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.

The impact and control of malignant catarrhal fever in Tanzania

Malignant Catarrhal Fever (MCF), an often-lethal infectious disease, presents as a variable complex of lesions in susceptible ungulate species. The disease is caused by a -herpesvirus following transmission from an inapparent carrier host. Two major epidemiological forms exist: wildebeest-associated MCF (WA-MCF), in which the virus is transmitted to susceptible species by wildebeest calves less than approximately four months of age, and sheepassociated MCF (SA-MCF) in which the virus is spread by sheep (primarily adolescents). Due to the lack of an in-vitro propagation system for the causative agent of the more economically significant SA-MCF, and with the expectation that cross-protective immunity may be provided, vaccine development has focused on the more easily propagated alcelaphine herpesvirus-1 (AlHV-1) that causes WA-MCF. In 2008 a direct viral challenge trial showed that a novel vaccine, employing an attenuated AlHV-1 (atAlHV-1) `C5000 virus strain, protected British Friesian-Holstein (FH) cattle against an intranasal challenge with virulent AlHV-1 `C5000 virus. For cattle keeping people living near wildebeest calving areas in sub-Saharan Africa an effective vaccine would have value as it would release them from the costly annual disease avoidance strategy of having to move their herds away from the oncoming wildebeest. On the other hand, an effective vaccine will release herd owners from the need to avoid MCF, allowing them to graze their cattle alongside wildebeest on the highly nutritious pastures of the calving areas. As such conservationists have raised concerns that the development of a vaccine might lead to detrimental grazing competition. The principle objective of this study was to test the novel vaccine on Tanzanian shorthorn zebu cross cattle (SZC).We did this firstly using a natural challenge field trial (Chapter Two) which demonstrated that immunisation with the atAlHV-1 vaccine was well tolerated and induced an oro-nasopharyngeal AlHV-1-specific and -neutralising antibody response. This resulted in an immunity in SZC cattle that was partially protective and reduced naturally transmitted infection by 56%. We also demonstrated that non-fatal infections occurred with a much higher frequency than previously thought. Because the calculated efficacy of the vaccine was less than that seen in British FH cattle we wanted to determine whether host factors, particular to SZC cattle, had impacted the outcomes of the field trial. To do this we repeated the 2008 direct viral challenge trial using SZC cattle (Chapter Four). During this trial we also investigated whether the recombinant bacterial flagellin monomer (FliC), when used as an adjuvant, might improve the vaccine’s efficacy. The findings from this trial indicated that direct challenge with pathogenic AlHV-1 is effective at inducing MCF in SZC cattle and that FliC is not an appropriate adjuvant for this vaccine. Furthermore, with less control group cattle dying of MCF than expected we speculate that SZC cattle may have a degree of resistance to MCF that affords them protection from infection and developing fatal disease. In Chapter Three we investigated aspects of the epidemiology of MCF, specifically whether wildebeest placenta, long implicated by Maasai cattle owners as a source of MCF, might play a role in viral transmission. Additionally, through comparative sequence analysis, at two specific genes (A9.5 and ORF50) of wild-type and atAlHV-1, we investigated whether the `C5000 strain, the source of which was taken from Africa more than 40 years ago, was appropriate for vaccine development. The detection of AlHV-1 virus in approximately 50% of placentae indicated that infection can occur in-utero and that this tissue might play a role in disease transmission. And, despite describing three new alleles of the A9.5 gene (supporting previous evidence that this gene is polymorphic and encodes a secretory protein with interleukin-4 as the major homologue), the observation that the most frequently detected haplotypes, in both wild-type and attenuated AlHV-1, were identical suggests that AlHV-1 has a slow molecular clock and that the attenuated strain was appropriate for vaccine development. In Chapter Five we present the first quantitative assessment of the annual MCF avoidance costs that Maasai pastoralists incur. In particular we estimated that as a result of MCF avoidance 64% of the total daily milk yield during the MCF season was not available to be used by the 81% of the family unit remaining at the permanent boma. This represents an upper-bound loss of approximately 8% of a household0s annual income. Despite these considerable losses we concluded that, given an incidence of fatal MCF in cattle living in wildebeest calving areas of 5% to 10%, if herd owners were to stop trying to avoid MCF by allowing their cattle to graze alongside wildebeest, any gains made through increased availability of milk, improved body condition and reduced energy demands would be offset by an increase in MCF-incidence. With the development of an effective vaccine, however, this alternative strategy might become optimal. The overall conclusion we draw therefore is that, despite the substantial costs incurred each year avoiding MCF, the partial protection afforded by the novel vaccine strategy is not sufficient to warrant a wholesale change in disease avoidance strategy. Nonetheless, even the partial protection provided by this vaccine could be of value to protect animals that cannot be moved, for example where some of the herd remain at the boma to provide milk or where land-use changes make traditional disease avoidance difficult. Furthermore, the vaccine may offer a feasible solution to some of the current land-use challenges and conflicts, providing a degree of protection to valuable livestock where avoidance strategies are not possible, but with less risk of precipitating the potentially damaging environmental consequences, such as overgrazing of highly nutritious seasonal pastures, that might result if herd owners decide they no longer need to avoid wildebeest.