DisMech: A Discrete Differential Geometry-based Physical Simulator for Soft Robots and Structures

Fast, accurate, and generalizable simulations are a key enabler of modern advances in robot design and control. However, existing simulation frameworks in robotics either model rigid environments and mechanisms only, or if they include flexible or soft structures, suffer significantly in one or more of these performance areas. To close this "sim2real" gap, we introduce DisMech, a simulation environment that models highly dynamic motions of rod-like soft continuum robots and structures, quickly and accurately, with arbitrary connections between them. Our methodology combines a fully implicit discrete differential geometry-based physics solver with fast and accurate contact handling, all in an intuitive software interface. Crucially, we propose a gradient descent approach to easily map the motions of hardware robot prototypes to control inputs in DisMech. We validate DisMech through several highly-nuanced soft robot simulations while demonstrating an order of magnitude speed increase over previous state of the art. Our real2sim validation shows high physical accuracy versus hardware, even with complicated soft actuation mechanisms such as shape memory alloy wires. With its low computational cost, physical accuracy, and ease of use, DisMech can accelerate translation of sim-based control for both soft robotics and deformable object manipulation.Comment: IEEE Robotics and Automation Letters (RA-L 2024). Youtube video: https://www.youtube.com/watch?v=0jE9h5GpOe

Coupling, Conservation, and Performance in Numerical Simulations

This thesis considers three aspects of the numerical simulations, which arecoupling, conservation, and performance. We conduct a project and addressone challenge from each of these aspects.We propose a novel penalty force to enforce contacts with accurate Coulombfriction. The force is compatible with fully-implicit time integration and theuse of optimization-based integration. In addition to processing collisionsbetween deformable objects, the force can be used to couple rigid bodies todeformable objects or the material point method. The force naturally leads tostable stacking without drift over time, even when solvers are not run toconvergence. The force leads to an asymmetrical system, and we provide apractical solution for handling these.Next we present a new technique for transferring momentum and velocity betweenparticles and MAC grids based on the Affine-Particle-In-Cell (APIC) frameworkpreviously developed for co-locatedgrids. We extend the original APIC paper and show thatthe proposed transfers preserve linear and angular momentum and also satisfyall of the original APIC properties.Early indications in the original APIC paper suggested that APIC might besuitable for simulating high Reynolds fluids due to favorable retention ofvortices, but these properties were not studied further. We use twodimensional Fourier analysis to investigate dissipation in the limit \dt=0.We investigate dissipation and vortex retention numerically to quantify theeffectiveness of APIC compared with other transfer algorithms.Finally we present an efficient solver for problems typically seen inmicrofluidic applications.Microfluidic ``lab on a chip'' devices are small devices that operate on smalllength scales on small volumes of fluid. Designs for microfluidic chips aregenerally composed of standardized and often repeated components connected bylong, thin, straight fluid channels. We propose a novel discretizationalgorithm for simulating the Stokes equations on geometry with these features,which produces sparse linear systems with many repeated matrix blocks. Thediscretization is formally third order accurate for velocity and second orderaccurate for pressure in the $L^\infty$ norm. We also propose a novel linearsystem solver based on cyclic reduction, reordered sparse Gaussian elimination,and operation caching that is designed to efficiently solve systems withrepeated matrix blocks

Solving variational inequalities and cone complementarity problems in nonsmooth dynamics using the alternating direction method of multipliers

This work presents a numerical method for the solution of variational inequalities arising in nonsmooth flexible multibody problems that involve set-valued forces. For the special case of hard frictional contacts, the method solves a second order cone complementarity problem. We ground our algorithm on the Alternating Direction Method of Multipliers (ADMM), an efficient and robust optimization method that draws on few computational primitives. In order to improve computational performance, we reformulated the original ADMM scheme in order to exploit the sparsity of constraint jacobians and we added optimizations such as warm starting and adaptive step scaling. The proposed method can be used in scenarios that pose major difficulties to other methods available in literature for complementarity in contact dynamics, namely when using very stiff finite elements and when simulating articulated mechanisms with odd mass ratios. The method can have applications in the fields of robotics, vehicle dynamics, virtual reality, and multiphysics simulation in general

Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations

We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid-structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid-structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid-structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations.Comment: 24 pages, 3 figure

Mehrskalige Modellierung von Gummi-Hysteresereibung auf rauen Oberflächen

The performance of car tires on road tracks is strongly affected by hysteretic friction. In order to optimize driving characteristics, like minimizing fuel consumption, improving skid resistance, increasing tire durability, and increasing vehicle controllability during steering and braking, the rolling friction coefficient should be predicted properly. The accurate and efficient modeling and prediction of the hysteretic friction is still a challenge. In the past decade, two different modeling frameworks have attracted significant attention. They are the viscoelastic half-space (VHS)-based contact mechanics model, based on linear kinematics and implemented with the boundary element method (BEM), and the viscoelastic contact model in the finite deformation framework implemented with the finite element method (FEM). The first one has the ability to model all involved length scales at once with a reduced computational cost under the assumption of a flat geometry of the rough surface and small deformations. The second one does not have these limitations and is able to predict the friction coefficient accurately in the finite deformation framework, but at much higher computational cost. It is not able to investigate all involved length scales at once since it needs an extremely fine mesh refinement, which leads to an impractically slow simulation. This work has two major aims. The first goal is to study the accuracy of geometrical and rheological linearity assumptions in evaluation of rolling friction coefficient. This is done by comparing the simulation results of tire tread block in contact with a sinusoidal road track surface using the linear VHS-based model and the finite deformation model in terms of rolling friction coefficient, contact area, and pressure distributions. It has been found that accurate rolling friction predictions can be obtained through the linear VHS-based model within Reynolds assumption for moderate values of root mean square slopes, whereas finite deformation computations should be adopted for large root mean square slopes. The contact area is much more sensitive to the geometrical and rheological nonlinearities than the rolling friction coefficient. The second goal of the thesis is to establish a new hybrid (nonlinear FEM/linear BEM) multiscale method which combines the advantages of both methods. The presented hybrid multiscale approach has proven to be a suitable tool to study rolling-friction coefficient within a plausible degree of accuracy for relative large contact area and low sliding velocities. It allows a more faster calculation of friction coefficient than the finite deformation model.Das Verhalten von Pkw-Reifen auf Straßenoberflächen wird stark von hysteretischer Reibung beeinflusst. Um die Fahreigenschaften zu optimieren, beispielsweise zur Reduktion des Kraftstoffverbrauchs, der Verbesserung der Griffigkeit, der Erhöhung der Reifenhaltbarkeit und der Verbesserung der Kontrolle während des Lenkens und Bremsens, sollte die hysteretische Reibung richtig vorhergesagt werden. Die genaue und effiziente Vorhersage von hysteretischer Reibung, sowohl von theoretischer wie numerischer Seite, ist eine Herausforderung. Im letzten Jahrzehnt haben zwei verschiedene Modellierungsverfahren an Aufmerksamkeit gewonnen. Sie sind: das viskoelastische Halbraummodell, das auf einer linearen Kinematik basiert und mit der Randelemente-Methode implementiert wurde, sowie das viskoelastische Kontaktmodell im Rahmen finiter Deformationen, das mit der Finite-Elemente-Methode implementiert wurde. Mit der ersten Methode können alle beteiligten Längenskalen gleichzeitig und mit reduziertem Berechnungsaufwand simuliert werden, wobei eine flache Geometrie der rauen Oberfläche und lineare Verformungen angenommen werden. Die zweite Methode hat diese Einschränkungen nicht und kann den Reibkoeffizienten genau vorhersagen, jedoch bei weitaus höherer Berechnungszeit. Hierbei können jedoch nicht alle beteiligten Längenskalen gleichzeitig untersucht werden, da ein sehr feines Netz benötigt würde, was zu inakzeptabel langen Simulationen führt. Diese Arbeit hat zwei Hauptziele. Das erste Ziel besteht darin, die Auswirkungen geometrischer und rheologischer Linearitätsannahmen bei der Berechnung des Reibkoeffizienten zu untersuchen. Dies erfolgt durch Vergleich der Simulationsergebnisse eines Reifenprofilblocks in Kontakt mit einer sinusförmigen Oberfläche, unter Verwendung des linearen viskoelastischen Halbraummodells, das mit der Randelemente-Methode implementiert wurde, und des viskoelastischen Kontaktmodells im Rahmen finiter Deformationenund der Finite-Elemente-Methode. Betrachtet wurden Reibkoeffizient, Kontaktfläche und Druckverteilung. Es wurde festgestellt, dass mit dem viskoelastischen Halbraum Modell innerhalb der Linearitätsannahmen genaue Vorhersagen der Reibung für kleine Werte der lokaler Oberflächen-Steigung erhalten werden können, wohingegen für große Steigungen finite Deformationen berücksichtigt werden sollten. Das zweite Ziel dieser Arbeit ist die Etablierung einer neuen, hybriden (nichtlinearerFiniten-Elemente / linearer Randelemente) -Multiskalenmethode, die die Vorteile beider Verfahren kombiniert. Die vorgestellte Hybrid-Multiskalen-Methode hat sich als geeignetes Werkzeug erwiesen, um den Reibkoeffizienten mit einem angemessenen Genauigkeitsgrad für niedrige Gleitgeschwindigkeiten zu untersuchen; Sie ermöglicht eine schnellere Berechnung des Reibkoeffizienten als das nichtlineare FE-Modell

DESIGN, MODELING, AND CONTROL OF SOFT DYNAMIC SYSTEMS

Soft physical systems, be they elastic bodies, fluids, and compliant-bodied creatures, are ubiquitous in nature. Modeling and simulation of these systems with computer algorithms enable the creation of visually appealing animations, automated fabrication paradigms, and novel user interfaces and control mechanics to assist designers and engineers to develop new soft machines. This thesis develops computational methods to address the challenges emerged during the automation of the design, modeling, and control workflow supporting various soft dynamic systems. On the design/control side, we present a sketch-based design interface to enable non-expert users to design soft multicopters. Our system is endorsed by a data-driven algorithm to generate system identification and control policies given a novel shape prototype and rotor configurations. We show that our interactive system can automate the workflow of different soft multicopters\u27 design, simulation, and control with human designers involved in the loop. On the modeling side, we study the physical behaviors of fluidic systems from a local, collective perspective. We develop a prior-embedded graph network to uncover the local constraint relations underpinning a collective dynamic system such as particle fluid. We also proposed a simulation algorithm to model vortex dynamics with locally interacting Lagrangian elements. We demonstrate the efficacy of the two systems by learning, simulating and visualizing complicated dynamics of incompressible fluid

Preoperative Systems for Computer Aided Diagnosis based on Image Registration: Applications to Breast Cancer and Atherosclerosis

Computer Aided Diagnosis (CAD) systems assist clinicians including radiologists and cardiologists to detect abnormalities and highlight conspicuous possible disease. Implementing a pre-operative CAD system contains a framework that accepts related technical as well as clinical parameters as input by analyzing the predefined method and demonstrates the prospective output. In this work we developed the Computer Aided Diagnostic System for biomedical imaging analysis of two applications on Breast Cancer and Atherosclerosis. The aim of the first CAD application is to optimize the registration strategy specifically for Breast Dynamic Infrared Imaging and to make it user-independent. Base on the fact that automated motion reduction in dynamic infrared imaging is on demand in clinical applications, since movement disarranges time-temperature series of each pixel, thus originating thermal artifacts that might bias the clinical decision. All previously proposed registration methods are feature based algorithms requiring manual intervention. We implemented and evaluated 3 different 3D time-series registration methods: 1. Linear affine, 2. Non-linear Bspline, 3. Demons applied to 12 datasets of healthy breast thermal images. The results are evaluated through normalized mutual information with average values of 0.70±0.03, 0.74±0.03 and 0.81±0.09 (out of 1) for Affine, BSpline and Demons registration, respectively, as well as breast boundary overlap and Jacobian determinant of the deformation field. The statistical analysis of the results showed that symmetric diffeomorphic Demons registration method outperforms also with the best breast alignment and non-negative Jacobian values which guarantee image similarity and anatomical consistency of the transformation, due to homologous forces enforcing the pixel geometric disparities to be shortened on all the frames. We propose Demons registration as an effective technique for time-series dynamic infrared registration, to stabilize the local temperature oscillation. The aim of the second implemented CAD application is to assess contribution of calcification in plaque vulnerability and wall rupture and to find its maximum resistance before break in image-based models of carotid artery stenting. The role of calcification inside fibroatheroma during carotid artery stenting operation is controversial in which cardiologists face two major problems during the placement: (i) “plaque protrusion” (i.e. elastic fibrous caps containing early calcifications that penetrate inside the stent); (ii) “plaque vulnerability” (i.e. stiff plaques with advanced calcifications that break the arterial wall or stent). Finite Element Analysis was used to simulate the balloon and stent expansion as a preoperative patient-specific virtual framework. A nonlinear static structural analysis was performed on 20 patients acquired using in vivo MDCT angiography. The Agatston Calcium score was obtained for each patient and subject-specific local Elastic Modulus (EM) was calculated. The in silico results showed that by imposing average ultimate external load of 1.1MPa and 2.3MPa on balloon and stent respectively, average ultimate stress of 55.7±41.2kPa and 171±41.2kPa are obtained on calcifications. The study reveals that a significant positive correlation (R=0.85, p<0.0001) exists on stent expansion between EM of calcification and ultimate stress as well as Plaque Wall Stress (PWS) (R=0.92, p<0.0001), comparing to Ca score that showed insignificant associations with ultimate stress (R=0.44, p=0.057) and PWS (R=0.38, p=0.103), suggesting minor impact of Ca score in plaque rupture. These average data are in good agreement with results obtained by other research groups and we believe this approach enriches the arsenal of tools available for pre-operative prediction of carotid artery stenting procedure in the presence of calcified plaques

A Green’s Function Molecular Dynamics Approach to the Mechanical Contact between Thin Elastic Sheets and Randomly Rough Surfaces

Adhesion of biological systems is often made possible through thin elastic layers, such as human skin. To address the question of when a layer is sufficiently thin to become adhesive, we extended Green’s function molecular dynamics (GFMD) to account for the finite thickness of an elastic body that is supported by a fluid foundation. We observed that thin layers can much better accommodate rough counterfaces than thick structures. As a result, the contact area is enlarged, in particular, when the width of the layer w approaches or even falls below the short-wavelength cutoff λs of the surface spectra. In the latter case, the proportionality coefficient between area and load scales is (w/λs)3, which is consistent with Persson’s contact mechanics theory