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.

An investigation of the possible health-promoting modes of action of regular- and super- doses of phytase in the broiler chicken

The overall objective of this thesis was to study the effects of regular and high (super-) doses of phytase in the gut of broilers, with the aim of documenting the mechanism of their action leading to improvements in animal health. Phytase is often supplemented to commercial broiler diets to facilitate the hydrolysis of plant phytate and release of phosphorus for utilisation. Although not the original intention of its addition, phytase supplementation leads to improvements in growth performance parameters and enhanced nutrient utilisation. Further benefits have also been observed following the addition of super-doses of phytase which are not explained by an increase in phosphorus release, and thus have been termed ‘extra-phosphoric effects’. Using diets formulated to be adequate or marginally deficient in available phosphorus (aP; forming the negative control, NC), phytase was supplemented at 1,500 and 3,000 FTU/kg phytase in the first study (both super-doses) and the partitioning of nutrients within the body was investigated. It appeared that there were some metabolic changes between 1,500 and 3,000 FTU/kg, switching between protein and fat accretion, potentially as a consequence of nutrient availability, although these changes were not reflected by changes in growth performance parameters. However, the loss of the NC treatment without phytase on day 12 limits the comparison of the phytase within the NC treatment, but does allow for comparison of each dose at adequate or low dietary aP levels. As expected, a greater degree of phytate hydrolysis was achieved with 3,000 than with 1,500 FTU/kg phytase, but changes in carcass accretion characteristics were greater with 1,500 than 3,000 FTU/kg. Using these findings and the observation that there were no further changes in the parameters measured by increasing phytase from 1,500 to 3,000 FTU/kg (aside from phytate hydrolysis), 1,500 FTU/kg phytase was selected as the super-dose to be used in subsequent studies. The next study considered the influence of regular (500 FTU/kg) and super doses (1,500 FTU/kg) of phytase from within the gut. Overall, it was observed that changes were occurring to the gut environment, which ultimately would influence the absorptive capacity and conditions for further phytate hydrolysis. Dietary treatment influenced gut conditions such as pH, intestinal morphology and bacterial populations which can subsequently influence nutrient utilisation and potential for growth. The subsequent study was designed to investigate the effects within the gut in more detail. The release of nutrients from phytate hydrolysis and their bioavailability within the digesta can influence conditions within intestine, facilitating enhanced absorption. One of the parameters investigated was the expression of genes involved in the transport of nutrients in the intestine. Overall, there were few significant dietary treatment influences on gene expression in the intestine, however there was a dose-dependent response of phytase on the expression of the jejunual divalent mineral transporter. This indicates a change in divalent mineral bioavailability in the intestine, with correlations with inositol phosphate esters (IPs) being identified. This is likely explained by the IPs produced by phytase hydrolysis and accumulating in the digesta, differing between regular and high doses of phytase. It became apparent that interactions between the products of phytate hydrolysis (IP3, IP4) and minerals in the digesta had the potential to influence the gut environment and subsequent nutrient bioavailability and overall phytase action. The final study was designed to increase the content of the IPs, and investigate the influence of phytase under these conditions. As the complete hydrolysis of phytate to myo-inositol has been reported to be beneficial due to its proposed insulin mimetic effects, myo-inositol was also supplemented to one of the diets to see if any further benefits would be observed when supplemented alongside super-doses of phytase. Neither increased concentrations of the higher IP esters (IP6, IP5 and IP4) nor myo-inositol (myo-) had any effect on broiler growth performance, however there were still apparent beneficial influences of phytase supplementation. The results suggest considerable and important interactions between minerals and IP esters within the digesta, which ultimately have the potential to influence gut conditions and thus nutrient utilisation and growth performance. Reduced concentrations of blood glucose in the high IP ester diet with additional phytase supplementation suggest some insulin-like effects of myo- production. Additionally, the lack of effect of myo- supplementation on blood glucose and insulin concentrations suggests a difference between the structure of phytase-produced myo- and supplemented myo-. Although there were no improvements in growth performance by increasing phytase from 500 to 1,500 FTU/kg, there were changes occurring at the level of the gut and expression of genes in the intestine, influencing nutrient utilisation and the partitioning of nutrients within the body. There are many factors to be considered when supplementing phytase, with dietary nutrient content and nutrient release and IP production during phytate hydrolysis having an influence on phytase action, nutrient absorption and conditions within the gut. Super-doses of phytase may be beneficial for maintaining optimal gut conditions, clearing IP esters from the digesta, reducing their potential to form complexes with minerals and other nutrients, ultimately influencing the efficiency of production.