In this paper we present a new approach to solve the fuel-efficient powered descent guidance problem on large planetary bodies with no atmosphere (e.g., Moon or Mars) using the recently developed Theory of Functional Connections. The problem is formulated using the indirect method which casts the optimal guidance problem as a system of nonlinear two-point boundary value problems. Using the Theory of Functional Connections, the problem's linear constraints are analytically embedded into a functional, which maintains a free-function that is expanded using orthogonal polynomials with unknown coefficients. The constraints are always analytically satisfied regardless of the values of the unknown coefficients (e.g., the coefficients of the free-function) which converts the two-point boundary value problem into an unconstrained optimization problem. This process reduces the whole solution space into the admissible solution subspace satisfying the constraints and, therefore, simpler, more accurate, and faster numerical techniques can be used to solve it. In this paper a nonlinear least-squares method is used. In addition to the derivation of this technique, the method is validated in two scenarios and the results are compared to those obtained by the general purpose optimal control software, GPOPS-II. In general, the proposed technique produces solutions of accuracy. Additionally, for the proposed test cases, it is reported that each individual TFC-based inner-loop iteration converges within 6 iterations, each iteration exhibiting a computational time between 72 and 81 milliseconds, with a total execution time of 2.1 to 2.6 seconds using MATLAB. Consequently, the proposed methodology is potentially suitable for real-time computation of optimal trajectories.

Recent advances with space navigation technologies developed by NASA in space-based atomic clocks and pulsar X-ray navigation, combined with past successes in autonomous navigation using optical imaging, brings to the forefront the need to compare space navigation using optical, radiometric, and pulsar-based measurements using a common set of assumptions and techniques. This review article examines these navigation data types in two different ways. First, a simplified deep space orbit determination problem is posed that captures key features of the dynamics and geometry, and then each data type is characterized for its ability to solve for the orbit. The data types are compared and contrasted using a semi-analytical approach with geometric dilution of precision techniques. The results provide useful parametric insights into the strengths of each data type. In the second part of the paper, a high-fidelity, Monte Carlo simulation of a Mars cruise, approach, and entry navigation problem is studied. The results found complement the semi-analytic results in the first part, and illustrate specific issues such as each data type's quantitative impact on solution accuracy and their ability to support autonomous delivery to a planet.

It is often necessary to identify a pattern of observed craters in a single image of the lunar surface and without any prior knowledge of the camera's location. This so-called "lost-in-space" crater identification problem is common in both crater-based terrain relative navigation (TRN) and in automatic registration of scientific imagery. Past work on crater identification has largely been based on heuristic schemes, with poor performance outside of a narrowly defined operating regime (e.g., nadir pointing images, small search areas). This work provides the first mathematically rigorous treatment of the general crater identification problem. It is shown when it is (and when it is not) possible to recognize a pattern of elliptical crater rims in an image formed by perspective projection. For the cases when it is possible to recognize a pattern, descriptors are developed using invariant theory that provably capture all of the viewpoint invariant information. These descriptors may be pre-computed for known crater patterns and placed in a searchable index for fast recognition. New techniques are also developed for computing pose from crater rim observations and for evaluating crater rim correspondences. These techniques are demonstrated on both synthetic and real images.

Stand-alone deep-space CubeSats are the future of the space sector. For limited budget reasons, these spacecraft need to follow operational-compliant (OC) trajectories: transfers with thrusting and coasting periods imposed at pre-defined time instants. Traditional trajectory optimisation algorithms exhibit convergence problems when handling discontinuous constraints. In this work, a homotopic direct collocation approach is presented. It employs a continuation algorithm that maps the classical bang-bang trajectory of a fuel-optimal low-thrust problem into an OC solution. M-ARGO CubeSat mission is considered as case study for validation, including a realistic thruster model with variable specific impulse and maximum thrust. The trajectories computed with the developed algorithm are compared with non-operational-compliant solutions. Our algorithm produces transfers similar to the optimal solutions with no operational constraint, both in terms of thrusting profile and propellant mass.

Several commercial organizations have recently launched or plan to launch constellations containing thousands of satellites. Such large constellations potentially adversely affect astronomical observations. This study formulates a set of indicators that assess the impact of light pollution from different constellations on ground-based visible band astronomy. These include the statistically expected number of visible and sunlit satellites above ground-based observers, as well as the number that are also expected to be brighter than the currently recommended limit for constellation satellites. The latter indicator provides a consolidated means to evaluate the potential for a constellation to affect ground-based astronomy too severely, by simultaneously accounting for the effects of constellation population, orbital distribution as well as brightness magnitude and variability. For existing constellations, the evaluation process incorporates actual satellite photometric brightness measurements, which are becoming increasingly available in web-accessible databases and repositories. For proposed constellations, a semi-empirical method allows rough approximations of pre-launch light pollution levels, based on observed brightness distributions observed of currently orbiting analog satellites.

This work presents a study of the dynamics in the vicinity of the stable halo orbits in the Earth-Moon system of the circular restricted three-body problem. These solutions include partially elliptic, partially hyperbolic, and elliptic quasi-halo orbits. The first two types of orbits are 2-dimensional quasi-periodic tori, whereas the elliptic orbits are 3-dimensional quasi-periodic tori. Motivated by the Lunar Gateway, this work computes these orbits to explore the 3-parameter family of solutions lying in the vicinity of the stable halo orbits. An algorithm is presented to quantify the size of the invariant surfaces which gives perspective on the size of the orbits. A stability bifurcation is detected where the partially elliptic tori become partially hyperbolic. A nonlinear behavior of the Jacobi constant is observed which differs from the behavior of the quasi-halo orbits emanating from the unstable halo orbits which makeup the majority of the quasi-halo family. Uses of the orbits in the vicinity of the stable halo orbits are identified, and the results highlight characteristics and structure of the family to broaden the understanding of the dynamical structure of the circular restricted three-body problem.

The increasing number and variety of spacecraft that are expected to operate within cislunar space and other multi-body gravitational environments throughout the solar system necessitates the continued development of strategies for rapid trajectory design and design space exploration. In the field of robotics, similar needs have been addressed using motion primitives that capture the fundamental building blocks of motion and are used to rapidly construct complex paths. Inspired by this concept, this paper leverages motion primitives to construct a framework for rapid and informed spacecraft trajectory design in a multi-body gravitational system. First, motion primitives of fundamental solutions, e.g., selected periodic orbits and their stable and unstable manifolds, are generated via clustering to form a discrete summary of segments of the phase space. Graphs of motion primitives are then constructed and searched to produce primitive sequences that form candidate initial guesses for transfers of distinct geometries. Continuous transfers are computed from each initial guess using multi-objective constrained optimization and collocation. This approach is demonstrated by constructing an array of geometrically distinct transfers between libration point orbits in the Earth-Moon circular restricted three-body problem with impulsive maneuvers.

This paper documents the results from the highly successful Lunar flashlight Optical Navigation Experiment with a Star tracker (LONEStar). Launched in December 2022, Lunar Flashlight (LF) was a NASA-funded technology demonstration mission. After a propulsion system anomaly prevented capture in lunar orbit, LF was ejected from the Earth-Moon system and into heliocentric space. NASA subsequently transferred ownership of LF to Georgia Tech to conduct an unfunded extended mission to demonstrate further advanced technology objectives, including LONEStar. From August to December 2023, the LONEStar team performed on-orbit calibration of the optical instrument and a number of different OPNAV experiments. This campaign included the processing of nearly 400 images of star fields, Earth and Moon, and four other planets (Mercury, Mars, Jupiter, and Saturn). LONEStar provided the first on-orbit demonstrations of heliocentric navigation using only optical observations of planets. Of special note is the successful in-flight demonstration of (1) instantaneous triangulation with simultaneous sightings of two planets with the LOST algorithm and (2) dynamic triangulation with sequential sightings of multiple planets.