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.

Self-report depressive symptoms do not directly predict suicidality in nonclinical individuals: Contributions toward a more psychosocial approach to suicide risk

Although suicidality is associated with mental illness in general and depression in particular, many depressed individuals do not attempt suicide and some individuals who attempt to or do die by suicide do not present depressive symptoms. This article aims to contribute to a more psychosocial approach to understanding suicide risk in nonclinical populations. In advocating a psychosocial perspective rather than a depression-focused approach, this article presents four diverse studies that demonstrate sampling and measurement invariance in findings across different populations and specific measures. Study 1 tests the mediation effects of 2 interpersonal variables, thwarted belongingness and perceived burdensomeness, in the association between depressive symptoms and recent suicidality. Studies 2 and 3 evaluate the contribution of hopelessness and psychache, beyond depressive symptoms, to suicidality. Study 4 tests the contribution of life events behind depressive symptoms, and other relevant sociodemographic and clinical variables, to the estimation of “future suicidality.” Overall, results demonstrate that depressive symptoms do not directly predict suicidality in nonclinical individuals, but that other psychosocial variables mediate the association between depressive symptoms and suicidality or predict suicidality when statistically controlling for depressive symptoms. The article contributes to understanding some of the nonpsychopathological factors that potentially link depressive symptoms to suicide risk and that might themselves contribute to suicidality, even when controlling for depressive symptoms.

Gender differences in first-year College students’ academic expectations

Based on a multidimensional definition of academic expectations (AEs), the authors examine students’ AE component scores across countries and genders. Two samples (343 Portuguese and 358 Spanish students) completed the Academic Perceptions Questionnaire (APQ) six months after enrolling in their universities. Factorial invariance was ensured across countries and genders, allowing us to study AEs using the APQ for both genders and in both countries. No significant differences in factor means were found between countries, indicating that AEs are not an obstacle to student mobility. Gender differences were found in some AE factor means, Training for employment, Personal and social development, Student mobility, Political engagement and citizenship, and Social pressure, with males exhibiting higher scores. Because these differences are not supported by most literature in this domain, further studies are needed to clarify the causes of women’s lower expectations and, therefore, risk of adaptation difficulties.

Shaping transverse beam distributions by means of adiabatic crossing of resonances

Non-linear effects are responsible for peculiar phenomena in charged particles dynamics in circular accelerators. Recently, they have been used to propose novel beam manipulations where one can modify the transverse beam distribution in a controlled way, to fulfil the constraints posed by new applications. One example is the resonant beam splitting used at CERN for the Multi-Turn Extraction (MTE), to transfer proton beams from PS to SPS. The theoretical description of these effects relies on the formulation of the particle's dynamics in terms of Hamiltonian systems and symplectic maps, and on the theory of adiabatic invariance and resonant separatrix crossing. Close to resonance, new stable regions and new separatrices appear in the phase space. As non-linear effects do not preserve the Courant-Snyder invariant, it is possible for a particle to cross a separatrix, changing the value of its adiabatic invariant. This process opens the path to new beam manipulations. This thesis deals with various possible effects that can be used to shape the transverse beam dynamics, using 2D and 4D models of particles' motion. We show the possibility of splitting a beam using a resonant external exciter, or combining its action with MTE-like tune modulation close to resonance. Non-linear effects can also be used to cool a beam acting on its transverse beam distribution. We discuss the case of an annular beam distribution, showing that emittance can be reduced modulating amplitude and frequency of a resonant oscillating dipole. We then consider 4D models where, close to resonance, motion in the two transverse planes is coupled. This is exploited to operate on the transverse emittances with a 2D resonance crossing. Depending on the resonance, the result is an emittance exchange between the two planes, or an emittance sharing. These phenomena are described and understood in terms of adiabatic invariance theory.

Lie symmetries in cortical inspired CNNs

Our scope in this thesis is to propose architectures of CNNs in such a way to model the early visual pathway, including the Lateral Geniculate Nucleus and the Horizontal Connectivity of the primary visual cortex. Moreover, we will show how cortically inspired architectures allow to perform contrast perceptual invariance as well as grouping and the emergence of visual percepts. Particularly, the LGN is modeled with a first layer l0 containing a single filter Ψ0 that pre-filters the image I. Since the RPs of the LGN cells can be modeled as a LoG, we expect to obtain a radially symmetric filter with a similar shape; to this end, we prove the rotational invariance of Ψ0 and we study the influence of this filter to the subsequent layer. Indeed, we compare the statistic distribution of the filters in the second layer l1 of our architecture with the statistic distribution of the RPs of V1 cells of a macaque. Then, we model the horizontal connectivity of V1 implementing a transition kernel K1 to the layer l1. In this setting, we study the vector fields and the association fields induced by the connectivity kernel K1. To this end, we first approximate the filters bank in l1 with a Gabor function and use the parameters just found to re-parameterize the kernel. Thanks to this step, the kernel is now re-parameterized into a sub-Riemmanian space R2 × S1. Now we are able to compare the vector and association fields induced by K1 with the models of the horizontal connectivity.

On Reasonable Space and Time Cost Models for the λ-Calculus

Slot and van Emde Boas Invariance Thesis states that a time (respectively, space) cost model is reasonable for a computational model C if there are mutual simulations between Turing machines and C such that the overhead is polynomial in time (respectively, linear in space). The rationale is that under the Invariance Thesis, complexity classes such as LOGSPACE, P, PSPACE, become robust, i.e. machine independent. In this dissertation, we want to find out if it possible to define a reasonable space cost model for the lambda-calculus, the paradigmatic model for functional programming languages. We start by considering an unusual evaluation mechanism for the lambda-calculus, based on Girard's Geometry of Interaction, that was conjectured to be the key ingredient to obtain a space reasonable cost model. By a fine complexity analysis of this schema, based on new variants of non-idempotent intersection types, we disprove this conjecture. Then, we change the target of our analysis. We consider a variant over Krivine's abstract machine, a standard evaluation mechanism for the call-by-name lambda-calculus, optimized for space complexity, and implemented without any pointer. A fine analysis of the execution of (a refined version of) the encoding of Turing machines into the lambda-calculus allows us to conclude that the space consumed by this machine is indeed a reasonable space cost model. In particular, for the first time we are able to measure also sub-linear space complexities. Moreover, we transfer this result to the call-by-value case. Finally, we provide also an intersection type system that characterizes compositionally this new reasonable space measure. This is done through a minimal, yet non trivial, modification of the original de Carvalho type system.