303 research outputs found
Fully implicit frictional dynamics with soft constraints
Dynamics simulation with frictional contacts is important for a wide range of
applications, from cloth simulation to object manipulation. Recent methods
using smoothed friction forces have enabled robust and differentiable
simulation of elastodynamics with friction. However, the resulting frictional
behaviors can be qualitatively inaccurate and may not converge to analytic
solutions. Here we propose an alternative, fully implicit, formulation for
simulating elastodynamics subject to frictional contacts with realistic
friction behavior. Furthermore, we demonstrate how higher-order time
integration can be used in our method, as well as in incremental potential
methods. We develop an inexact Newton method with forward-mode automatic
differentiation that simplifies the implementation and improves performance.
Finally, we show how our method can be extended to respond to volume changes
using a unified penalty function derived from first principles and capable of
emulating compressible as well as nearly incompressible media
DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact
Cloth simulation has wide applications in computer animation, garment design,
and robot-assisted dressing. This work presents a differentiable cloth
simulator whose additional gradient information facilitates cloth-related
applications. Our differentiable simulator extends a state-of-the-art cloth
simulator based on Projective Dynamics (PD) and with dry frictional contact. We
draw inspiration from previous work to propose a fast and novel method for
deriving gradients in PD-based cloth simulation with dry frictional contact.
Furthermore, we conduct a comprehensive analysis and evaluation of the
usefulness of gradients in contact-rich cloth simulation. Finally, we
demonstrate the efficacy of our simulator in a number of downstream
applications, including system identification, trajectory optimization for
assisted dressing, closed-loop control, inverse design, and real-to-sim
transfer. We observe a substantial speedup obtained from using our gradient
information in solving most of these applications
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Multi-Scale Models to Simulate Interactions between Liquid and Thin Structures
In this dissertation, we introduce a framework for simulating the dynamics between liquid and thin structures, including the effects of buoyancy, drag, capillary cohesion, dripping, and diffusion. After introducing related works, Part I begins with a discussion on the interactions between Newtonian fluid and fabrics. In this discussion, we treat both the fluid and the fabrics as continuum media; thus, the physical model is built from mixture theory. In Part II, we discuss the interactions between Newtonian fluid and hairs. To have more detailed dynamics, we no longer treat the hairs as continuum media. Instead, we treat them as discrete Kirchhoff rods. To deal with the thin layer of liquid that clings to the hairs, we augment each hair strand with a height field representation, through which we introduce a new reduced-dimensional flow model to solve the motion of liquid along the longitudinal direction of each hair. In addition, we develop a faithful model for the hairs' cohesion induced by surface tension, where a penalty force is applied to simulate the collision and cohesion between hairs. To enable the discrete strands interact with continuum-based, shear-dependent liquid, in Part III, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. Accordingly, we extend the reduced-dimensional flow model to simulate liquid with elastoviscoplastic behavior. Furthermore, we use a constraint-based model to replace the penalty-force model to handle contact, which enables an accurate simulation of the frictional and adhesive effects between wet strands. We also present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps.
We demonstrate a wide range of effects, including the challenging animation scenarios involving splashing, wringing, and colliding of wet clothes, as well as flipping of hair, animals shaking, spinning roller brushes from car washes being dunked in water, and intricate hair coalescence effects. For complex liquids, we explore a series of challenging scenarios, including strands interacting with oil paint, mud, cream, melted chocolate, and pasta sauce
NeuralClothSim: Neural Deformation Fields Meet the Kirchhoff-Love Thin Shell Theory
Cloth simulation is an extensively studied problem, with a plethora of
solutions available in computer graphics literature. Existing cloth simulators
produce realistic cloth deformations that obey different types of boundary
conditions. Nevertheless, their operational principle remains limited in
several ways: They operate on explicit surface representations with a fixed
spatial resolution, perform a series of discretised updates (which bounds their
temporal resolution), and require comparably large amounts of storage.
Moreover, back-propagating gradients through the existing solvers is often not
straightforward, which poses additional challenges when integrating them into
modern neural architectures. In response to the limitations mentioned above,
this paper takes a fundamentally different perspective on physically-plausible
cloth simulation and re-thinks this long-standing problem: We propose
NeuralClothSim, i.e., a new cloth simulation approach using thin shells, in
which surface evolution is encoded in neural network weights. Our
memory-efficient and differentiable solver operates on a new continuous
coordinate-based representation of dynamic surfaces, i.e., neural deformation
fields (NDFs); it supervises NDF evolution with the rules of the non-linear
Kirchhoff-Love shell theory. NDFs are adaptive in the sense that they 1)
allocate their capacity to the deformation details as the latter arise during
the cloth evolution and 2) allow surface state queries at arbitrary spatial and
temporal resolutions without retraining. We show how to train our
NeuralClothSim solver while imposing hard boundary conditions and demonstrate
multiple applications, such as material interpolation and simulation editing.
The experimental results highlight the effectiveness of our formulation and its
potential impact.Comment: 27 pages, 22 figures and 3 tables; project page:
https://4dqv.mpi-inf.mpg.de/NeuralClothSim
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
Novel Degrees of Freedom, Constraints, and Stiffness Formulation for Physically Based Animation
I identify and improve upon three distinct components of physically simulated systems with the aim of increasing both robustness and efficiency for the application of computer graphics: A) the degrees of freedom of a system; B) the constraints put on that system; C) and the stiffness that derives from force differentiation and in turn enables implicit integration techniques. These three components come up in many implementations of physics-based simulation in computer animation. From a combination of these components, I explore four novel ideas implemented and experimented on over the course of my graduate degree. Eulerian-on-Lagrangian Cloth Simulation resolves a longstanding problem of simulating contact-mediated interaction of cloth and sharp geometric features by exploring a combination of all three of our components. Bilateral Staggered Projections for Joints explores the constrained degrees of freedom of articulated rigid bodies in a reduced state to extend the popular Staggered Projects technique into a novel formulation for rapid evaluation of frictional articulated dynamics. Condensation Jacobian with Adaptivity looks at using reduction methods to improve the efficiency of soft body deformations by allowing larger time step in dynamics simulations. Finally, Ldot: Boosting Deformation Performance with Cholesky Extrapolation explores the inner workings of sparse direct solvers to introduce a Cholesky factorization that is linearly extrapolated in time, which can improve the performance when encapsulated inside an iterative nonlinear solver
Stable Constrained Dynamics
International audienceWe present a unification of the two main approaches to simulate deformable solids, namely elasticity and constraints. Elasticity accurately handles soft to moderately stiff objects, but becomes numerically hard as stiffness increases. Constraints efficiently handle high stiffness, but when integrated in time they can suffer from instabilities in the nullspace directions, generating spurious transverse vibrations when pulling hard on thin inextensible objects or articulated rigid bodies. We show that geometric stiffness, the tensor encoding the change of force directions (as opposed to intensities) in response to a change of positions, is the missing piece between the two approaches. This previously neglected stiffness term is easy to implement and dramatically improves the stability of inextensible objects and articulated chains, without adding artificial bending forces. This allows time step increases up to several orders of magnitude using standard linear solvers
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