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.

Estimation of whole body muscle, adipose/fat mass, validation in health and during weight loss. Development of prediction equations using MRI as reference method

Background: Body composition is affected by diseases, and affects responses to medical treatments, dosage of medicines, etc., while an abnormal body composition contributes to the causation of many chronic diseases. While we have reliable biochemical tests for certain nutritional parameters of body composition, such as iron or iodine status, and we have harnessed nuclear physics to estimate the body’s content of trace elements, the very basic quantification of body fat content and muscle mass remains highly problematic. Both body fat and muscle mass are vitally important, as they have opposing influences on chronic disease, but they have seldom been estimated as part of population health surveillance. Instead, most national surveys have merely reported BMI and waist, or sometimes the waist/hip ratio; these indices are convenient but do not have any specific biological meaning. Anthropometry offers a practical and inexpensive method for muscle and fat estimation in clinical and epidemiological settings; however, its use is imperfect due to many limitations, such as a shortage of reference data, misuse of terminology, unclear assumptions, and the absence of properly validated anthropometric equations. To date, anthropometric methods are not sensitive enough to detect muscle and fat loss. Aims: The aim of this thesis is to estimate Adipose/fat and muscle mass in health disease and during weight loss through; 1. evaluating and critiquing the literature, to identify the best-published prediction equations for adipose/fat and muscle mass estimation; 2. to derive and validate adipose tissue and muscle mass prediction equations; and 3.to evaluate the prediction equations along with anthropometric indices and the best equations retrieved from the literature in health, metabolic illness and during weight loss. Methods: a Systematic review using Cochrane Review method was used for reviewing muscle mass estimation papers that used MRI as the reference method. Fat mass estimation papers were critically reviewed. Mixed ethnic, age and body mass data that underwent whole body magnetic resonance imaging to quantify adipose tissue and muscle mass (dependent variable) and anthropometry (independent variable) were used in the derivation/validation analysis. Multiple regression and Bland-Altman plot were applied to evaluate the prediction equations. To determine how well the equations identify metabolic illness, English and Scottish health surveys were studied. Statistical analysis using multiple regression and binary logistic regression were applied to assess model fit and associations. Also, populations were divided into quintiles and relative risk was analysed. Finally, the prediction equations were evaluated by applying them to a pilot study of 10 subjects who underwent whole-body MRI, anthropometric measurements and muscle strength before and after weight loss to determine how well the equations identify adipose/fat mass and muscle mass change. Results: The estimation of fat mass has serious problems. Despite advances in technology and science, prediction equations for the estimation of fat mass depend on limited historical reference data and remain dependent upon assumptions that have not yet been properly validated for different population groups. Muscle mass does not have the same conceptual problems; however, its measurement is still problematic and reference data are scarce. The derivation and validation analysis in this thesis was satisfactory, compared to prediction equations in the literature they were similar or even better. Applying the prediction equations in metabolic illness and during weight loss presented an understanding on how well the equations identify metabolic illness showing significant associations with diabetes, hypertension, HbA1c and blood pressure. And moderate to high correlations with MRI-measured adipose tissue and muscle mass before and after weight loss. Conclusion: Adipose tissue mass and to an extent muscle mass can now be estimated for many purposes as population or groups means. However, these equations must not be used for assessing fatness and categorising individuals. Further exploration in different populations and health surveys would be valuable.