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 principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Shape-Time Photography

We introduce a new method to describe, in a single image, changes in shape over time. We acquire both range and image information with a stationary stereo camera. From the pictures taken, we display a composite image consisting of the image data from the surface closest to the camera at every pixel. This reveals the 3-d relationships over time by easy-to-interpret occlusion relationships in the composite image. We call the composite a shape-time photograph. Small errors in depth measurements cause artifacts in the shape-time images. We correct most of these using a Markov network to estimate the most probable front surface, taking into account the depth measurements, their uncertainties, and layer continuity assumptions.

Air photography Samoylov Island

For the qualitative description of surface properties like vegetation cover or land-water-ratio of Samoylov Island as well as for the evaluation of fetch homogeneity considerations of the eddy covariance measurements and for the up-scaling of chamber flux measurements, a detailed surface classification of the island at the sub-polygonal scale is necessary. However, up to know only grey-scale Corona satellite images from the 1960s with a resolution of 2 x 2 m and recent multi-spectral LandSat images with a resolution of 30 x 30 m were available for this region. Both are not useable for the desired classification because of missing spectral information and inadequate resolution, respectively. During the Lena 2003 expedition, a survey of the island by air photography was carried out in order to obtain images for surface classification. The photographs were taken from a helicopter on 10.07.2002, using a Canon EOS100 reflex camera, a Soligor 19-23 mm lens and colour slide film. The height from which the photographs were taken was approximately 600 meters. Due to limited flight time, not all the area of the island could be photographed and some regions could only be photographed with a slanted view. As a result, the images are of a varying quality and resolution. In Potsdam, after processing the films were scanned using a Nikon LS-2000 scanner at maximal resolution setting. This resulted in a ground resolution of the scanned images of approximately 0.3x0.3 m. The images were subsequently geo-referenced using the ENVI software and a referenced Corona image dating from 18.07.1964 (Spott, 2003). Geo-referencing was only possible for the Holocene river terrace areas; the floodplain regions in the western part of the island could not be referenced due to the lack of ground reference points. In Figure 3.7-1, the aerial view of Samoylov Island composed of the geo-referenced images is shown. Further work is necessary for the classification and interpretation of the images. If possible, air photography surveys will be carried out during future expeditions in order to determine changes in surface pattern and composition.

The effects of varying time under tension and volume load on acute neuromuscular responses

The purpose of this study was to examine the effects of different methods of measuring training volume, controlled in different ways, on selected variables that reflect acute neuromuscular responses. Eighteen resistance-trained males performed three fatiguing protocols of dynamic constant external resistance exercise, involving elbow flexors, that manipulated either time-under-tension (TUT) or volume load (VL), defined as the product of training load and repetitions. Protocol A provided a standard for TUT and VL. Protocol B involved the same VL as Protocol A but only 40% concentric TUT; Protocol C was equated to Protocol A for TUT but only involved 50% VL. Fatigue was assessed by changes in maximum voluntary isometric contraction (MVIC), interpolated doublet (ID), muscle twitch characteristics (peak twitch, time to peak twitch, 0.5 relaxation time, and mean rates of force development and twitch relaxation). All protocols produced significant changes (P

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Time alone

Time Alone is the introductory image to the exhibition Lightsite, which toured Western Australian galleries from February 2006 to November 2007. It is a five-minute-long exposure photographic image captured inside an abandoned building which the author converted into a camera obscura. It depicts an inverted image of the outside environment and the text 'time' - which is constructed by torch-light within the building interior and during the photographic exposure. The image evokes isolation and the temporality of inhabitation within the remote farmlands of the Great Southern Region of Western Australia: the region of focus for all of the twelve works in Lightsite. Indeed the owner of this now-abandoned house passed away and was not found for a week - bringing poignancy to the central theme of this creative work.

Max Dupain and the photography of Australian architecture

This thesis considers Max Dupain (1911-1992) and his contribution to the development of architectural photography in Australia. Through his continuous and prolific output over six decades of professional photography Dupain greatly stimulated awareness of and interest in Australian architecture. Before Dupain began specialising in the field, little consistent professional architectural photography had been practised in Australia. He and some of his close associates subsequently developed architectural photography as both a specialised branch of photography and - perhaps more significantly - as a necessary adjunct to architectural practice. In achieving these dual accomplishments, Dupain and like-minded practitioners succeeded in elevating architectural photography to the status of a discipline in its own right. They also gave Australians generally a deeper understanding of the heritage represented by the nation's built environment. At the same time, some of the photographic images he created became firmly fixed in the public imagination as historical icons within the development of a distinctive Australian tradition in the visual arts. Within his chosen field Dupain was the dominant Australian figure of his time. He was instrumental in breaking the link with Pictorialism by bringing Modernist and Documentary perspectives to Australian architectural photography. He was an innovator in the earlier decades of his professional career, however, his photographic techniques and practice did not develop beyond that. By the end of the 1980s he had largely lost touch with the technology and techniques of contemporary practice. Dupain's reputation, which has continued growing since his death in 1992, therefore arises from reasons other than his photographic images alone. It reflects his accomplishment in raising his fellow citizens' awareness of a worthwhile home-grown artistic tradition.

The short-term effect of air pollution on cardiovascular mortality in Tianjin, China : comparison of time series and case–crossover analyses

Background: Many studies have illustrated that ambient air pollution negatively impacts on health. However, little evidence is available for the effects of air pollution on cardiovascular mortality (CVM) in Tianjin, China. Also, no study has examined which strata length for the time-stratified case–crossover analysis gives estimates that most closely match the estimates from time series analysis. Objectives: The purpose of this study was to estimate the effects of air pollutants on CVM in Tianjin, China, and compare time-stratified case–crossover and time series analyses. Method: A time-stratified case–crossover and generalized additive model (time series) were applied to examine the impact of air pollution on CVM from 2005 to 2007. Four time-stratified case–crossover analyses were used by varying the stratum length (Calendar month, 28, 21 or 14 days). Jackknifing was used to compare the methods. Residual analysis was used to check whether the models fitted well. Results: Both case–crossover and time series analyses show that air pollutants (PM10, SO2 and NO2) were positively associated with CVM. The estimates from the time-stratified case–crossover varied greatly with changing strata length. The estimates from the time series analyses varied slightly with changing degrees of freedom per year for time. The residuals from the time series analyses had less autocorrelation than those from the case–crossover analyses indicating a better fit. Conclusion: Air pollution was associated with an increased risk of CVM in Tianjin, China. Time series analyses performed better than the time-stratified case–crossover analyses in terms of residual checking.

Creating new narratives through shared time and space : the performer/audience connection in multi-site dance events

Site-specific performance provides choices in audience experience via degrees of scale, proximity, levels of immersion and viewing perspectives. Beyond these choices, multi-site promenade events also form a connected audience/performer relationship in which moving together in time and space can produce a shared narrative and aesthetic sensibility of collective, yet individuated and shifting meanings. This paper interrogates this notion through audience/performer experiences in two separate multi-site, dance-led events. here/there/then/now occurred in four intimate sites within the Brisbane Powerhouse, providing a theatricalised platform for audiences to create linked narratives through open-ended and fragmented intertextuality. Accented Body, based on the concept of “the body as site and in site” and notions of connectivity, provided a more expansive platform for a similar, but heightened, shared engagement. Audiences traversed 6 outdoor and 2 indoor Brisbane sites moving to varying levels of a large complex. Eleven, predominantly interactive, screens provided links to other sites as well as to distributed presences in Seoul and London. The differentiation in scale and travel time between sites deepened the immersive experiences of audiences who reported transformative engagements with both site and architecture, accompanied by a sense of extended and yet quickened time.

It's only temporary: Time frame and the dynamics of creative project teams

The success of many knowledge-intensive industries depends on creative projects that lie at the heart of their logic of production. The temporality of such projects, however, is an issue that is insufficiently understood. To address this, we study the perceived time frame of teams that work on creative projects and its effects on project dynamics. An experiment with 267 managers assigned to creative project teams with varying time frames demonstrates that compared to creative project teams with a relatively longer time frame, project teams with a shorter time frame focus more on the immediate present, are less immersed in their task, and utilize a more heuristic mode of information processing. Furthermore, we find that time frame moderates the negative effect of team conflict on team cohesion. These results are consistent with our theory that the temporary nature of creative projects shapes different time frames among project participants, and that it is this time frame that is an important predictor of task and team processes.