129,239 research outputs found
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Fast Simulation of Mass-Spring Systems
We describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton’s method. Although the asymptotic convergence of Newton’s method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton’s. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton’s iteration
Towards Real-Time Simulation Of Hyperelastic Materials
We propose a new method for physics-based simulation supporting many different types of hyperelastic materials from mass-spring systems to three-dimensional finite element models, pushing the performance of the simulation towards real-time. Fast simulation methods such as Position Based Dynamics exist, but support only limited selection of materials; even classical materials such as corotated linear elasticity and Neo-Hookean elasticity are not supported. Simulation of these types of materials currently relies on Newton\u27s method, which is slow, even with only one iteration per timestep. In this work, we start from simple material models such as mass-spring systems or as-rigid-as-possible materials. We express the widely used implicit Euler time integration as an energy minimization problem and introduce auxiliary projection variables as extra unknowns. After our reformulation, the minimization problem becomes linear in the node positions, while all the non-linear terms are isolated in individual elements. We then extend this idea to efficiently simulate a more general spatial discretization using finite element method. We show that our reformulation can be interpreted as a quasi-Newton method. This insight enables very efficient simulation of a large class of hyperelastic materials. The quasi-Newton interpretation also allows us to leverage ideas from numerical optimization. In particular, we show that our solver can be further accelerated using L-BFGS updates (Limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm). Our final method is typically more than ten times faster than one iteration of Newton\u27s method without compromising quality. In fact, our result is often more accurate than the result obtained with one iteration of Newton\u27s method. Our method is also easier to implement, implying reduced software development costs
A Massively-Parallel 3D Simulator for Soft and Hybrid Robots
Simulation is an important step in robotics for creating control policies and
testing various physical parameters. Soft robotics is a field that presents
unique physical challenges for simulating its subjects due to the nonlinearity
of deformable material components along with other innovative, and often
complex, physical properties. Because of the computational cost of simulating
soft and heterogeneous objects with traditional techniques, rigid robotics
simulators are not well suited to simulating soft robots. Thus, many engineers
must build their own one-off simulators tailored to their system, or use
existing simulators with reduced performance. In order to facilitate the
development of this exciting technology, this work presents an
interactive-speed, accurate, and versatile simulator for a variety of types of
soft robots. Cronos, our open-source 3D simulation engine, parallelizes a
mass-spring model for ultra-fast performance on both deformable and rigid
objects. Our approach is applicable to a wide array of nonlinear material
configurations, including high deformability, volumetric actuation, or
heterogenous stiffness. This versatility provides the ability to mix materials
and geometric components freely within a single robot simulation. By exploiting
the flexibility and scalability of nonlinear Hookean mass-spring systems, this
framework simulates soft and rigid objects via a highly parallel model for near
real-time speed. We describe an efficient GPU CUDA implementation, which we
demonstrate to achieve computation of over 1 billion elements per second on
consumer-grade GPU cards. Dynamic physical accuracy of the system is validated
by comparing results to Euler-Bernoulli beam theory, natural frequency
predictions, and empirical data of a soft structure under large deformation
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Why do Large Animals Never Actuate Their Jumps with Latch-Mediated Springs? Because They can Jump Higher Without Them.
As animals get smaller, their ability to generate usable work from muscle contraction is decreased by the muscle's force-velocity properties, thereby reducing their effective jump height. Very small animals use a spring-actuated system, which prevents velocity effects from reducing available energy. Since force-velocity properties reduce the usable work in even larger animals, why don't larger animals use spring-actuated jumping systems as well? We will show that muscle length-tension properties limit spring-actuated systems to generating a maximum one-third of the possible work that a muscle could produce-greatly restricting the jumping height of spring-actuated jumpers. Thus a spring-actuated jumping animal has a jumping height that is one-third of the maximum possible jump height achievable were 100% of the possible muscle work available. Larger animals, which could theoretically use all of the available muscle energy, have a maximum jumping height that asymptotically approaches a value that is about three times higher than that of spring-actuated jumpers. Furthermore, a size related "crossover point" is evident for these two jumping mechanisms: animals smaller than this point can jump higher with a spring-actuated mechanism, while animals larger than this point can jump higher with a muscle-actuated mechanism. We demonstrate how this limit on energy storage is a consequence of the interaction between length-tension properties of muscles and spring stiffness. We indicate where this crossover point occurs based on modeling and then use jumping data from the literature to validate that larger jumping animals generate greater jump heights with muscle-actuated systems than spring-actuated systems
Modelling Rod-like Flexible Biological Tissues for Medical Training
This paper outlines a framework for the modelling of slender rod-like biological tissue structures in both global and local scales. Volumetric discretization of a rod-like structure is expensive in computation and therefore
is not ideal for applications where real-time performance is essential. In our approach, the Cosserat rod model is introduced to capture the global shape changes, which models the structure as a one-dimensional entity, while the
local deformation is handled separately. In this way a good balance in accuracy and efficiency is achieved. These advantages make our method appropriate for
the modelling of soft tissues for medical training applications
On the speed of fast and slow rupture fronts along frictional interfaces
The transition from stick to slip at a dry frictional interface occurs
through the breaking of the junctions between the two contacting surfaces.
Typically, interactions between the junctions through the bulk lead to rupture
fronts propagating from weak and/or highly stressed regions, whose junctions
break first. Experiments find rupture fronts ranging from quasi-static fronts
with speeds proportional to external loading rates, via fronts much slower than
the Rayleigh wave speed, and fronts that propagate near the Rayleigh wave
speed, to fronts that travel faster than the shear wave speed. The mechanisms
behind and selection between these fronts are still imperfectly understood.
Here we perform simulations in an elastic 2D spring--block model where the
frictional interaction between each interfacial block and the substrate arises
from a set of junctions modeled explicitly. We find that a proportionality
between material slip speed and rupture front speed, previously reported for
slow fronts, actually holds across the full range of front speeds we observe.
We revisit a mechanism for slow slip in the model and demonstrate that fast
slip and fast fronts have a different, inertial origin. We highlight the long
transients in front speed even in homogeneous interfaces, and we study how both
the local shear to normal stress ratio and the local strength are involved in
the selection of front type and front speed. Lastly, we introduce an
experimentally accessible integrated measure of block slip history, the Gini
coefficient, and demonstrate that in the model it is a good predictor of the
history-dependent local static friction coefficient of the interface. These
results will contribute both to building a physically-based classification of
the various types of fronts and to identifying the important mechanisms
involved in the selection of their propagation speed.Comment: 29 pages, 21 figure
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