...

Ridesharing options for secondary payloads to be delivered to regions beyond geostationary altitude are increasingly available with propulsive evolved expendable launch vehicle secondary payload adapter rings. The preliminary mission design for secondary payloads must consider the variability of the dropoff orbit orientation: a factor that is a fun...

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...

Stable or nearly stable orbits do not generally possess well-distinguished manifold structures that assist in designing trajectories for departing from or arriving onto a periodic orbit. For some potential missions, the orbits of interest are selected as nearly stable to reduce the possibility of rapid departure. However, the linearly stable nature...

Autonomy is an increasingly essential component of future space missions, and new technologies are necessary to accommodate off-nominal occurrences onboard that may pose risks to mission success. In search of a satisfactory maneuver plan to correct for an unanticipated event, the initial identification of a suitable basin of convergence remains cha...

Space missions to Near Rectilinear Halo Orbits (NRHOs) in the Earth-Moon system are upcoming. A rendezvous technique in the cislunar space is proposed in this investigation, one that leverages coupled orbit and attitude dynamics in the Circular Restricted Three-body Problem (CR3BP). An autonomous Guidance, Navigation and Control (GNC) technique is...

Examining the properties of quasi-periodic orbits provides insight into the Sun-perturbed environment in cislunar space. In this investigation, quasi-periodic trajectories and their properties are explored in the Sun-Earth-Moon four-body problem. Computation and the stability characteristics of families of invariant tori are detailed. Furthermore,...

Secondary payloads provide lower-cost mission opportunities to the Moon, a prime target for future space missions. Intuitive Machines’ Khon-1 mission is one such example, planned to launch in 2023 to provide communications to the lunar surface. The trajectory design for the mission is associated with demanding challenges: the limited propulsive cap...

While the Earth-Moon Circular Restricted Three-body Problem (CR3BP) provides useful dynamical structures that are successfully leveraged for actual missions, transitioning the CR3BP solutions into a higher-fidelity ephemeris model remains nontrivial. The transitioning procedure may benefit by more consistently incorporating information from an inte...

Examining the properties of quasi-periodic orbits provides insight into the Sun-perturbed environment in cislunar space. In this investigation, quasi-periodic trajectories and their properties are explored in a Sun-Earth-Moon Bicircular Restricted Four-Body Problem (BCR4BP). Additionally, computation and stability of invariant torus families in the...

Low-energy transfers leverage multi-body dynamical structures to produce propellant efficient paths. Such trajectories often require a longer flight duration to achieve reduced propellant costs. One type of low-energy transfer in the Earth-Moon-Sun system is termed a ballistic lunar transfer (BLT). The goal of a BLT is to traverse a path from the E...

A compact formalism for rigid body motion dynamics is presented in a general reference frame based on geometric mechanics. This formalism, proposed on the special Euclidean space of the Lie group, naturally accounts for the orbit/attitude coupling due to the gravitational moments and forces for the full N-body problem. Furthermore, the expressions...

As a greater number of low-thrust missions are proposed to operate in the cislunar vicinity, an expanded capability for flow-informed low-thrust transfer design is warranted. However, inclusion of low-thrust forcing terms in the Circular Restricted Three Body Problem (CRTBP) yields a non-autonomous system lacking the same symmetry properties levera...

In the coming decades, numerous spacecraft are expected to populate cislunar space, reaching beyond GEO and out to the lunar vicinity. The complex cislunar dynamical environment necessitates the use of new and unique orbits for sustaining long-term operations and surveillance. In this investigation, resonant orbits are incorporated into the traject...

A proposed Gateway facility in a lunar near rectilinear halo orbit (NRHO) will serve as an outpost in cislunar space, with various spacecraft periodically arriving and departing. The dynamics in the proximity of an NRHO are complex; the motion is primarily influenced by the Earth and Moon within the vicinity of the NRHO, but spacecraft are signific...

The development of a methodology to move through cislunar space along fundamental dynamical pathways is relevant to NASA’s goals for a cislunar transportation network. To enable an informed design approach for transfer trajectories departing from or arriving at a Near Rectilinear Halo Orbit (NRHO), higher-period orbits that bifurcate from the NRHO...

The objective of the present investigation is to present a framework to produce low-energy trajectories between the vicinities of adjacent moons of a planetary system leveraging libration point orbits in multi-body environments. The current development includes an extension of the Moon-to-Moon Analytical Transfer (MMAT) method previously proposed b...

We present a transformative professional development project with a focus on equity, diversity and social justice (EDSJ) to raise cultural awareness among faculty, increase agency, and promote positive change through transformative projects. Twenty-three faculty members from nine different colleges located at a Research I university were provided w...

Rideshares increase launch capabilities and decrease the launch costs. However, the range of orbits available for secondary payloads is dependent on launch constraints for the primary mission. Additionally, communications constraints and limited propellant options must be incorporated in the preliminary mission design strategy for secondary payload...

While the interest in future missions devoted to Phobos and Deimos increases, missions that explore both moons are expensive in terms of maneuver capabilities partly due to the lack of readily available low-energy transfer options. A design framework that generates transfer trajectories between the Martian moons while leveraging resonant orbits to...

Quasi-periodic orbits offer an extended range of destinations in cislunar space. This investigation focuses on a framework for construction of low-energy transfer trajectories to quasi-periodic orbits in a Sun-perturbed cislunar environment. First, construction of quasi-periodic orbits in the Bicircular Restricted Four-Body Problem (BCR4BP) is deta...

View Video Presentation: https://doi.org/10.2514/6.2022-1276.vid Quasi-periodic or bounded motion in the ephemeris model is generally constructed by transitioning a solution from a lower-fidelity model, such as the Circular Restricted Three-Body Problem (CR3BP). Increased interest in the Earth-Moon L2 Near Rectilinear Halo Orbits (NRHOs) within the...

View Video Presentation: https://doi.org/10.2514/6.2022-1131.vid The Astrodynamics Software and Science Enabling Toolkit (ASSET) is a newly developed spacecraft trajectory optimizing toolkit for deep-space, lunar, and icy worlds exploration. ASSET brings together many practical tools for trajectory optimization into one comprehensive package. To fa...

View Video Presentation: https://doi.org/10.2514/6.2022-1777.vid Satellites deployed from the Gateway in a Near Rectilinear Halo Orbit (NRHO) must be safely delivered to their desired destinations in cislunar space and beyond. The presence of simultaneously significant gravitational forces from the Moon, the Earth, and the Sun, along with the absen...

Computationally efficient guidance is challenging for stationkeeping applications in nonlinear dynamical regions, where a potential onboard control method must satisfy mission requirements on accuracy, computational footprint, and propellant consumption. Furthermore, determining maneuver locations and frequencies is often accomplished heuristically...

Designing tours that involve two or more moons and potentially libration point orbits is a challenging problem with many factors playing important roles. The focus of the present investigation is an efficient and general strategy that aids in the design of tour missions that involve transfers between two or more moons located in their true orbital...

This investigation focuses on examining ballistic lunar transfers that exploit lunar flybys. Properly leveraging lunar flybys to access destinations in cislunar space reduces the required Earth departure energy. Poincaré maps represent information about manifold structures from periodic and quasi-periodic orbits that inform the generation of initia...

Near Rectilinear Halo Orbits (NRHOs) are stable or nearly stable orbits that are defined as part of the L1 and L2 halo orbit families in the circular restricted three-body problem. Within the Earth-Moon regime, the L1 and L2 NRHOs are proposed as long horizon trajectories for cislunar exploration missions, including NASA’s upcoming Gateway mission....

Given the interest in future space missions devoted to the exploration of key moons in the solar system and that may involve libration point orbits, an efficient design strategy for transfers between moons is introduced that leverages the dynamics in these multi-body systems. The moon-to-moon analytical transfer (MMAT) method is introduced, compris...

With an expanding array of activities being examined in the vicinity of near rectilinear halo orbits (NRHOs), nearby destinations for small spacecraft are an essential component. Transfer trajectories from an NRHO to a low lunar orbit (LLO) is one such example, where the significant design challenges are associated with the low level of acceleratio...

As human interest expands outward towards the Moon again, there exists a growing focus on Space Domain Awareness to effectively regulate and track objects in the cislunar region. This investigation explores orbits in the Circular Restricted Three-Body Problem that offer behaviors that are favorable to adequately survey cislunar space between the Ea...

The focus of the present investigation is an efficient and general design strategy for transfers between planetary moons that fulfill specific requirements. The strategy leverages Finite-Time Lyapunov Exponent (FTLE) maps within the context of the Moon-to-Moon Analytical Transfer (MMAT) scheme previously proposed by the authors. Incorporating FTLE...

Stable or nearly stable orbits do not always possess well-distinguished manifold structures that assist in departing from or arriving onto the orbit. Generally, for potential missions, the orbits of interest are nearly stable to reduce the possibility of rapid departure. The stable nature of these orbits also serves as a drawback for insertion or d...

Low-energy ballistic lunar transfers offer propellant efficient paths to the Moon in exchange for longer duration flights. These trajectories rely on the gravitational influence of the Sun to reduce maneuvers at lunar orbit insertion. Due to the sensitive nature of transfers navigating between cislunar and heliocentric space, developing ballistic l...

Given the interest in future space missions devoted to the exploration of key moons in the solar system and that may involve libration point orbits, an efficient design strategy for transfers between moons is introduced that leverages the dynamics in these multi-body systems. The moon-to-moon analytical transfer (MMAT) method is introduced, compris...

Multi-body gravitational systems are inherently chaotic and present unique challenges for spacecraft path planning. Incorporating quasi-periodic orbits into the preliminary design process offers a wide range of options to meet mission constraints in a complex trade space. Linear stability and characterization of families of quasi-periodic orbits is...

Onboard autonomy is an essential component in enabling increasingly complex missions into deep space. In nonlinear dynamical environments, computationally efficient guidance strategies are challenging. Many traditional approaches rely on either simplifying assumptions in the dynamical model or on abundant computational resources. This research effo...

Path planning in the circular restricted 3-body problem (CR3BP) is frequently guided by the forbidden regions and manifold arcs. However, when low thrust is employed to modify the spacecraft trajectory, these dynamical structures pulsate with the varying Hamiltonian value. In a combined CR3BP, low-thrust (CR3BP + LT) model, an additional low-thrust...

The current Gateway baseline orbit, a Near Rectilinear Halo Orbit (NRHO), is a nearly stable orbit that requires regular orbit maintenance (OM) maneuvers for long-term retention of a spacecraft. With missed OM maneuvers, particularly over extended intervals, spacecraft naturally depart from the baseline orbit. In response, a strategy to recover ina...

In space missions, numerical techniques for minimizing the fuel consumption of spacecraft using low-thrust propulsion are desirable. Among various nonlinear optimization methods, convex optimization has been attracting attention because it allows optimal solutions to emerge robustly and requires short computation times. In particular, trajectory de...

The L1 and L2 Near Rectilinear Halo Orbits (NRHOs) are proposed long horizon trajectories for cislunar exploration missions. Due to unmodeled forces as well as orbit determination errors in this dynamically sensitive region, the spacecraft deviates from the desired path. The current investigation focuses on an extended analysis of an impulsive stat...

In the next decades, multiple missions are proposed or planned that originate in the vicinity of the Moon and are to be delivered to heliocentric space, such as servicing missions to the Nancy Roman or the James Webb Space Telescopes, as well as departures from Gateway to other interplanetary destinations. The Earth-Moon-Sun transit dynamics are co...

While the interest in future missions devoted to Phobos and Deimos increases, missions that explore both moons are expensive in terms of maneuver capabilities partly due to low-energy transfer options that may not be readily available. The proposed approach in this investigation includes Mars-Deimos resonant orbits that offer repeated Deimos flybys...

Recent advancements demonstrate machine learning as a potentially effective approach for onboard guidance. Neural network controllers overcome challenging dynamical regions of space and, in contrast to traditional iterative approaches, evaluate in constant time. However, neural networks frequently behave unpredictably, and the resulting control sol...