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.

Studies on the protective immune response to Plasmodium chabaudi in mice

Inbred strains of C5731 and NIH nice infected with the A/S strain of Plasmodium chaubaudi usually developed high parasitaemias but infections were rarely fatal in immunocompetent mice and in most mice the parasites could be eradicated within 53 days or less. The immune response of C57B1 and NTH mice to infection with the A/S strain of P. chabaudi was studied. The principle method used in this study for investigating the immune response of the mice was to examine the immunity conferred on syngeneic mice, either X-irradiated or non-irradiated, by transferring to them lymphoid cells or serum from immune or semi-immune donors. The lymphoid cell populations examined were unfractionated spleen cells, nylon wool column enriched subpopulations of thymus-derived lymphocytes (T cells) and the so-called bursa-derived lymphocytes (B cells), bone marrow cells and phagocytic cells. In the course of these experiments observations were made on the effect of X-irradiation on the subsequent growth and multiplication of the parasite. In addition, an in vitro assay for antibody-dependent cell mediated cytotoxicity was used to investigate the activity of splenic K cells during malaria infection. K cells are lymphoid cells which may include lymphocytes of an undefined category, but possess receptors for the Fc portion of antibody on their surface and have the ability to non-specifically lyse target cells coated in antibodies. a) The adoptive transfer of immunity to P.chabaudi with immune spleen cells. Spleen cells from mice which had previously been infected with P.chabaudi were able to confer some immunity on syngeneic mice which had been irradiated with 600 or 800 rads. The protection was detected as a shortened patent parasitaemia in immune cell recipients compared to controls. The early experiments indicated the value of using irradiated recipients rather than non-irradiated recipients. In irradiated mice, a) smaller numbers of immune cells were required to promote detectable immunity than in non-irradiated mice, b) there was an amplification of the difference in the duration of primary parasitaemias in recipients of immune cells and normal cells compared to non-irradiated mice and c) as the irradiated host is immunodepressed, the protective effect of donor cells can be examined with a reduced contribution by the hosts own immune system. An initial non-specific resistance to P.chabaudi infection was observed in irradiated mice, although the infection in most of these mice was subsequently more severe than in non-irradiated mice. The non-specific resistance could be reduced or abolished by injecting lymphoid cells into mice shortly after irradiation or by infecting irradiated mice more than 15 days after irradiation. Other workers suggest that following irradiation, the reticulo-endothelial system is stimulated at the time that the non-specific resistance to P.chabaudi was observed. b) the adoptive transfer of immunity in syngeneic mice with enriched subpopulations of splenic immune T cells, B. cells, bone marrow cells and phagocytes. Immunity to P.chabaudi could be adoptively transferred with enriched spleen subpopulations of immune T cells or immune B cells in mice which had been irradiated 600 or 300 rads. The protective effects of unfractionated immune cells was, however, usually better than that of either immune T or F cell subpopulations. In most experiments enriched immune T cell recipients were more likely to suffer relapsing patent parasitaemias than either enriched immune B cell recipients or unfractionated immune cell recipients. In one experiment a comparison was made of the course of P.chabaudi infection in mice which had been irradiated with either 600 rads or 300 rads and which received injections of different immune cells. A dose of 600 rads permits the immune system of mice to recover from the effects of irradiation, but a dose of 800 rads is lethal to mice unless lymphoid cells are injected after irradiation. It was found that in recipients of enriched immune T or B cells, which had been irradiated with 600 rads, the parasitaemia became subpatent before their equivalents irradiated with 800 rads, but that there was little difference in parasitaemias between recipients of unfractionated immune cells given 600 or 800 rads. Experiments in which enriched immune T cells and B cells were recombined and injected into syngeneic mice gave inconclusive results as to whether the immune subpopulations acted synergistically. Similar experiments in which immune subpopulations of lymphoid cells were recombined with normal subpopulations of lymphoid cells demonstrated that the latter cells did not enhance the protective effect of the former cells. Bone marrow cells from immune mice were able to confer some protection on syngeneic recipients, but were not as protective as enriched immune T cells or B cells. The results obtained in adoptive transfer experiments using phagocytic cells from the spleen of immune mice depended on the length of time spleen cells were incubated in petri-dishes at 37° C before harvesting the phagocytes. Using C57B1 mice, phagocytes harvested after 15 hours incubation were as protective as unfractionated immune cells in a cell transfer experiment, but phagocytes harvested after 16 hours incubation were not protective. Examination of NIH phagocytic cells after 2.5 hours incubation at 37°C, which were as protective as unfractionated immune spleen cells in a cell transfer experiment, demonstrated that the petri-dish adherent cells may have contained B lymphocytes. c) The passive transfer of immunity with serum from P.chabaudi infected mice. The passive transfer of serum from C57B1 mice which had been previously infected with P.chabaudi to normal or irradiated syngeneic mice demonstrated that the serum recipients were initially protected from infection. Irradiated mice, however, were delayed longer in the onset of parasitaemia compared to non-irradiated mice. Using NIH mice, sera were collected from unfractionated immune spleen cell recipients, enriched immune T cell recipients and normal spleen recipients on the 11th day of a P.chabaudi infection, just after peak parasitaemia, and also on the 14th day of infection. On day 14, all immune cells recipients and most of the enriched immune T cell recipients had become subpatent but all normal cell recipients still had patent infections. Sera collected from the different spleen cell recipients on the 11th day of infection and passively transferred to irradiated mice demonstrated little protection. Sera collected on the 14th day of infect ion, however, reflected the immune status of the donors in their protective properties in mice infected with P.chabaudi. The serum from unfractionated immune cell recipients was the most protective of the 3 sera when compared to normal NIH serum and the serum from enriched immune T cell recipients was slightly protective, but the serum from normal cell recipients produced an enhanced infection in mice infected with P.chabaudi. d) Antibody-dependent cell-mediated cytotoxicity of spleen cells in P.chabaudi infected mice. In a preliminary investigation of K cell activity in the spleens of P.chabaudi infected mice, it was found that there was an increased activity of K cells collected at around peak parasitaemia compared to the activity of K cells in non-infected mice, and that this increased activity could also be found in mice which had recently become subpatent. As the target cell for antibody-dependent cell-mediated cytotoxicity employed was the thick red blood cell, it is not known whether the K cell is involved in the killing of P.chabaudi parasites. These results suggest that both T cells and B cells and antibody may be important in the immune response to P.chabaudi in mice. Primed T cells may act as helper cells in the production of malarial antibodies, but, as enriched primed T cells could confer protection on immunodepressed mice, it is possible that a cell-mediated mechanism of immunity may also exist.

Development of dendritic cells in the intestine

The intestinal tract is exposed to a large variety of antigens such as food proteins, commensal bacteria and pathogens and contains one of the largest arms of the immune system. The intestinal immune system has to discriminate between harmless and harmful antigens, inducing tolerance to harmless antigens and active immunity towards pathogens and other harmful materials. Dendritic cells (DC) in the mucosal lamina propria (LP) are central to this process, as they sample bacteria from the local environment and constitutively migrate to the draining mesenteric lymph nodes (MLN), where they present antigen to naïve T cells in order to direct an appropriate immune response. Despite their crucial role, understanding the function and phenotype of LP DC has been hampered by the fact that they share phenotypic markers with macrophages (mφ), which are the dominant population of mononuclear phagocyte (MP) in the LP. Recent work in our own and other laboratories has established gating strategies and phenotyping panels that allow precise discrimination between intestinal DC and mφ using the mφ specific markers CD64 and F4/80. In this way four bona fide DC subsets with distinct functions have been identified in adult LP based on their expression of CD11b and CD103 and a major aim of my project was to understand how these subsets might develop in the neonatal intestine. At the beginning of my PhD, the laboratory had used these new methods to show that signal regulatory protein α (SIRPα), an inhibitory receptor expressed by myeloid cells, was expressed by mφ and most DC in the intestine, except for those expressing CD103 alone. In addition, mice carrying a non-signalling mutation in SIRPα (SIRPα mt) had a selective reduction in CD103+CD11b+ DC, a subset which is unique to the intestinal LP. This was the basis for the initial experiments of my project, described in Chapter 3, where I investigated if the phenotype in SIRPα mt mice was intrinsic to haematopoietic cells or not. To explore this, I generated bone marrow (BM) chimeric mice by reconstituting irradiated WT mice with SIRPα mt BM, or SIRPα mt animals with WT BM. These experiments suggested that the defect in CD103+CD11b+ DC was not replicated in DC derived from BM of SIRPα origin. However as this seemed inconsistent with other data, I considered the possibility that 18 the phenotype may have been lost with age, as the BM chimeric mice were considerably older than those used in the original studies of SIRPα function. However a comparison of DC subsets in the intestine of WT and SIRPα mt mice as they aged provided no conclusive evidence to support this idea. As these experiments did show age-dependent effects on DC subsets, in Chapter 4, I went on to investigate how the DC populations appeared in the intestine and other tissues in the neonatal period. These experiments showed there were few CD103+CD11b+ DC present in the LP and migratory DC compartment of the MLN in the neonate and that as this population gradually increased in proportion with age, there was a reciprocal decrease in the relative proportion of CD103-CD11b+ DC. Interestingly, most of the changes in DC numbers in the intestine were found during the second or third week of life when the weaning process began. To validate my findings that there were few CD103+CD11b+ DC in the neonate and that this was not merely an absence of CD103 upregulation, I examined the expression of CD101 and Trem-1, markers that other work in the laboratory had suggested were specific to the CD103+CD11b+ DC lineage. My work showed that CD101 and Trem-1 were co- expressed by most CD103+CD11b+ DC in small intestine (SI) LP, as well as a small subset of CD103-CD11b+ DC in this tissue. Interestingly, Trem-1 was highly specific to the SI LP and migratory DC in the MLN, but absent from the colon and other tissues. CD101 expression was also only found on CD11b+ DC, but showed a less restricted pattern of distribution, being found in several tissues as well as the SI LP. The relative timing of their development suggested there might be a relationship between CD103+CD11b+ and CD103-CD11b+ DC and this was supported by microarray analysis. I hypothesised that the CD103-CD11b+ DC that co-expressed CD101 and Trem-1 may be the cells that developed into CD103+CD11b+ DC. To investigate this I analysed how CD101 and Trem-1 expression changed with age amongst the DC subsets in SI LP, colonic LP (CLP) and MLN. The proportion of CD101+Trem-1+ cells increased amongst CD103+CD11b+ DC in the SI LP and MLN with age, while amongst CD103+CD11b+ DC in the CLP this decreased. This was not the same in CD103-CD11b+ DC, where CD101 and Trem-1 expression was more varied with age in all tissues. CD101 and Trem-1 were not expressed to any great extent on CD103+CD11b- or CD103-CD11b- DC. The phenotypic development of the 19 intestinal DC subsets was paralleled by the gradual upregulation of CD103 expression, while the production of retinoic acid (RA), as assessed by the AldefluorTM assay, was low early in life and did not attain adult levels until after weaning. Thus DC in the neonatal intestine take some time to acquire the adult pattern of phenotypic subsets and are functionally immature compared with their adult counterparts. In Chapter 5, I used CD101 and Trem-1 to explore the ontogeny of intestinal DC subsets in CCR2-/- and SIRPα mt mice, both of which have selective defects in one particular group of DC. The selective defect seen amongst CD103+CD11b+ DC in adult SIRPα mt mice was more profound in mice at D7 and D14 of age, indicating that it may be intrinsic to this population and not highly dependent on environmental factors that change after birth. The expression of CD101 and Trem-1 by both CD103+CD11b+ and CD103-CD11b+ DC was reduced in SIRPα mt mice, again indicating that this entire lineage was affected by the lack of SIRPα signalling. However there was also a generalised defect in the numbers of all DC subsets in many tissues from early in life, suggesting there was compromised development, recruitment or survival of DC in the absence of SIRPα signalling. In contrast to the findings in SIRPα mt mice, more CD103+CD11b+ DC co-expressed CD101 and Trem-1 in CCR2-/- mice, while there were no differences in the expression of these molecules amongst CD103-CD11b+ DC. This may suggest that CCR2+ CD103-CD11b+ DC are not the cells that express CD101 and Trem-1 that are predicted to be the direct precursors of CD103+CD11b+ DC. I also examined the expression of DC growth factor receptors on DC subsets from mice of different ages, but no clear age or subset- related patterns of the expression of mRNA for Csf2ra, Irf4, Tgfbr1 and Rara could be observed. Next, I investigated whether Trem-1 played any role in DC development. Preliminary experiments in Trem-1-/- mice show no differences between any of the DC subsets, nor were there any selective effects on individual subsets when DC development from Trem-1-/- KO and WT BM was compared in competitive chimeras. However these experiments were difficult to interpret due to viability problems and because I found an unexpected defect in the ability of Trem-1-/- BM to generate all DC, irrespective of whether they expressed Trem-1 or not. 20 The final experiments I carried out were to examine the role of the microbiota in driving the differentiation of intestinal DC subsets, based on the hypothesis that this could be one of the environmental factors that might influence events in the developing intestine. To this end I performed experiments in both antibiotic treated and germ free adult mice, both of which showed no significant phenotypic differences amongst any of the DC subsets. However the study of germ free mice was compromised by recent contamination of the colony and may not be the conclusive answer. Together the data in this thesis have shown that the population of CD103+CD11b+ DC, which is unique to the intestine, is not present at birth. These cells gradually increase in frequency over time and as this occurs there is a reciprocal decrease in the frequency of CD103-CD11b+ DC. Along with other results, this leads to the idea that there may be a linear developmental pathway from CD103-CD11b+ DC to CD103+CD11b+ DC that is driven by non-microbial factors that are located preferentially in the small intestine. My project indicates that markers such as CD101 and Trem-1 may assist the dissection of this process and highlights the importance of the neonatal period for these events.