Robust interactive simulation of deformable solids with detailed geometry using corotational FEM

This thesis focuses on the interactive simulation of highly detailed deformable solids modelled with the Corotational Finite Element Method. Starting from continuum mechanics we derive the discrete equations of motion and present a simulation scheme with support for user-in-the-loop interaction, geometric constraints and contact treatment. The interplay between accuracy and computational cost is discussed in depth, and practical approximations are analyzed with an emphasis on robustness and efficiency, as required by interactive simulation. The first part of the thesis focuses on deformable material discretization using the Finite Element Method with simplex elements and a corotational linear constitutive model, and presents our contributions to the solution of widely reported robustness problems in case of large stretch deformations and finite element degeneration. First,we introduce a stress differential approximation for quasi-implicit corotational linear FEM that improves its results for large deformations and closely matches the fullyimplicit solution with minor computational overhead. Next, we address the problem ofrobustness and realism in simulations involving element degeneration, and show that existing methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new continuous-time approach, degeneration-aware polar decomposition, that avoids such flaws and yields robust degeneration recovery. In the second part we focus on geometry representation and contact determination for deformable solids with highly detailed surfaces. Given a high resolution closed surface mesh we automatically build a coarse embedding tetrahedralization and a partitioned representation of the collision geometry in a preprocess. During simulation, our proposed contact determination algorithm finds all intersecting pairs of deformed triangles using a memory-efficient barycentric bounding volume hierarchy, connects them into potentially disjoint intersection curves and performs a topological flood process on the exact intersection surfaces to discover a minimal set of contact points. A novel contact normal definition is used to find contact point correspondences suitable for contact treatment.Aquesta tesi tracta sobre la simulació interactiva de sòlids deformables amb superfícies detallades, modelats amb el Mètode dels Elements Finits (FEM) Corotacionals. A partir de la mecànica del continuu derivem les equacions del moviment discretes i presentem un esquema de simulació amb suport per a interacció d'usuari, restriccions geomètriques i tractament de contactes. Aprofundim en la interrelació entre precisió i cost de computació, i analitzem aproximacions pràctiques fent èmfasi en la robustesa i l'eficiència necessàries per a la simulació interactiva. La primera part de la tesi es centra en la discretització del material deformable mitjançant el Mètode dels Elements Finits amb elements de tipus s'implex i un model constituent basat en elasticitat linial corotacional, i presenta les nostres contribucions a la solució de problemes de robustesa àmpliament coneguts que apareixen en cas de sobreelongament i degeneració dels elements finits. Primer introduïm una aproximació dels diferencials d'estress per a FEM linial corotacional amb integració quasi-implícita que en millora els resultats per a deformacions grans i s'apropa a la solució implícita amb un baix cost computacional. A continuació tractem el problema de la robustesa i el realisme en simulacions que inclouen degeneració d'elements finits, i mostrem que els mètodes existents presenten inconvenients que posen en perill la robustesa plausibilitat de la simulació en aplicacions interactives. Proposem un enfocament nou basat en temps continuu, la descomposició polar amb coneixement de degeneració, que evita els inconvenients esmentats i permet corregir la degeneració de forma robusta. A la segona part de la tesi ens centrem en la representació de geometria i la determinació de contactes per a sòlids deformables amb superfícies detallades. A partir d'una malla de superfície tancada construím una tetraedralització englobant de forma automàtica en un preprocés, i particionem la geometria de colisió. Proposem un algorisme de detecció de contactes que troba tots els parells de triangles deformats que intersecten mitjançant una jerarquia de volums englobants en coordenades baricèntriques, els connecta en corbes d'intersecció potencialment disjuntes i realitza un procés d'inundació topològica sobre les superfícies d'intersecció exactes per tal de descobrir un conjunt mínim de punts de contacte. Usem una definició nova de la normal de contacte per tal de calcular correspondències entre punts de contacte útils per al seu tractament.Postprint (published version

Plenoptic Signal Processing for Robust Vision in Field Robotics

This thesis proposes the use of plenoptic cameras for improving the robustness and simplicity of machine vision in field robotics applications. Dust, rain, fog, snow, murky water and insufficient light can cause even the most sophisticated vision systems to fail. Plenoptic cameras offer an appealing alternative to conventional imagery by gathering significantly more light over a wider depth of field, and capturing a rich 4D light field structure that encodes textural and geometric information. The key contributions of this work lie in exploring the properties of plenoptic signals and developing algorithms for exploiting them. It lays the groundwork for the deployment of plenoptic cameras in field robotics by establishing a decoding, calibration and rectification scheme appropriate to compact, lenslet-based devices. Next, the frequency-domain shape of plenoptic signals is elaborated and exploited by constructing a filter which focuses over a wide depth of field rather than at a single depth. This filter is shown to reject noise, improving contrast in low light and through attenuating media, while mitigating occluders such as snow, rain and underwater particulate matter. Next, a closed-form generalization of optical flow is presented which directly estimates camera motion from first-order derivatives. An elegant adaptation of this "plenoptic flow" to lenslet-based imagery is demonstrated, as well as a simple, additive method for rendering novel views. Finally, the isolation of dynamic elements from a static background is considered, a task complicated by the non-uniform apparent motion caused by a mobile camera. Two elegant closed-form solutions are presented dealing with monocular time-series and light field image pairs. This work emphasizes non-iterative, noise-tolerant, closed-form, linear methods with predictable and constant runtimes, making them suitable for real-time embedded implementation in field robotics applications

Plenoptic Signal Processing for Robust Vision in Field Robotics

This thesis proposes the use of plenoptic cameras for improving the robustness and simplicity of machine vision in field robotics applications. Dust, rain, fog, snow, murky water and insufficient light can cause even the most sophisticated vision systems to fail. Plenoptic cameras offer an appealing alternative to conventional imagery by gathering significantly more light over a wider depth of field, and capturing a rich 4D light field structure that encodes textural and geometric information. The key contributions of this work lie in exploring the properties of plenoptic signals and developing algorithms for exploiting them. It lays the groundwork for the deployment of plenoptic cameras in field robotics by establishing a decoding, calibration and rectification scheme appropriate to compact, lenslet-based devices. Next, the frequency-domain shape of plenoptic signals is elaborated and exploited by constructing a filter which focuses over a wide depth of field rather than at a single depth. This filter is shown to reject noise, improving contrast in low light and through attenuating media, while mitigating occluders such as snow, rain and underwater particulate matter. Next, a closed-form generalization of optical flow is presented which directly estimates camera motion from first-order derivatives. An elegant adaptation of this "plenoptic flow" to lenslet-based imagery is demonstrated, as well as a simple, additive method for rendering novel views. Finally, the isolation of dynamic elements from a static background is considered, a task complicated by the non-uniform apparent motion caused by a mobile camera. Two elegant closed-form solutions are presented dealing with monocular time-series and light field image pairs. This work emphasizes non-iterative, noise-tolerant, closed-form, linear methods with predictable and constant runtimes, making them suitable for real-time embedded implementation in field robotics applications

Doctor of Philosophy

dissertationEach year in the United States, a quarter million cases of stroke are caused directly by atherosclerotic disease of the cervical carotid artery. This represents a significant portion of health care costs that could be avoided if high-risk carotid artery lesions could be detected early on in disease progression. There is mounting evidence that Magnetic Resonance Imaging of the carotid artery can better classify subjects who would benefit from interventions. Turbo Spin Echo sequences are a class of Magnetic Resonance Imaging sequences that provide a variety of tissue contrasts. While high resolution Turbo Spin Echo images have demonstrated important details of carotid artery morphology, it is evident that pulsatile blood and wall motion related to the cardiac cycle are still significant sources of image degradation. In addition, patient motion artifacts due to the relatively long scan times of Turbo Spin Echo sequences result in an unacceptable fraction of noninterpretable studies. This dissertation presents work done to detect and correct for types of voluntary and physiological patient motion

Microsphere Traction Force Microscopy

This work is a culmination of our efforts in understanding cellular mechanics at the scale of single cells and small tissues. We developed methods to quantify cell-generated traction forces using cell-sized, synthetic, functionalized hydrogel microspheres. Cell-sized solid microspheres can provide information regarding cell-generated normal and shear forces while allowing natural cell-cell interactions and facilitating a convex cell-hydrogel interface. Therefore, they are a better mimic than the current methods for understanding the natural cell-cell interactions in a physiologically relevant geometry. In the analysis of the microsphere deformations, we use a boundary spectral method based on spherical harmonics decomposition of the traction field on the spherical gel surface. Using the techniques developed here, we measure the boundary traction profiles that mammalian cells exert on the synthetic microspherical hydrogel bodies. In this report, we briefly review the state of the art in cellular force quantification methods and discuss the contributions of our work to the field and its strengths as well as its limitations

Modeling, Analysis, and Optimization Issues for Large Space Structures

Topics concerning the modeling, analysis, and optimization of large space structures are discussed including structure-control interaction, structural and structural dynamics modeling, thermal analysis, testing, and design

Underwater Vehicles

For the latest twenty to thirty years, a significant number of AUVs has been created for the solving of wide spectrum of scientific and applied tasks of ocean development and research. For the short time period the AUVs have shown the efficiency at performance of complex search and inspection works and opened a number of new important applications. Initially the information about AUVs had mainly review-advertising character but now more attention is paid to practical achievements, problems and systems technologies. AUVs are losing their prototype status and have become a fully operational, reliable and effective tool and modern multi-purpose AUVs represent the new class of underwater robotic objects with inherent tasks and practical applications, particular features of technology, systems structure and functional properties