ABSTRACT:  We present a new discrete velocity-level formulation of frictional contact dynamics that reduces to a pair of coupled projections and introduce a simple fixed-point property of this coupled system. This allows us to construct a novel algorithm for accurate frictional contact resolution based on a simple staggered sequence of projections. The algorithm accelerates performance using warm starts to leverage the potentially high temporal coherence between contact states and provides users with direct control over frictional accuracy. Applying this algorithm to rigid and deformable systems, we obtain robust and accurate simulations of frictional contact behavior not previously possible, at rates suitable for interactive haptic simulations, as well as large-scale animations. By construction, the proposed algorithm guarantees exact, velocity-level contact constraint enforcement and obtains long-term stable and robust integration. Examples are given to illustrate the performance, plausibility and accuracy of the obtained solutions.

Project Page

ABSTRACT:  Algorithms for rigid body dynamics with contact are well known, but challenging to implement due to the interplay between large time steps, general purpose collision detection packages and pragmatic approximations of the underlying inequality constrained contact problems. While research on rigid body simulation has focused heavily both on contact resolution and collision detection, contact generation has largely been ignored. Most contact resolution algorithms presume that an ideal set of contacts, fully characterizing system constraints, are available, while collision detection methods generally presume that their task is finished once a set of intersecting primitives has been identified. Bridging the gap between these domains, by generating representative contact samples, contact point locations and their associated normals, is crucial for the accuracy, robustness and speed of simulation. We address these issues by developing an adaptive contact generation approach that tightly integrates hierarchical collision detection with the generation of well sampled contact constraints.

Technical Sketch

ABSTRACT:  Motivated by applications in rigid body contact simulation we develop a numerically robust, randomized Quadratic Programming algorithm. We show that the resulting solver remains robust under highly constrained and redundant conditions, while also detecting infeasibility conditions. Its expected complexity is linear in the number constraints imposed and our experiments show that it performs well in practice for low-dimensional examples.

Technical Report

ABSTRACT:  We describe an efficient algorithm for the simulation of large sets of non-convex rigid bodies. The algorithm finds a simultaneous solution for a multi-body system that is linear in the total number of contacts detected in each iteration. We employ a novel contact model that uses mass, location, and velocity information from all contacts, at the moment of maximum compression, to constrain rigid body velocities. We also develop a new friction model in the configuration space of rigid bodies. These models are used to compute the feasible velocity and the frictional response of each body. Implementation is simple and leads to a fast rigid body simulator that computes steps on the order of seconds for simulations involving over one thousand non-convex objects in high contact configurations.

Project Page

ABSTRACT:  We examine the interaction of complex two-dimensional rigid bodies with friction. Given their idealized description, many different feasible solutions for frictional contact and collision are possible. The usual assumptions of noninterpenetration and negligible deformation at the global scale constrain contact behaviors, while incomplete descriptions of material properties at the local scale allow for a large amount of latitude in solution methods. We propose a method that generalizes Moreau’s impact law to formulate a simple but complete contact law in which both multiple constraints and multiple contacts are possible. 

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