Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Shared control for natural motion and safety in hands-on robotic surgery

Hands-on robotic surgery is where the surgeon controls the tool's motion by applying forces and torques to the robot holding the tool, allowing the robot-environment interaction to be felt though the tool itself. To further improve results, shared control strategies are used to combine the strengths of the surgeon with those of the robot. One such strategy is active constraints, which prevent motion into regions deemed unsafe or unnecessary. While research in active constraints on rigid anatomy has been well-established, limited work on dynamic active constraints (DACs) for deformable soft tissue has been performed, particularly on strategies which handle multiple sensing modalities. In addition, attaching the tool to the robot imposes the end effector dynamics onto the surgeon, reducing dexterity and increasing fatigue. Current control policies on these systems only compensate for gravity, ignoring other dynamic effects. This thesis presents several research contributions to shared control in hands-on robotic surgery, which create a more natural motion for the surgeon and expand the usage of DACs to point clouds. A novel null-space based optimization technique has been developed which minimizes the end effector friction, mass, and inertia of redundant robots, creating a more natural motion, one which is closer to the feeling of the tool unattached to the robot. By operating in the null-space, the surgeon is left in full control of the procedure. A novel DACs approach has also been developed, which operates on point clouds. This allows its application to various sensing technologies, such as 3D cameras or CT scans and, therefore, various surgeries. Experimental validation in point-to-point motion trials and a virtual reality ultrasound scenario demonstrate a reduction in work when maneuvering the tool and improvements in accuracy and speed when performing virtual ultrasound scans. Overall, the results suggest that these techniques could increase the ease of use for the surgeon and improve patient safety.Open Acces

Numerical modelling of a road restraint system

Dissertação de mestrado integrado em Engenharia Mecânica (área de especialização em Sistemas Mecatrónicos)The most important aspect when developing roads is safety. This factor represents a notable cost in development activities involving the construction of highways, and is, therefore, a factor widely studied in the academic community as well. As it is known, the finite element method is used to predict and simulate different phenomena in engineering applications, being increasingly used because it represents a significant cost savings, as it replaces the execution of experimental tests at full scale. Furthermore, it allows for geometric, behavioural (material) and boundary conditions definition changes. Finite element modelling also allows for calculations that involve the rigorous evaluation of fundamental engineering quantities, which in a mechanical test can be difficult to obtain or measure, because they are difficult to access or because they require equipment with limited access. For the modelling of the different components that make up the safety barrier model studied in this work, the Solidworks software was used, with the Sheet Metal tool, which allows to model the geometry in a similar way to the forming process. In the numerical simulation two approaches are presented. The first employs three-dimensional elements and solid screws in bolted connections. The second uses shell elements and connectors (connection functionalities) available in the finite element software libraries used. As the first approach did not achieve the desired success, the second approach constitutes a more detailed analysis for modelling an impact test. In addition to developing a model for future analysis of the barrier under study, an analysis of two modelling techniques that uses scripting and an interface is also carried out. The main limitation of this study is that it was not possible to validate the numerical model with experimental information, given the logistics involved. However, by comparing the information available in the literature, and analysing the current standards for the production of the studied containment solution, it was possible to conclude that the work carried out led to the production of a set of very consistent results.O aspeto mais importante aquando do desenvolvimento de estradas é a segurança. Este fator representa um custo destacável nas atividades de desenvolvimento que envolvem a construção de rodovias, sendo por isso um fator amplamente estudado também na comunidade académica. Como é sabido, o método dos elementos finitos é utilizado para prever e simular fenómenos diversos em aplicações de engenharia, sendo cada vez mais utilizado por representar uma poupança de custos significativa, pois substitui a execução de ensaios experimentais à escala real. Além disto, permite a realização de alterações geométricas, comportamentais (materiais) e de definição de condições de fronteira. A modelação por elementos finitos permite também a realização de cálculos que envolvem a avaliação rigorosa de grandezas fundamentais em engenharia, que num ensaio mecânico podem ser difíceis de obter ou medir, por serem de difícil acessibilidade ou por requerem equipamentos de acesso limitado. Na modelação dos diferentes componentes que constituem o modelo de barreira de segurança estudado neste trabalho, empregou-se o software Solidworks, com a ferramenta Sheet Metal, que permite modelar a geometria de uma maneira semelhante ao processo de conformação. Na simulação numérica são apresentadas duas abordagens. A primeira emprega elementos tridimensionais e parafusos sólidos nas ligações aparafusadas. A segunda recorre a elementos de casca e conectores (funcionalidades de ligação) disponíveis nas livrarias do software de elementos finitos utilizado. Sendo que na primeira abordagem não se alcançou o sucesso desejado, a segunda abordagem constitui uma análise mais detalhada para a modelação de um ensaio de impacto. Além de desenvolver um modelo para futuras análises à barreira em estudo, é também feita uma análise a duas técnicas de modelação que recorre a scripting e a uma interface. A principal limitação deste estudo reside em não ter sido possível validar o modelo numérico com informação experimental, atendendo à logística envolvida. No entanto, por comparação com a informação disponível na literatura, e analisadas as normas vigentes para a produção da solução de contenção estudada, foi possível concluir que o trabalho desenvolvido conduziu à produção de um conjunto de resultados muito coerentes.This work was supported by “ANI – Agência Nacional de Inovação”, through the project with the reference “COMPETE-2020/03/SI/2017 Nº033497”, entitled “Barreiras de segurança rodoviária”, with the acronym “BarRod”, through the “Programa Operacional Competitividade e Internacionalização” and the “Programa Operacional Competitividade e Internacionalização e o Programa Operacional Regional de Lisboa”, supported by “FEDER”

Tools for fluid simulation control in computer graphics

L’animation basée sur la physique peut générer des systèmes aux comportements complexes et réalistes. Malheureusement, contrôler de tels systèmes est une tâche ardue. Dans le cas de la simulation de fluide, le processus de contrôle est particulièrement complexe. Bien que de nombreuses méthodes et outils ont été mis au point pour simuler et faire le rendu de fluides, trop peu de méthodes offrent un contrôle efficace et intuitif sur une simulation de fluide. Étant donné que le coût associé au contrôle vient souvent s’additionner au coût de la simulation, appliquer un contrôle sur une simulation à plus haute résolution rallonge chaque itération du processus de création. Afin d’accélérer ce processus, l’édition peut se faire sur une simulation basse résolution moins coûteuse. Nous pouvons donc considérer que la création d’un fluide contrôlé peut se diviser en deux phases: une phase de contrôle durant laquelle un artiste modifie le comportement d’une simulation basse résolution, et une phase d’augmentation de détail durant laquelle une version haute résolution de cette simulation est générée. Cette thèse présente deux projets, chacun contribuant à l’état de l’art relié à chacune de ces deux phases. Dans un premier temps, on introduit un nouveau système de contrôle de liquide représenté par un modèle particulaire. À l’aide de ce système, un artiste peut sélectionner dans une base de données une parcelle de liquide animé précalculée. Cette parcelle peut ensuite être placée dans une simulation afin d’en modifier son comportement. À chaque pas de simulation, notre système utilise la liste de parcelles actives afin de reproduire localement la vision de l’artiste. Une interface graphique intuitive a été développée, inspirée par les logiciels de montage vidéo, et permettant à un utilisateur non expert de simplement éditer une simulation de liquide. Dans un second temps, une méthode d’augmentation de détail est décrite. Nous proposons d’ajouter une étape supplémentaire de suivi après l’étape de projection du champ de vitesse d’une simulation de fumée eulérienne classique. Durant cette étape, un champ de perturbations de vitesse non-divergent est calculé, résultant en une meilleure correspondance des densités à haute et à basse résolution. L’animation de fumée résultante reproduit fidèlement l’aspect grossier de la simulation d’entrée, tout en étant augmentée à l’aide de détails simulés.Physics-based animation can generate dynamic systems of very complex and realistic behaviors. Unfortunately, controlling them is a daunting task. In particular, fluid simulation brings up particularly difficult problems to the control process. Although many methods and tools have been developed to convincingly simulate and render fluids, too few methods provide efficient and intuitive control over a simulation. Since control often comes with extra computations on top of the simulation cost, art-directing a high-resolution simulation leads to long iterations of the creative process. In order to shorten this process, editing could be performed on a faster, low-resolution model. Therefore, we can consider that the process of generating an art-directed fluid could be split into two stages: a control stage during which an artist modifies the behavior of a low-resolution simulation, and an upresolution stage during which a final high-resolution version of this simulation is driven. This thesis presents two projects, each one improving on the state of the art related to each of these two stages. First, we introduce a new particle-based liquid control system. Using this system, an artist selects patches of precomputed liquid animations from a database, and places them in a simulation to modify its behavior. At each simulation time step, our system uses these entities to control the simulation in order to reproduce the artist’s vision. An intuitive graphical user interface inspired by video editing tools has been developed, allowing a nontechnical user to simply edit a liquid animation. Second, a tracking solution for smoke upresolution is described. We propose to add an extra tracking step after the projection of a classical Eulerian smoke simulation. During this step, we solve for a divergence-free velocity perturbation field resulting in a better matching of the low-frequency density distribution between the low-resolution guide and the high-resolution simulation. The resulting smoke animation faithfully reproduces the coarse aspect of the low-resolution input, while being enhanced with simulated small-scale details

Evaluating on-street parking policy

This paper uses a formal model to examine the welfare gains from a marginal increase in the price of on-street parking. The benefits of such a policy are shown to depend on the improvement in search externalities in the on-street parking market itself, plus effects on other distorted urban transport markets, including congested freeway and backroad use, mass-transit and off-street parking. The paper makes two further contributions. The model is sufficiently general that several well-known results from the parking literature emerge as special cases. The model is used to review the existing literature and highlights findings in separate parts of literature. Finally, a numerical simulation model is used to investigate the order of magnitude of an optimal urban parking fee. In particular, these results confirm the importance of taking into accounts effects on other distorted transport markets when deciding upon the level of the price for on-street parking. The model confirms that while parking pricing reform may lead to substantial improvements in parking search times, there is little overall impact on road congestion levels.

Doctor of Philosophy in Computing

dissertationPhysics-based animation has proven to be a powerful tool for creating compelling animations for film and games. Most techniques in graphics are based on methods developed for predictive simulation for engineering applications; however, the goals for graphics applications are dramatically different than the goals of engineering applications. As a result, most physics-based animation tools are difficult for artists to work with, providing little direct control over simulation results. In this thesis, we describe tools for physics-based animation designed with artist needs and expertise in mind. Most materials can be modeled as elastoplastic: they recover from small deformations, but large deformations permanently alter their rest shape. Unfortunately, large plastic deformations, common in graphical applications, cause simulation instabilities if not addressed. Most elastoplastic simulation techniques in graphics rely on a finite-element approach where objects are discretized into a tetrahedral mesh. Using these approaches, maintaining simulation stability during large plastic flows requires remeshing, a complex and computationally expensive process. We introduce a new point-based approach that does not rely on an explicit mesh and avoids the expense of remeshing. Our approach produces comparable results with much lower implementation complexity. Points are a ubiquitous primitive for many effects, so our approach also integrates well with existing artist pipelines. Next, we introduce a new technique for animating stylized images which we call Dynamic Sprites. Artists can use our tool to create digital assets that interact in a natural, but stylized, way in virtual environments. In order to support the types of nonphysical, exaggerated motions often desired by artists, our approach relies on a heavily modified deformable body simulator, equipped with a set of new intuitive controls and an example-based deformation model. Our approach allows artists to specify how the shape of the object should change as it moves and collides in interactive virtual environments. Finally, we introduce a new technique for animating destructive scenes. Our approach is built on the insight that the most important visual aspects of destruction are plastic deformation and fracture. Like with Dynamic Sprites, we use an example-based model of deformation for intuitive artist control. Our simulator treats objects as rigid when computing dynamics but allows them to deform plastically and fracture in between timesteps based on interactions with the other objects. We demonstrate that our approach can efficiently animate the types of destructive scenes common in film and games. These animation techniques are designed to exploit artist expertise to ease creation of complex animations. By using artist-friendly primitives and allowing artists to provide characteristic deformations as input, our techniques enable artists to create more compelling animations, more easily

Numerical optimal control with applications in aerospace

This thesis explores various computational aspects of solving nonlinear, continuous-time dynamic optimization problems (DOPs) numerically. Firstly, a direct transcription method for solving DOPs is proposed, named the integrated residual method (IRM). Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct collocation, this new approach alternates between minimizing and constraining the squared norm of the dynamic constraint residuals integrated along the whole solution trajectories. The method is capable of obtaining solutions of higher accuracy for the same mesh compared to direct collocation methods, enabling a flexible trade-off between solution accuracy and optimality, and providing reliable solutions for challenging problems, including those with singular arcs and high-index differential-algebraic equations. A number of techniques have also been proposed in this work for efficient numerical solution of large scale and challenging DOPs. A general approach for direct implementation of rate constraints on the discretization mesh is proposed. Unlike conventional approaches that may lead to singular control arcs, the solution of this on-mesh implementation has better numerical properties, while achieving computational speedups. Another development is related to the handling of inactive constraints, which do not contribute to the solution of DOPs, but increase the problem size and burden the numerical computations. A strategy to systematically remove the inactive and redundant constraints under a mesh refinement framework is proposed. The last part of this work focuses on the use of DOPs in aerospace applications, with a number of topics studied. Using example scenarios of intercontinental flights, the benefits of formulating DOPs directly according to problem specifications are demonstrated, with notable savings in fuel usage. The numerical challenges with direct collocation are also identified, with the IRM obtaining solutions of higher accuracy, and at the same time suppressing the singular arc fluctuations.Open Acces

Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines

This paper uses a divergence-conforming B-spline fluid discretization to address the long-standing issue of poor mass conservation in immersed methods for computational fluid–structure interaction (FSI) that represent the influence of the structure as a forcing term in the fluid subproblem. We focus, in particular, on the immersogeometric method developed in our earlier work, analyze its convergence for linear model problems, then apply it to FSI analysis of heart valves, using divergence-conforming B-splines to discretize the fluid subproblem. Poor mass conservation can manifest as effective leakage of fluid through thin solid barriers. This leakage disrupts the qualitative behavior of FSI systems such as heart valves, which exist specifically to block flow. Divergence-conforming discretizations can enforce mass conservation exactly, avoiding this problem. To demonstrate the practical utility of immersogeometric FSI analysis with divergence-conforming B-splines, we use the methods described in this paper to construct and evaluate a computational model of an in vitro experiment that pumps water through an artificial valve