Missions to explore near-Earth asteroids are gaining popularity thanks to their enormous scientific and technological fallouts. As a matter of fact, missions to asteroids are not only being conceived for their obvious scientific implications and contributions to our understanding of the evolution processes of the Solar System formation, but there is also a growing interest asteroid missions both, as potential assets for mining and resource exploitation, and for planetary defense purposes, so asteroid deflection technologies can be demonstrated, in case they were needed one day. The dynamical environment around asteroids is complex and highly nonlinear, so spacecraft operations around these bodies requires, among other things, extremely accurate information of their gravitational field. This information is not only vital for the safe operations of the spacecraft, but can also provide valuable information from which scientific data can be derived, such as the asteroid's composition, internal structure and physical properties. Different techniques are available for determining the gravity field of a celestial body; however, for the case of asteroids and due to a lack of on-ground infrastructure, the only methods available are those based on inference from the perturbed orbital motion of a spacecraft orbiting the asteroid. These techniques, however, are only as accurate as the orbit determination data is, and also depend strongly on the orbital altitude, the number of available measurements and their ground coverage, or rather, the asteroid locations that the spacecraft flies over (and thus, the spherical harmonics to which the spacecraft is exposed to). In order to overcome some of the aforementioned limitations, using a $swarm$ of small satellites deployed from a main satellite (i.e. a mothership) could potentially contribute to obtaining a higher number of measurements (thus providing higher redundancy and robustness of the solution), and of more diverse characteristics (i.e. measurements at different altitudes and flying over different locations on the surface), than only a single spacecraft could provide; therefore, a swarm could potentially improve the number and quality of the data, and thus yield a better fidelity of the gravity field determination solution. Hence, the use of satellite swarms presents a novel approach to the problem of gravity field determination of an asteroids, which is investigated in this thesis in an attempt to develop new, innovative methods for asteroid gravimetry. In particular, the main interrogative is whether the determination of an asteroid gravity field from orbital data can be enhanced via the deployment of multiple small-sized spacecraft that provide inter-satellite relative position measurements. To this end, this study focuses on: 1) understanding if, and how, the proposed emph{swarm} approach can improve the accuracy of the gravity field solutions; and 2) assessing the performances of these newly developed method when different kinds of observables and swarm deployment configurations are considered. In brief, the main objective was to create the basis for a feasibility study of a real mission scenario based on the aforementioned ideas. To obtain these results, the gravitational field was modeled with a spherical harmonics expansion, which is uniquely characterised by a set of gravitational coefficients. With this model, a non-linear optimisation algorithm was proposed and implemented to compute estimates of the gravity field based on orbital data. Two more novel approaches were also treated, one focused on retrieving in a direct way a mascon model of the asteroid, where lumped masses were located in fixed positions on the asteroid's approximating ellipsoid, while the other intended to formulate an augmentation of the Orbit determination algorithm proposed by Nayfeh. The aforementioned framework was then used to analyze different approaches to the problem of estimation of the gravitational parameters using a swarm of satellites. The advantage of a swarm is that it allows for inter-satellite relative measurements, and for this reason techniques of relative motion propagation were investigated an implemented. Additionally, different swarm deployment strategies were proposed and analyzed based on the their performances in the different configurations and observables available, such as relative position in Cartesian coordinates, range and range-rate. Based on these analyses, it was possible to make a preliminary assessment of the technological complexity of such a distributed gravity sensing system, and the number of spacecraft that the swarm would be comprised of to provide reliable estimates. The robustness of the proposed approach was evaluated introducing uncertainties, noise, and neglected dynamics, while assessing its sensitivity to some of the model parameters.
Le missioni per esplorare asteroidi vicini alla Terra stanno diventando sempre più popolari a causa della ricaduta scientifico-tecnologica che possono generare. Infatti, oltre ad avere implicazioni sugli attuali modelli di formazione del nostro Sistema Solare, l’interesse è crescente verso lo studio della deflessione di asteroidi, la difesa planetaria e verso tecnologie di mining per lo sfruttamento delle risorse in-situ. Sfortunatamente queste operazioni necessitano di informazioni estremamente precise sul campo gravitazionale del corpo di interesse. E’ inoltre necessario caratterizzare l’ambiente asteroidale per selezionare i candidati per missioni esplorative e stabilirne composizione e proprietà fisiche. La gravità di un corpo si osserva tipicamente misurandone l’effetto sulla traiettoria di un satellite che orbita presso lo stesso. Riuscendo a misurare il movimento di un satellite è possibile stimare le proprietà gravitazionali del corpo centrale, ma l’accuratezza della stessa stima dipende dal numero, dalla precisione e dalla diversità geometrica delle misurazioni. L’uso di uno “sciame” di piccoli satelliti tutti uguali tra loro (autonomi o no) dispiegati da un satellite principale, potrebbe porre una soluzione al problema, nonché diminuire il rischio associato alla missione a causa della ridondanza dei satelliti stessi. Sulla necessità di investigare metodi e soluzioni innovativi per la gravimetria asteroidale getta le basi questo studio, il cui obiettivo è quindi di sviluppare nuovi approcci al problema e di ottenere una strategia efficace per la determinazione della gravimetria degli asteroidi. In particolare, il principale interrogativo proposto riguarda il miglioramento della stima di campo gravitazionale in caso di un approccio multi-satellite con misure relative. A differenza di altri studi, ci si soffermerà a capire se e come un approccio del genere possa dare luogo a stime più accurate, e successivamente a studiarne le performances utilizzando diversi tipi di misura delle coordinate relative. Lo scopo è principalmente quello di creare le fondamenta per uno studio di fattibilità per una missione reale basato sulle idee precedentemente menzionate. oindent Per ottenere questi risultati, in primo luogo il campo gravitazionale è stato modellato tramite uno sviluppo in armoniche sferiche, il quale è unicamente caratterizzato dai valori dei coefficienti gravitazionali. Con questo modello sono stati proposti ed implementati algoritmi di ottimizazione non-lineare utilizzati per la stima del campo gravitazionale basata su dati orbitali. In più, sono stati trattati altri approcci innovativi: uno basato sulla stima diretta del campo gravitazionale modellato con mascon models, dove le masse concentrate sono state posizionate in dei punti equispaziati sull'ellissoide che approssima l'asteroide; l'altro invece propone un nuovo algoritmo di stima del campo gravitazionale basato sull'algoritmo di determinazione orbitale di Nayfeh. Successivamente si sfrutterà questo framework per analizzare vari approcci di determinazione dei parametri gravitazionali mediante sciami (“swarm”) di satelliti. Il vantaggio dello sciame è che permette di ottenere misurazioni relative infra-satellite, ragion per cui sono state inoltre implementate tecniche di propagazione basate sul moto relativo. A questo proposito sono state proposte una serie di strategie di dispiegamento ed in base ad esse analizzate le performances del sistema nelle varie configurazioni e tipi di misurazioni disponibili, dalla semplice distanza relativa infra-satellite e arrivando alla completa disponibilità di posizioni relative in riferimento Cartesiano. In base a queste analisi si è stabilita la complessità tecnologica delle misure necessaria per gli individui dello sciame, e il numero di particelle necessarie per una stima affidabile. Verrà inoltre valutata la robustezza del metodo infine adottato introducendo incertezze, rumori di misura e dinamiche trascurate, mentre infine è stata studiata la sensitività del modello ai diversi parametri dello stesso.
Asteroid gravity field determination using swarm of satellites
PIETRODANGELO, ANDREA
2020/2021
Abstract
Missions to explore near-Earth asteroids are gaining popularity thanks to their enormous scientific and technological fallouts. As a matter of fact, missions to asteroids are not only being conceived for their obvious scientific implications and contributions to our understanding of the evolution processes of the Solar System formation, but there is also a growing interest asteroid missions both, as potential assets for mining and resource exploitation, and for planetary defense purposes, so asteroid deflection technologies can be demonstrated, in case they were needed one day. The dynamical environment around asteroids is complex and highly nonlinear, so spacecraft operations around these bodies requires, among other things, extremely accurate information of their gravitational field. This information is not only vital for the safe operations of the spacecraft, but can also provide valuable information from which scientific data can be derived, such as the asteroid's composition, internal structure and physical properties. Different techniques are available for determining the gravity field of a celestial body; however, for the case of asteroids and due to a lack of on-ground infrastructure, the only methods available are those based on inference from the perturbed orbital motion of a spacecraft orbiting the asteroid. These techniques, however, are only as accurate as the orbit determination data is, and also depend strongly on the orbital altitude, the number of available measurements and their ground coverage, or rather, the asteroid locations that the spacecraft flies over (and thus, the spherical harmonics to which the spacecraft is exposed to). In order to overcome some of the aforementioned limitations, using a $swarm$ of small satellites deployed from a main satellite (i.e. a mothership) could potentially contribute to obtaining a higher number of measurements (thus providing higher redundancy and robustness of the solution), and of more diverse characteristics (i.e. measurements at different altitudes and flying over different locations on the surface), than only a single spacecraft could provide; therefore, a swarm could potentially improve the number and quality of the data, and thus yield a better fidelity of the gravity field determination solution. Hence, the use of satellite swarms presents a novel approach to the problem of gravity field determination of an asteroids, which is investigated in this thesis in an attempt to develop new, innovative methods for asteroid gravimetry. In particular, the main interrogative is whether the determination of an asteroid gravity field from orbital data can be enhanced via the deployment of multiple small-sized spacecraft that provide inter-satellite relative position measurements. To this end, this study focuses on: 1) understanding if, and how, the proposed emph{swarm} approach can improve the accuracy of the gravity field solutions; and 2) assessing the performances of these newly developed method when different kinds of observables and swarm deployment configurations are considered. In brief, the main objective was to create the basis for a feasibility study of a real mission scenario based on the aforementioned ideas. To obtain these results, the gravitational field was modeled with a spherical harmonics expansion, which is uniquely characterised by a set of gravitational coefficients. With this model, a non-linear optimisation algorithm was proposed and implemented to compute estimates of the gravity field based on orbital data. Two more novel approaches were also treated, one focused on retrieving in a direct way a mascon model of the asteroid, where lumped masses were located in fixed positions on the asteroid's approximating ellipsoid, while the other intended to formulate an augmentation of the Orbit determination algorithm proposed by Nayfeh. The aforementioned framework was then used to analyze different approaches to the problem of estimation of the gravitational parameters using a swarm of satellites. The advantage of a swarm is that it allows for inter-satellite relative measurements, and for this reason techniques of relative motion propagation were investigated an implemented. Additionally, different swarm deployment strategies were proposed and analyzed based on the their performances in the different configurations and observables available, such as relative position in Cartesian coordinates, range and range-rate. Based on these analyses, it was possible to make a preliminary assessment of the technological complexity of such a distributed gravity sensing system, and the number of spacecraft that the swarm would be comprised of to provide reliable estimates. The robustness of the proposed approach was evaluated introducing uncertainties, noise, and neglected dynamics, while assessing its sensitivity to some of the model parameters.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/183558