Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft

The idea of spacecraft formations, flying in tight configurations with maximum baselines of a few hundred meters in low-Earth orbits, has generated widespread interest over the last several years. Nevertheless, controlling the movement of spacecraft in formation poses difficulties, such as in-orbit high-computing demand and collision avoidance capabilities, which escalate as the number of units in the formation is increased and complicated nonlinear effects are imposed to the dynamics, together with uncertainty which may arise from the lack of knowledge of system parameters. These requirements have led to the need of reliable linear and nonlinear controllers in terms of relative and absolute dynamics. The objective of this thesis is, therefore, to introduce new control methods to allow spacecraft in formation, with circular/elliptical reference orbits, to efficiently execute safe autonomous manoeuvres. These controllers distinguish from the bulk of literature in that they merge guidance laws never applied before to spacecraft formation flying and collision avoidance capacities into a single control strategy. For this purpose, three control schemes are presented: linear optimal regulation, linear optimal estimation and adaptive nonlinear control. In general terms, the proposed control approaches command the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory (TVNT), while the threat of collision between the followers is reduced by repelling accelerations obtained from the collision avoidance scheme during the periods of closest proximity. Linear optimal regulation is achieved through a Riccati-based tracking controller. Within this control strategy, the controller provides guidance and tracking toward a desired TVNT, optimizing fuel consumption by Riccati procedure using a non-infinite cost function defined in terms of the desired TVNT, while repelling accelerations generated from the CAS will ensure evasive actions between the elements of the formation. The relative dynamics model, suitable for circular and eccentric low-Earth reference orbits, is based on the Tschauner and Hempel equations, and includes a control input and a nonlinear term corresponding to the CAS repelling accelerations. Linear optimal estimation is built on the forward-in-time separation principle. This controller encompasses two stages: regulation and estimation. The first stage requires the design of a full state feedback controller using the state vector reconstructed by means of the estimator. The second stage requires the design of an additional dynamical system, the estimator, to obtain the states which cannot be measured in order to approximately reconstruct the full state vector. Then, the separation principle states that an observer built for a known input can also be used to estimate the state of the system and to generate the control input. This allows the design of the observer and the feedback independently, by exploiting the advantages of linear quadratic regulator theory, in order to estimate the states of a dynamical system with model and sensor uncertainty. The relative dynamics is described with the linear system used in the previous controller, with a control input and nonlinearities entering via the repelling accelerations from the CAS during collision avoidance events. Moreover, sensor uncertainty is added to the control process by considering carrier-phase differential GPS (CDGPS) velocity measurement error. An adaptive control law capable of delivering superior closed-loop performance when compared to the certainty-equivalence (CE) adaptive controllers is finally presented. A novel noncertainty-equivalence controller based on the Immersion and Invariance paradigm for close-manoeuvring spacecraft formation flying in both circular and elliptical low-Earth reference orbits is introduced. The proposed control scheme achieves stabilization by immersing the plant dynamics into a target dynamical system (or manifold) that captures the desired dynamical behaviour. They key feature of this methodology is the addition of a new term to the classical certainty-equivalence control approach that, in conjunction with the parameter update law, is designed to achieve adaptive stabilization. This parameter has the ultimate task of shaping the manifold into which the adaptive system is immersed. The performance of the controller is proven stable via a Lyapunov-based analysis and Barbalat’s lemma. In order to evaluate the design of the controllers, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) are implemented, extending the number of elements in the formation into scenarios with reconfigurations and on-orbit position switching in elliptical low-Earth reference orbits. An extensive analysis and comparison of the performance of the controllers in terms of total Δv and fuel consumption, with and without the effects of the CAS, is presented. These results show that the three proposed controllers allow the followers to asymptotically track the desired nominal trajectory and, additionally, those simulations including CAS show an effective decrease of collision risk during the performance of the manoeuvre.

Tracing outsideness: young women's institutional journeys and the geographies of closed space

Understanding confinement and its complex workings between individuals and society has been the stated aim of carceral geography and wider studies on detention. This project contributes ethnographic insights from multiple sites of incarceration, working with an under-researched group within confined populations. Focussing on young female detainees in Scotland, this project seeks to understand their experiences of different types of ‘closed’ space. Secure care, prison and closed psychiatric facilities all impact on the complex geographies of these young women’s lives. The fluid but always situated relations of control and care provide the backdrop for their journeys in/out and beyond institutional spaces. Understanding institutional journeys with reference to age and gender allows an insight into the highly mobile, often precarious, and unfamiliar lives of these young women who live on the margins. This thesis employs a mixed-method qualitative approach and explores what Goffman calls the ‘tissue and fabric’ of detention as a complex multi-institutional practice. In order to be able to understand the young women’s gendered, emotional and often repetitive experiences of confinement, analysis of the constitution of ‘closed space’ represents a first step for inquiry. The underlying nature of inner regimes, rules and discipline in closed spaces, provide the background on which confinement is lived, perceived and processed. The second part of the analysis is the exploration of individual experiences ‘on the inside’, ranging from young women’s views on entering a closed institution, the ways in which they adapt or resist the regime, and how they cope with embodied aspects of detention. The third and final step considers the wider context of incarceration by recovering the young women’s journeys through different types of institutional spaces and beyond. The exploration of these journeys challenges and re-develops understandings of mobility and inertia by engaging the relative power of carceral archipelagos and the figure of femina sacra. This project sits comfortably within the field of carceral geography while also pushing at its boundaries. On a conceptual level, a re-engagement with Goffman’s micro-analysis challenges current carceral-geographic theory development. Perhaps more importantly, this project pushes for an engagement with different institutions under the umbrella of carceral geography, thus creating new dialogues on issues like ‘care’ and ‘control’. Finally, an engagement with young women addresses an under-represented population within carceral geography in ways that raise distinctly problematic concerns for academic research and penal policy. Overall, this project aims to show the value of fine grained micro-level research in institutional geographies for extending thinking and understanding about society’s responses to a group of people who live on the margins of social and legal norms.

Exploring redox-driven self-assembly of mixed metal polyoxometalates

How can we control the experimental conditions towards the isolation of specific structures? Why do particular architectures form? These are some challenging questions that synthetic chemists try to answer, specifically within polyoxometalate (POM) chemistry, where there is still much unknown regarding the synthesis of novel molecular structures in a controlled and predictive manner. This work covers a wide range of POM chemistry, exploring the redox self-assembly of polyoxometalate clusters, using both “one-pot”, flow and hydrothermal conditions. For this purpose, different vanadium, molybdenum and tungsten reagents, heteroatoms, inorganic salts and reducing agents have been used. The template effect of lone-pair containing pyramidal heteroatoms has been investigated. Efforts to synthesize new POM clusters displaying pyramidal heteroanions (XO32-, where X= S, Se, Te, P) are reported. The reaction of molybdenum with vanadium in the presence of XO32- heteroatoms is explored, showing how via the cation and experimental control it is possible to direct the self-assembly process and to isolate isostructural compounds. A series of four isostructural (two new, namely {Mo11V7P} and {Mo11V7Te} and two already known, namely {Mo11V7Se} and {Mo11V7S} disordered egg-shaped Polyoxometalates have been reported. The compounds were characterized by X-ray structural analysis, TGA, UV-Vis, FT-IR, Elemental and Flame Atomic Absorption Spectroscopy (FAAS) analysis and Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES). Cyclic Voltammetry measurements have been carried out in all four compounds showing the effect of the ionic density of the heteroatom on the potential. High-Resolution ESI-MS studies have revealed that the structures retain their integrity in solution. Efforts to synthesize new mixed-metal compounds led to isolation, structural, and electronic characterization of the theoretically predicted, but experimentally elusive δ-isomer of the Keggin polyoxometalate cluster anion, {H2W4V9O33(C6H13NO3)}, by the reaction of tungstate(VI) and vanadium(V) with triethanolammonium ions (TEAH), acting as a tripodal ligand grafted to the surface of the cluster. Control experiments (in the absence of the organic compound) have proven that the tripodal ligand plays crucial role on the formation of the isomer. The six vanadium metal centres, which consist the upper part of the cluster, are bonded to the “capping” TEA tripodal ligand. This metal-ligand bonding directs and stabilises the formation of the final product. The δ-Keggin species was characterized by single-crystal X-ray diffraction, FT-IR, UV-vis, NMR and ESI-MS spectrometry. Electronic structure and structure-stability correlations were evaluated by means of DFT calculations. The compounds exhibited photochromic properties by undergoing single-crystal-to-single-crystal (SC-SC) transformations and changing colour under light. Non-conventional synthetic approaches are also used for the synthesis of the POM clusters comparing the classical “one-pot” reaction conditions and exploring the synthetic parameters of the synthesis of POM compounds. Reactions under hydrothermal and flow conditions, where single crystals that depend on the solubility of the minerals under hot water and high pressure can be synthesized, resulted in the isolation of two isostructural compounds, namely, {Mo12V3Te5}. The compound isolated from a continuous processing method, crystallizes in a hexagonal crystal system, forming a 2D porous plane net, while the compound isolated using hard experimental conditions (high temperature and pressure) crystallizes in monoclinic system, resulting in a different packing configuration. Utilizing these alternative synthetic approaches, the most kinetically and thermodynamically compounds would possibly be isolated. These compounds were characterised by single-crystal X-ray diffraction, FT-IR and UV-vis spectroscopy. Finally, the redox-controlled driven oscillatory template exchange between phosphate (P) and vanadate (V) anions enclosed in an {M18O54(XO4)2} cluster is further investigated using UV-vis spectroscopy as a function of reaction time, showed that more than six complete oscillations interconverting the capsule species present in solution from {P2M18} to {V2M18} were possible, provided that a sufficient concentration of the TEA reducing agent was present in solution. In an effort to investigate the periodicity of the exchange of the phosphate and vanadate anions, time dependent Uv-vis measurements were performed for a period at a range of 170-550 hours. Different experimental conditions were also applied in order to investigate the role of the reducing agent, as well as the effect of other experimental variables on the oscillatory system.