Asynchronous contact mechanics

Abstract

Figure 1. A prescribed particle slowly moves through a set of curtains, then impulsively shifts to a very high velocity. The slow and fast phases highlight the method's ability to handle smooth resting and sliding with deep stacking, and arbitrarily fast penetration-free movements in which collisions are treated when (as opposed to well before or after) they occur. The curtains continue to swing for a long time, even as controlled internal dissipation damps high frequencies. AbstractWe develop a method for reliable simulation of elastica in complex contact scenarios. Our focus is on firmly establishing three parameter-independent guarantees: that simulations of wellposed problems (a) have no interpenetrations, (b) obey causality, momentum-and energy-conservation laws, and (c) complete in finite time. We achieve these guarantees through a novel synthesis of asynchronous variational integrators, kinetic data structures, and a discretization of the contact barrier potential by an infinite sum of nested quadratic potentials. In a series of two-and threedimensional examples, we illustrate that this method more easily handles challenging problems involving complex contact geometries, sharp features, and sliding during extremely tight contact. MotivationEven as computer hardware benefits from Moore's Law, our ability to program, debug, and maintain software advances at a humbler pace. This observation shapes our priorities as we develop physical simulation tools for computer graphics. While making choices that yield up-front simplicity and blazing performance is important today, we prefer that these choices do not obstruct our long-term goals of extending functionality and improving realism. Laying aside ad-hoc models in favor of physical approaches might require a deeper initial investment, but it promises to pay off handsomely in predictability, controllability, and extensibility. From this vantage point, we propose to revisit the long-studied problem of simulating deformable objects in complex contact scenarios.Safety, correctness, progress Robust simulation of complex contact scenarios is critical to applications spanning graphics (training, virtual worlds, entertainment) and engineering (product design, safety analysis, experimental validation). Challenging scenarios involve dynamics with frequent and distributed points of contact, interaction with sharp boundaries, resting and sliding contact, and combinations thereof. Useful resolution of these scenarios requires consideration of the fundamental issues of geometric safety, physical correctness, and computational progress, with the respective meanings that (a) for well-posed problems the simulation does not enter an invalid (interpenetrating) state, (b) collision response obeys physical laws of causality and conservation (of mass, momentum, energy, etc.), and (c) the algorithm completes a simulation in finite, preferrably short, time.An ideal algorithm offers provable guarantees of safety, correctness, and progress. A safety guarantee eliminates the need to ite...

A nonsmooth Newton solver for capturing exact Coulomb friction in fiber assemblies

“…Though simple to implement and efficient, this method often fails to prevent excessive penetration if the stiffness factor k is not large enough, unless barrier functions are used [Kaldor et al 2008;Harmon et al 2009]. However most barrier functions suffer from unbounded second derivatives which ruin the stability of the fixed step integration schemes.…”

Kinetic Dependence Graphs

“…Colliding billiard balls are a useful abstraction of complex phenomena such as molecular dynamics [2] and deformable contact [18]. The problem is stated as follows: given the positions and initial velocities of some balls on a billiards table, simulate the motion of these balls for some amount of time.…”

“…Applications considered in this paper include (i) asynchronous variational integrators (AVI), which are used in computational mechanics and in graphics for solving complicated contact mechanics problems [27] like simulating the tying of ribbons and the crushing of rabbits in a trash compactor [1,18], (ii) discrete-event simulation (DES) [9], (iii) the simulation of collisions between a set of moving bodies like billiard balls [2,18], and (iv) graph analytics algorithms such as Breadth-First Search (BFS), Minimumweight Spanning Tree (MST), and tree traversals. The inadequacy of conventional task graphs for these applications arises from the fact that the dependence graph computed from a particular program state may not remain valid after a task has executed because new tasks may have been created and dependences between existing tasks may have changed.…”

Coupling cloth and rigid bodies for dexterous manipulation

“…ARCSim adapts the elastic model formulation from several different approaches [Bridson et al 2003;Grinspun et al 2003;Müller and Gross 2004;Wang et al 2011] and used different algorithms for collision handling. There has been a rich body of research on contact and collision for cloth simulation [Bridson et al 2002;Baraff et al 2003;Harmon et al 2008;Kaufman et al 2008;Otaduy et al 2009;Harmon et al 2009;Tang et al 2010;Miguel and Otaduy 2011;Ainsley et al 2012]. The core algorithm for collision handling in ARCSim is based on Bridson et al [Bridson et al 2002], who uses a geometry-based repulsive impulse to handle collision robustly.…”