Astrodynamics, Guidance, Navigation and Control

An innovative trajectory technique for a magnetotail mapping mission is described. With this technique, it is possible to control the apsidal rotation of an elliptical Earth orbit and keep its apogee segment insie the tail region. Robert Farquhar is the lead author, but he died in 2015.

The libration point orbits in the Sun-Earth/Moon system are formed by concurrent gravitational influences by various celestial bodies, originating in a nonlinear dynamical regime. Coupled with the unstable nature of the orbit, the impact of any perturbations are expected to increase rapidly. The feasibility of a flow-based, Cauchy-Green tensor control strategy for station-keeping is examined. An orbit consistent with the mission objectives is selected for examination. The station-keeping process is stochastic, thus Gaussian random errors are introduced for simulation. The evolution of a velocity perturbation over time is monitored, beyond which the attainable state in the accessible region nearest to the target state is employed as a feedback to compute the necessary full, three-component corrective maneuver. The application and appropriateness of single axis control maneuvers for orbit maintenance are also evaluated. The selection procedure for certain parameters such as tolerances and weighting values are developed to incorporate the available dynamical information, yielding a versatile and straightforward strategy. Weighting matrices within the target point approach are effective in influencing the station-keeping costs as well as size and direction of maneuvers. Moreover, selection of appropriate tolerance values in the application of the Cauchy-Green tensor exploits the dominant stretching direction of the perturbation magnitude to inform the maneuver construction process. The work is demonstrated in the context of the upcoming Aditya-1 mission to a Sun-Earth/Moon L1 halo orbit for solar observations and the James Webb Telescope to a Sun-Earth/Moon L2 halo orbit for astronomy.

This paper develops the ontology of space objects for theoretical and computational ontology applied to the space (astronautical/astronomical) domain. It follows “An ontological architecture for Orbital Debris Data” (Rovetto, 2015) and “Preliminaries of a Space Situational Awareness Ontology” (Rovetto, Kelso, 2016). Important considerations for developing a space object ontology, or more broadly, a space domain ontology are presented. The main category term ‘Space Object’ is analyzed from a philosophical perspective, and the ontological commitments of legal definitions for artificial space objects are also discussed. Space object taxonomies are offered and space object terms are defined. Part of the taxonomy of my Space Object Ontology (SOO), a computational ontology under-development using Protege ontology editor, is introduced. Given the narrow scope of an SOO, it serves as a part or module of a broader Space Situational Awareness Ontology, or alternatively an Orbital Space Environment Ontology (Rovetto, 2016).

The orbits of interest for potential missions are stable or nearly stable to maintain long-term presence for conducting scientific studies and to reduce the possibility of rapid departure. Near Rectilinear Halo Orbits (NRHOs) offer such 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. These stable or nearly stable orbits do not possess well-distinguished unstable and stable manifold structures. As a consequence, existing tools for stationkeeping and transfer trajectory design that exploit such underlying manifold structures are not reliable for orbits that are linearly stable. The current investigation focuses on leveraging stretching direction as an alternative for visualizing the flow of perturbations in the neighborhood of a reference trajectory. The information supplemented by the stretching directions are utilized to investigate the impact of maneuvers for two contrasting applications; the stationkeeping problem, where the goal is to maintain a spacecraft near a reference trajectory for a long period of time, and the transfer trajectory design application, where rapid departure and/or insertion is of concern.

Particularly, for the stationkeeping problem, a spacecraft incurs continuous deviations due to unmodeled forces and orbit determination errors in the complex multi-body dynamical regime. The flow dynamics in the region, using stretching directions, are utilized to identify appropriate maneuver and target locations to support a long lasting presence for the spacecraft near the desired path. The investigation reflects the impact of various factors on maneuver cost and boundedness. For orbits that are particularly sensitive to epoch time and possess distinct characteristics in the higher-fidelity ephemeris model compared to their CR3BP counterpart, an additional feedback control is applied for appropriate phasing. The effect of constraining maneuvers in a particular direction is also investigated for the 9:2 synodic resonant southern L2 NRHO, the current baseline for the Gateway mission. The stationkeeping strategy is applied to a range of L1 and L2 NRHOs, and validated in the higher-fidelity ephemeris model.

For missions with potential human presence, a rapid transfer between orbits of interest is a priority. The magnitude of the state variations along the maximum stretching direction is expected to grow rapidly and, therefore, offers information to depart from the orbit. Similarly, the maximum stretching in reverse time, enables arrival with a minimal maneuver magnitude. The impact of maneuvers in such sensitive directions is investigated. Further, enabling transfer design options to connect between two stable orbits. The transfer design strategy developed in this investigation is not restricted to a particular orbit but applicable to a broad range of stable and nearly stable orbits in the cislunar space, including the Distant Retrograde Orbit (DROs) and the Low Lunar Orbits (LLO) that are considered for potential missions. Examples for transfers linking a southern and a northern NRHO, a southern NRHO to a planar DRO, and a southern NRHO to a planar LLO are demonstrated.

The orbital debris problem presents an opportunity for international cooperation toward the mutually beneficial goals of orbital debris prevention, mitigation, remediation, and improved space situational awareness (SSA). Achieving these goals requires sharing orbital debris and other SSA data. Toward this, I present an ontological architecture for the orbital debris and related domains, taking steps in the creation of an orbital debris ontology. The purpose of the ontology is to capture general scientific domain knowledge; formally represent the entities within the domain; form, structure, and standardize (where needed) orbital and SSA terminology; and foster semantic interoperability and data-exchange. In doing so I hope to offer a scientifically accurate ontological representation of the orbital domain; contribute to research in astroinformatics, space ontology, and space data management; and improve spaceflight safety by providing a means to capture and communicate information associated with space debris.

It is well known that orbital debris about Earth impose increasingly
stringent restrictions on the operation and commissioning
of both current and future space applications. These
orbital debris, which are becoming ever so prevalent, can literally
destroy a satellite. Even particles of diminutive stature
can result in disastrous ramifications. Many of these endangered
satellites, of which humans are reliant upon for supplying
the infrastructure necessary to support modern life in
the twenty-first century, routinely have to perform avoidance
manoeuvres in response to ground data indicating that an object
is on a trajectory that could pose a threat, negating away
precious finite amounts fuel. These orbital debris are vexatious,
with respect to not only a spacecraft’s integrity, but also
its lifespan. It is imperative that a solution be realised. This
study aims to demonstrate the feasibility of utilising modular
CubeSats to deorbit space debris. A large high fidelity
simulation is constructed with the goal to simulate the CubeSat’s
orbital dynamics, as well as its autonomous functions.
Such autonomous functions will manifest in the development
of autonomous control algorithms to execute mitigation procedures,
such as path planning and rendezvous, with the intent
of substantiating their real-time implementability.

The main goal of this research is the development of a new approach of Poisson-Darboux problem solution in dual Lie algebra. Using the isomorphism between the Lie group of the rigid displacements SE3 and Lie group of the orthogonal dual tensors SO3 a new solution of this problem is given by recovering the rigid motion knowing its twist. The solution is the replica of the classical Poisson-Darboux problem in the algebra of dual numbers. The results are applied for giving a representation theorem of the six degrees of freedom relative orbital motion problem. Using the n-th order Cayley transformation of dual vectors, the minimal representation of this problem is obtained. The novelty of the method over existing solutions is discussed and the main advantages are revealed.

An assessment of the descending and landing phase of Marco Polo R and OSIRIS-REx missions is performed. A touch-and-go strategy has been analyzed for both scenarios of two distinct target asteroids with different landing requirements. In addition, a full landing with different requirements is also evaluated. The comparison of the different scenarios is done with Monte Carlo analyses using the GNC system and the MIL simulator developed for the previous Marco Polo mission. The result of these analyses is the first step in the research to improve and optimize the GNC requirements, strategy and algorithms for the proximity operations of missions to asteroids.

This paper provides a representation theorem of the onboard exact solution for the six-degree-of-freedom relative orbital motion problem. This problem is quite important, due to its numerous applications: spacecraft formation flying, rendezvous operations, autonomous missions. The common approach is to consider the relative translation and rotation dynamics for the leader–deputy spacecraft formation to be modeled using vector-based formalisms. The proposed approach makes use of a complete dual orthogonal tensor-based construction, which allows for a new description of the full-body relative orbital motion problem. The approach chosen for representing the solution is very short in comparison with the previous reports on the same problem and gives a new formulation that could give important computational benefits. Nomenclature A = real tensor A = dual tensor a = real number a = real vector a = dual number a = dual vector f c = true anomaly h c = specific angular momentum of the leader satellite L…V 3 ; V 3 † = dual-tensor set p c = conic parameter ^ q = real quaternion ^ q = dual quaternion R = real numbers set R = dual numbers set SO 3 = orthogonal real tensors set SO 3 = orthogonal dual-tensor set SO R 3 = time depending real tensorial functions SO R 3 = time depending dual tensorial functions U = unit dual quaternions set U R = time depending unit dual quaternions functions V 3 = real vectors set V 3 = dual vectors set V R 3 = time depending real vectorial functions V R 3 = time depending dual vectorial functions

Orbital debris poses an increasing risk to manned space missions and operational satellites. As
larger networks of electro-optical (EO) sensors are tasked for space surveillance in order to improve
spatiotemporal knowledge of the ever-growing resident space object (RSO) population, it is imperative
that survey designs be autonomously generated such that they optimally balance the visibility, coverage,
and estimation accuracy of RSOs as per the survey objective. To this end, we propose a framework to
quantitatively evaluate designs of EO RSO surveys. Where appropriate, we inherit existing language
and conventions regarding EO sensor and survey design. These functions exhibit good linearity for the
domain of angle and angle-rate measurements that are usually captured in a single image, so a rapid
linear evaluation is locally feasible. A simulation comparing the visibility and coverage of two survey
designs in the near geostationary orbit regime aligns with observer expectations.

Space debris poses an increasing risk for the geosynchronous orbit (GEO) satellites.
Further, space debris is increasing and at least two breakups have been reported
in this regime. Thus it is important to have the capability to detect GEO
objects and update the GEO catalog on a regular basis to ensure the safety of highvalue
assets in this congested orbit regime. It is also important to develop and
evaluate ground-based optical survey designs to help achieve these objectives. The
GEO resident space object environment and the observation properties of GEO
RSO orbits from an Earth-based observatory are studied thoroughly. Based on
this information, efficient and practical surveys will be designed for USU’s Space
Situational Awareness Telescope for Astrodynamics Research (USU-STAR).

The unobservability of space-based angles-only orbit determination can be mitigated by the inclusion of angle measurements from a second optical sensor fixed at a known baseline on the observing spacecraft. Previous approaches to the problem have used these stereoscopic angles to triangulate the position of a second satellite at a given time step. However, due to the nonlinearity of stereo triangulation, zero-mean Gaussian noise of these measurements cannot be assumed. This work investigates a modified approach in which the uncertainty of both angle measurements is used to bound a region for all possible positions of the second satellite. A Gaussian mixture that represents uniform uncertainty across the bounded region for the position of the second object is constructed at two initial time steps. Linkage of the Gaussian mixtures is performed using a new second-order relative Lambert solver in order to formulate a full state probability density function that can be further refined through processing subsequent measurement data in a Bayesian framework.

In this paper an extension of the classical attitude Wahba's problem to a new problem that involves both position and attitude is presented. This new problem is illustrated in the dual algebra of orthogonal dual tensors. Our approach makes use of the isomorphism between the special euclidean group SE 3 and the orthogonal dual tensors group SO 3 , which allows the development of a new technique for solving the proposed problem. This new Wahba problem is directly related to different applications such as point-to-point registration and sensor calibration.

The project had an aim to find out a point after which the forces due to the non-spherical shape of
the asteroid (a conservative force) had negligible effect on a spacecraft orbiting around the
asteroid. The non-spherical shape of asteroid makes it tough for a spacecraft to hover around in an
orbit thus the lifetime of the spacecraft is affected by them sometimes.
Spherical harmonics of the body had a role to make the effect of the aspherical body on the
spacecraft in a simulation done using MATLAB. Two-body and three-body problem also had to
be taken in count to make the conservative forces of the asteroid on spacecraft.
The effect of Keplerian elements on the point where the shape forces have no effect on the orbiter
was found out in the project using MATLAB. The effect of rotation and the radius of the asteroid
(considering asteroid shape to be ellipsoid) on the point was also observed in the project. It was
observed that first Keplerian element (that is the semi-major axis) of the orbit of the spacecraft and
radius of the asteroid were directly related as the semi major axis of the orbit of the orbiter had to
be twelve times (for two-body problem) and four and a half times (for three-body problem) more
than the radius of the asteroid dimension to get the point where the shape forces had no effect on
orbiter. Thus, these were the factors that were used to determine the point where the asteroid could
behave nearly as a point mass for a spacecraft.

This paper provides a representation theorem of the exact solution for the relative orbital motion problem when the motion of the deputy satellite has 6-DOF. This prob- lem is quite important, due to its numerous applications: spacecraft formation flying, rendezvous operations, autonomous missions. The common approach is to consider the relative translational and rotational dynamics for the chief-deputy spacecraft formation to be modeled using vector based formalisms. Our approach makes use of a complete ten- sor based construction which allows the division of the full body problem in a non-inertial frame into two classical full body problems in inertial frames: the Kepler problem and the Euler fixed-point problem.

The solar electric propulsion could be the best option for the transports of the future due to its high specific impulse when compared to the chemical propulsion. Electric propellants are being extensively used to assist the propulsion of terrestrial satellites for the maneuvers of orbit correction and as primary propulsion in missions toward other bodies of the solar system. In this work the optimization of interplanetary missions using solar electric propulsion (SEP) and Gravity Assisted Maneuver to reduce the costs of the mission, is considered. The high specific impulse of electric propulsion makes a Gravity Assisted Maneuver 1 year after departure convenient. Missions for several Near Earth Asteroids will be considered. The analysis suggests criteria for the definition of initial solutions demanded for the process of optimization of trajectories. Trajectories to the asteroid 2002TC70 are analyzed. Direct trajectories, trajectories with 1 gravity assisted at the Earth and with 2 gravity assisted with the Earth and either Mars are presented. Shall be analyzed missions with thrusters PPS1350 and the Phall 1 for performance comparison. An indirect optimization method will be used in the simulations.