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.

Administrative justice and the control of bureaucratic decision-making: A study investigating how decision-makers in local authority education departments respond to the work of redress mechanisms

This socio-legal thesis has explored the factors responsible for explaining whether and how redress mechanisms control bureaucratic decision-making. The research considered the three principal institutions of administrative justice: courts, tribunals, and ombudsman schemes. The field setting was the local authority education area and the thesis examined bureaucratic decision-making about admissions to school, home-to-school transport, and Special Educational Needs (SEN). The thesis adopted a qualitative approach, using interviews and documentary research, within a multiple embedded case study design. The intellectual foundations of the research were inter-disciplinary, cutting across law, socio-legal studies, public administration, organization studies, and social policy. The thesis drew on these scholarly fields to explore the nature of bureaucratic decision-making, the extent to which it can be controlled and the way that learning occurs in bureaucracies and, finally, the extent to which redress mechanisms might exercise control. The concept of control was studied across all its dimensions – in relation both to ex post control in specific cases and the more challenging notion of ex ante or structuring control. The aim of the thesis was not to measure the prevalence of bureaucratic control by redress mechanisms, but to understand the factors that might explain its presence or absence in a particular area. The findings of the research have allowed for a number of analytical refinements and extensions to be made to existing theoretical and empirical understandings. 14 factors, along with 87 supporting propositions, have been set out with the aim of making empirically derived suggestions which can be followed up in future research. In terms of the thesis’ contribution to existing knowledge, its comparative focus and its emphasis on the broad notion of control offered the potential for new insights to be developed. Overall, the thesis claims to have made three contributions to the conceptual framework for understanding the exercise of control by redress mechanisms: it emphasizes the importance of ‘feedback’ in relation to the nature of the cases referred to redress mechanisms; it calls attention to the structure of bureaucratic decision-making as well as its normative character; and it discusses how the operational modes of redress mechanisms relate to their control functions.