Alternating surgeries

This thesis is concerned with the question of when the double branched cover of an alternating knot can arise by Dehn surgery on a knot in S^3. We approach this problem using a surgery obstruction, first developed by Greene, which combines Donaldson's Diagonalization Theorem with the $d$-invariants of Ozsvath and Szabo's Heegaard Floer homology. This obstruction shows that if the double branched cover of an alternating knot or link L arises by surgery on S^3, then for any alternating diagram the lattice associated to the Goeritz matrix takes the form of a changemaker lattice. By analyzing the structure of changemaker lattices, we show that the double branched cover of L arises by non-integer surgery on S^3 if and only if L has an alternating diagram which can be obtained by rational tangle replacement on an almost-alternating diagram of the unknot. When one considers half-integer surgery the resulting tangle replacement is simply a crossing change. This allows us to show that an alternating knot has unknotting number one if and only if it has an unknotting crossing in every alternating diagram. These techniques also produce several other interesting results: they have applications to characterizing slopes of torus knots; they produce a new proof for a theorem of Tsukamoto on the structure of almost-alternating diagrams of the unknot; and they provide several bounds on surgeries producing the double branched covers of alternating knots which are direct generalizations of results previously known for lens space surgeries. Here, a rational number p/q is said to be characterizing slope for K in S^3 if the oriented homeomorphism type of the manifold obtained by p/q-surgery on K determines K uniquely. The thesis begins with an exposition of the changemaker surgery obstruction, giving an amalgamation of results due to Gibbons, Greene and the author. It then gives background material on alternating knots and changemaker lattices. The latter part of the thesis is then taken up with the applications of this theory.

Integrated visual perception architecture for robotic clothes perception and manipulation

This thesis proposes a generic visual perception architecture for robotic clothes perception and manipulation. This proposed architecture is fully integrated with a stereo vision system and a dual-arm robot and is able to perform a number of autonomous laundering tasks. Clothes perception and manipulation is a novel research topic in robotics and has experienced rapid development in recent years. Compared to the task of perceiving and manipulating rigid objects, clothes perception and manipulation poses a greater challenge. This can be attributed to two reasons: firstly, deformable clothing requires precise (high-acuity) visual perception and dexterous manipulation; secondly, as clothing approximates a non-rigid 2-manifold in 3-space, that can adopt a quasi-infinite configuration space, the potential variability in the appearance of clothing items makes them difficult to understand, identify uniquely, and interact with by machine. From an applications perspective, and as part of EU CloPeMa project, the integrated visual perception architecture refines a pre-existing clothing manipulation pipeline by completing pre-wash clothes (category) sorting (using single-shot or interactive perception for garment categorisation and manipulation) and post-wash dual-arm flattening. To the best of the author’s knowledge, as investigated in this thesis, the autonomous clothing perception and manipulation solutions presented here were first proposed and reported by the author. All of the reported robot demonstrations in this work follow a perception-manipulation method- ology where visual and tactile feedback (in the form of surface wrinkledness captured by the high accuracy depth sensor i.e. CloPeMa stereo head or the predictive confidence modelled by Gaussian Processing) serve as the halting criteria in the flattening and sorting tasks, respectively. From scientific perspective, the proposed visual perception architecture addresses the above challenges by parsing and grouping 3D clothing configurations hierarchically from low-level curvatures, through mid-level surface shape representations (providing topological descriptions and 3D texture representations), to high-level semantic structures and statistical descriptions. A range of visual features such as Shape Index, Surface Topologies Analysis and Local Binary Patterns have been adapted within this work to parse clothing surfaces and textures and several novel features have been devised, including B-Spline Patches with Locality-Constrained Linear coding, and Topology Spatial Distance to describe and quantify generic landmarks (wrinkles and folds). The essence of this proposed architecture comprises 3D generic surface parsing and interpretation, which is critical to underpinning a number of laundering tasks and has the potential to be extended to other rigid and non-rigid object perception and manipulation tasks. The experimental results presented in this thesis demonstrate that: firstly, the proposed grasp- ing approach achieves on-average 84.7% accuracy; secondly, the proposed flattening approach is able to flatten towels, t-shirts and pants (shorts) within 9 iterations on-average; thirdly, the proposed clothes recognition pipeline can recognise clothes categories from highly wrinkled configurations and advances the state-of-the-art by 36% in terms of classification accuracy, achieving an 83.2% true-positive classification rate when discriminating between five categories of clothes; finally the Gaussian Process based interactive perception approach exhibits a substantial improvement over single-shot perception. Accordingly, this thesis has advanced the state-of-the-art of robot clothes perception and manipulation.

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.