ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics

Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and therefore they are significantly more computationally expensive to simulate. Computing gradients with respect to physical design or controller parameters is typically even more computationally challenging. In this paper, we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical simulator for deformable objects, ChainQueen, based on the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects including contact and can be seamlessly incorporated into inference, control and co-design systems. We demonstrate that our simulator achieves high precision in both forward simulation and backward gradient computation. We have successfully employed it in a diverse set of control tasks for soft robots, including problems with nearly 3,000 decision variables.Comment: In submission to ICRA 2019. Supplemental Video: https://www.youtube.com/watch?v=4IWD4iGIsB4 Project Page: https://github.com/yuanming-hu/ChainQuee

A Material Point Method for Simulating Frictional Contact with Diverse Materials

We present an extension to the Material Point Method (MPM) for simulating elastic objects with various co-dimensions like hair (1D), thin shells (2D), and volumetric objects (3D). We simulate thin shells with frictional contact using a combination of MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Furthermore our technique naturally couples with other traditional MPM methods for simulating granular materials. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high resolution examples. For the simulation of hair and volumetric elastic objects, we utilize a Lagrangian mesh for internal force computation and an Eulerian mesh for self collision as well as coupling with external materials. While the updated Lagrangian discretization where the Eulerian grid degrees of freedom are used to take variations of the potential energy is effective in simulating thin shells, its frictional contact response strategy does not generalize to volumetric objects. Therefore, we develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with multiple elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling

Examining the Relationship Between Lignocellulosic Biomass Structural Constituents and Its Flow Behavior

Lignocellulosic biomass material sourced from plants and herbaceous sources is a promising substrate of inexpensive, abundant, and potentially carbon-neutral energy. One of the leading limitations of using lignocellulosic biomass as a feedstock for bioenergy products is the flow issues encountered during biomass conveyance in biorefineries. In the biorefining process, the biomass feedstock undergoes flow through a variety of conveyance systems. The inherent variability of the feedstock materials, as evidenced by their complex microstructural composition and non-uniform morphology, coupled with the varying flow conditions in the conveyance systems, gives rise to flow issues such as bridging, ratholing, and clogging. These issues slow down the conveyance process, affect machine life, and potentially lead to partial or even complete shutdown of the biorefinery. Hence, we need to improve our fundamental understanding of biomass feedstock flow physics and mechanics to address the flow issues and improve biorefinery economics. This dissertation research examines the fundamental relationship between structural constituents of diverse lignocellulosic biomass materials, i.e., cellulose, hemicellulose, and lignin, their morphology, and the impact of the structural composition and morphology on their flow behavior. First, we prepared and characterized biomass feedstocks of different chemical compositions and morphologies. Then, we conducted our fundamental investigation experimentally, through physical flow characterization tests, and computationally through high-fidelity discrete element modeling. Finally, we statistically analyzed the relative influence of the properties of lignocellulosic biomass assemblies on flow behavior to determine the most critical properties and the optimum values of flow parameters. Our research provides an experimental and computational framework to generalize findings to a wider portfolio of biomass materials. It will help the bioenergy community to design more efficient biorefining machinery and equipment, reduce the risk of failure, and improve the overall commercial viability of the bioenergy industry

A Material Point Method for Elastoplasticity with Ductile Fracture and Frictional Contact

Simulating physical materials with dynamic movements to photo-realistic resolution has always been one of the most crucial and challenging topics in Computer Graphics. This dissertation considers large-strain elastoplasticity theory applied to the low-to-medium stiffness regime, with topological changes and codimensional objects incorporated. We introduce improvements to the Material Point Method (MPM) for two particular objectives, simulating fracturing ductile materials and incorporation of MPM and Lagrangian Finite Element Method (FEM).Our first contribution, simulating ductile fracture, utilizes traditional particle-based MPM [SSC13, SCS94] as well as the Lagrangian energy formulation of [JSS15] which uses a tetrahedron mesh, rather than particle-based estimation of the deformation gradient and potential energy. We model failure and fracture via elastoplasticity with damage. The material is elastic until its deformation exceeds a Rankine or von Mises yield condition. At that point, we use a softening model that shrinks the yield surface until it reaches the damage thresh- old. Once damaged, the material Lam ́e coefficients are modified to represent failed material. This approach to simulating ductile fracture with MPM is successful, as MPM naturally captures the topological changes coming from the fracture. However, rendering the crack surfaces can be challenging. We design a novel visualization technique dedicated to rendering the material’s boundary and its intersection with the evolving crack surfaces. Our approach uses a simple and efficient element splitting strategy for tetrahedron meshes to create crack surfaces. It employs an extrapolation technique based on the MPM simulation. For traditional particle-based MPM, we use an initial Delaunay tetrahedralization to connect randomly sampled MPM particles. Our visualization technique is a post-process and can run after the MPM simulation for efficiency. We demonstrate our method with several challenging simulations of ductile failure with considerable and persistent self-contact and applications with thermomechanical models for baking and cooking.Our second contribution, hybrid MPM–Lagrangian-FEM, aims to simulate elastic objects like hair, rubber, and soft tissues. It utilizes a Lagrangian mesh for internal force computation and a Eulerian grid for self-collision, as well as coupling with external materials. While recent MPM techniques allow for natural simulation of hyperelastic materials represented with Lagrangian meshes, they utilize an updated Lagrangian discretization and use the Eulerian grid degrees of freedom to take variations of the potential energy. It often coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts. We develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM, e.g., sand, snow, etc. Furthermore, while recent MPM advances allow for resolution of frictional contact with codimensional simulation of hyperelasticity, they do not generalize to the case of volumetric materials. We show that our hybrid approach resolves these issues. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with various elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling

The Material Point Method for Solid and Fluid Simulation

The Material Point Method (MPM) has shown its high potential for physics-based simulation in the area of computer graphics. In this dissertation, we introduce a couple of improvements to the traditional MPM for different applications and demonstrate the advantages of our methods over the previous methods.First, we present a generalized transfer scheme for the hybrid Eulerian/Lagrangian method: the Polynomial Particle-In-Cell Method (PolyPIC). PolyPIC improves kinetic energy conservation during transfers, which leads to better vorticity resolution in fluid simulations and less numerical damping in elastoplasticity simulations. Our transfers are designed to select particle-wise polynomial approximations to the grid velocity that are optimal in the local mass-weighted L2 norm. Indeed our notion of transfers reproduces the original Particle-In-Cell Method (PIC) and recent Affine Particle-In-Cell Method (APIC). Furthermore, we derive a polynomial basis that is mass orthogonal to facilitate the rapid solution of the optimality condition. Our method applies to both of the collocated and staggered grid.As the second contribution, we present a novel method for the simulation of thin shells with frictional contact using a combination of MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high-resolution examples. Furthermore, we show that our technique naturally couples with other traditional MPM methods for simulating granular and related materials.In the third part, we present a new hybrid Lagrangian Material Point Method for simulating volumetric objects with frictional contact. The resolution of frictional contact in the thin shell simulation cannot be generalized to the case of volumetric materials directly. Also, even though MPM allows for the natural simulation of hyperelastic materials represented with Lagrangian meshes, it usually coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts, e.g., numerical cohesion. We demonstrate that our hybrid method can efficiently resolve these issues. We show the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with various elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling

Finite element simulation for the cold-joining of high power connectors

A method for the Finite-Element (FE) simulation of the Cold-Joining-Process (CJP) of massive copper contacts is developed in this thesis. The standard procedure for the calculation of interference fit connectors is not applicable to the joining process of massive copper components, since the contact area builds up in a context of considerable plastic deformation and high frictional loads. The new FE model not only shortens and optimizes the design cycle for novel High-Power-Connectors (HPCs), but also allows a deeper understanding of the CJP and the connector. The FE model is rolled out to real HPCs. The comparison between calculated and real features of the connector nails down the validity of the simulation. By means of this real example the capability of the new simulation method to set the ground for the design of future CJCs is demonstrated.Im Rahmen dieser Arbeit wird eine neue Methode zur Beschreibung von massiven Kupfer-Einpresskontakte entwickelt. Die Berechnung von Pressverbänden nach DIN 7190 ist bei der Auslegung von massiven Kupferkontakten nicht anwendbar da während des Fügevorganges hohe Verformungsgrade und Reibspannungen auftreten. Das neue Modell bietet nicht nur verkürzte und effiziente Auslegungszyklen für neue Hochleistungskontakte (HLK) an, sondern vertieft auch das Grundverständnis des Fügeprozesses und der Kontakteigenschaften. Nach einer kurzen Motivation des Themas und einer Einführung in die kalte Kontaktiertechnik, werden im dritten Kapitel die Grundlagen der experimentellen Arbeiten sowie der Simulationsmethoden erarbeitet. Die Herausforderungen bei der Modellierung von Fügeprozessen liegen in der Materialbeschreibung und Reibungscharakterisierung. Deshalb werden die beiden Themen in zwei eigenständigen Kapiteln vorgestellt, ausgehend vom jeweiligen Stand der Technik bis zur Validation der entwickelten Methoden und Modelle. Das vierte Kapitel beschäftigt sich mit der Materialbeschreibung und beinhaltet zwei neue Methoden zur bauteilnahen Ermittlung der Fließeigenschaften von Kupferwerkstoffen. Das Reibverhalten in einem Einpressvorgang wird im fünften Kapitel untersucht. Hierzu wurde ein neuer Prüfstand zur Ermittlung von Reibkoeffizienten und Beschreibung der auftretenden Verschleißmechanismen aufgebaut. Die Materialbeschreibung und die Reibungscharakterisierung sind eng miteinander verknüpft. Beide Modelle wurden deshalb in ein Finiten-Elementen (FE)-Tool zusammengeführt, um die komplexen Wechselwirkungen beschreiben zu können. Für eine genaue aber mit möglichst wenig Aufwand verbundene FE-Beschreibung von Einpressvorgängen werden Richtlinien erarbeitet und vorgeschlagen. Auf Basis des FE-Modells werden neue Hochstromkontakte entwickelt. Über den Vergleich der simulierten und der realen Eigenschaften wurde das Modell erfolgreich validiert und seine Aussagekraft eindrücklich nachgewiesen.A method for the Finite-Element (FE) simulation of the Cold-Joining -Process (CJP) of massive copper contacts is developed in this thesis. The standard procedure for the calculation of interference fit connectors is not applicable to the joining process of massive copper components, since the contact area builds up in a context of considerable plastic deformation and high frictional loads. The new FE model not only shortens and optimizes the design cycle for novel High-Power-Connectors (HPCs), but also allows a deeper understanding of the CJP and the connector. After a short introduction into the cold-joining technology and its relevance, the experimental details for the CJP and the general settings of the FE model are presented in the third chapter, as well as an overview of characteristic CJPes. The main challenges of the FE simulation of CJPes arise in the fields of material and friction characterization. Therefore each of the two areas will be developed in a separate chapter, beginning with the state of the art in the field, and ending with the assessment of the impact of the new methodology developed. The fourth chapter addresses the material characterization and includes two novel methods for the determination of flow curves and the characterization of the inhomogeneity at punched edges. The friction behavior during cold-joining is studied in chapter five. A new test bench is developed for the determination of friction coefficients and the study of wear disposition. Both material properties and friction behavior showed to be closely connected and interdependent. To cope with this complex interaction, both models were integrated in a FE tool. Guidelines are developed and proposed for an accurate FE representation of a certain CJP with the minimum modeling complexity. The FE model is rolled out to real HPCs. The comparison between calculated and real features of the connector nails down the validity of the simulation. By means of this real example the capability of the new simulation method to set the ground for the design of future CJCs is demonstrated

Homogeneous equilibrium model for geomechanical multi-material flow with compressible constituents

Multi-material flow generally describes a situation where several distinct materials separated by sharp material interfaces undergo large deformations. In order to model such flow situations in the context of geomechanics and geotechnical engineering, a theoretical framework is presented which introduces a possible two-phase coupled saturated granular material behavior among the different materials. This is achieved by extending the technique of local volume averaging to a hierarchy of three spatial scales, based on a product of two indicator functions. A homogeneous equilibrium mixture model is subsequently derived for an example flow consisting of bulk solid, bulk fluid, and undrained granular material with compressible constituents. The closure relations are provided at the macroscale, including those describing granular behavior covering the full frictional-collisional flow regime and bulk material volume fraction evolution. The paper discusses the advantages and restrictions of the proposed mixture model and addresses its application and full-scale numerical implementation.DFG, FOR 1136, Modellierung von geotechnischen Herstellungsvorgängen mit ganzheitlicher Erfassung des Spannungs-Verformungs-Verhaltens im Boden (GeoTech)DFG, SA 310/26-1, Numerische Modellierung der Herstellung von RüttelinjektionspfählenDFG, SA 310/26-2, Numerische Modellierung der Herstellung von Rüttelinjektionspfähle

ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method circumvents the main difficulties inherent to the non-smooth nature of frictional contact. We combine this new contact model with fully-implicit time integration to obtain a robust and efficient dynamics solver that is analytically differentiable. In conjunction with adjoint sensitivity analysis, our formulation enables gradient-based optimization with adaptive trade-offs between simulation accuracy and smoothness of objective function landscapes. We thoroughly analyse our approach on a set of simulation examples involving rigid bodies, visco-elastic materials, and coupled multi-body systems. We furthermore showcase applications of our differentiable simulator to parameter estimation for deformable objects, motion planning for robotic manipulation, trajectory optimization for compliant walking robots, as well as efficient self-supervised learning of control policies.Comment: Moritz Geilinger and David Hahn contributed equally to this wor