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.

A critical study of John Hick's religious pluralism

This study examines the pluralistic hypothesis advanced by the late Professor John Hick viz. that all religious faiths provide equally salvific pathways to God, irrespective of their theological and doctrinal differences. The central focus of the study is a critical examination of (a) the epistemology of religious experience as advanced by Professor Hick, (b) the ontological status of the being he understands to be God, and further asks (c) to what extent can the pluralistic view of religious experience be harmonised with the experience with which the Christian life is understood to begin viz. regeneration. Tracing the theological journey of Professor Hick from fundamentalist Christian to religious pluralist, the study notes the reasons given for Hick’s gradual disengagement from the Christian faith. In addition to his belief that the pre-scientific worldview of the Bible was obsolete and passé, Hick took the view that modern biblical scholarship could not accommodate traditionally held Christian beliefs. He conceded that the Incarnation, if true, would be decisive evidence for the uniqueness of Christianity, but rejected the same on the grounds of logical incoherence. This study affirms the view that the doctrine of the Incarnation occupies a place of crucial importance within world religion, but rejects the claim of incoherence. Professor Hick believed that God’s Spirit was at work in all religions, producing a common religious experience, or spiritual awakening to God. The soteriological dimension of this spiritual awakening, he suggests, finds expression as the worshipper turns away from self-centredness to the giving of themselves to God and others. At the level of epistemology he further argued that religious experience itself provided the rational basis for belief in God. The study supports the assertion by Professor Hick that religious experience itself ought to be trusted as a source of knowledge and this on the principle of credulity, which states that a person’s claim to perceive or experience something is prima facie justified, unless there are compelling reasons to the contrary. Hick’s argument has been extensively developed and defended by philosophers such as Alvin Plantinga and William Alston. This confirms the importance of Hick’s contribution to the philosophy of religion, and further establishes his reputation within the field as an original thinker. It is recognised in this thesis, however, that in affirming only the rationality of belief, but not the obligation to believe, Professor Hick’s epistemology is not fully consistent with a Christian theology of revelation. Christian theology views the created order as pre-interpreted and unambiguous in its testimony to God’s existence. To disbelieve in God’s existence is to violate one’s epistemic duty by suppressing the truth. Professor Hick’s critical realist principle, which he regards as the key to understanding what is happening in the different forms of religious experience, is examined within this thesis. According to the critical realist principle, there are realities external to us, yet we are never aware of them as they are in themselves, but only as they appear to us within our particular cognitive machinery and conceptual resources. All awareness of God is interpreted through the lens of pre-existing, culturally relative religious forms, which in turn explains the differing theologies within the world of religion. The critical realist principle views God as unknowable, in the sense that his inner nature is beyond the reach of human conceptual categories and linguistic systems. Professor Hick thus endorses and develops the view of God as ineffable, but employs the term transcategorial when speaking of God’s ineffability. The study takes the view that the notion of transcategoriality as developed by Professor Hick appears to deny any ontological status to God, effectively arguing him out of existence. Furthermore, in attributing the notion of transcategoriality to God, Professor Hick would appear to render incoherent his own fundamental assertion that we can know nothing of God that is either true or false. The claim that the experience of regeneration with which the Christian life begins can be classed as a mere species of the genus common throughout all faiths, is rejected within this thesis. Instead it is argued that Christian regeneration is a distinctive experience that cannot be reduced to a salvific experience, defined merely as an awareness of, or awakening to, God, followed by a turning away from self to others. Professor Hick argued against any notion that the Christian community was the social grouping through which God’s Spirit was working in an exclusively redemptive manner. He supported his view by drawing attention to (a) the presence, at times, of comparable or higher levels of morality in world religion, when contrasted with that evidenced by the followers of Christ, and (b) the presence, at times, of demonstrably lower levels of morality in the followers of Christ, when contrasted with the lives of other religious devotees. These observations are fully supported, but the conclusion reached is rejected, on the grounds that according to Christian theology the saving work of God’s Spirit is evidenced in a life that is changing from what it was before. Christian theology does not suggest or demand that such lives at every stage be demonstrably superior, when contrasted with other virtuous or morally upright members of society. The study concludes by paying tribute to the contribution Professor Hick has made to the field of the epistemology of religious experience.