A constraint‐stabilized time‐stepping approach for rigid multibody dynamics with joints, contact and friction

Abstract

We present a method for achieving geometrical constraint stabilization for a linear‐complementarity‐based time‐stepping scheme for rigid multibody dynamics with joints, contact, and friction. The method requires the solution of only one linear complementarity problem per step. We prove that the velocity stays bounded and that the constraint infeasibility is uniformly bounded in terms of the size of the time step and the current value of the velocity. Several examples, including one for joint‐only systems, are used to demonstrate the constraint stabilization effect. Copyright © 2004 John Wiley & Sons, Ltd.

A matrix-free cone complementarity approach for solving large-scale, nonsmooth, rigid body dynamics

“…Note, however, that, for bodies with generic shapes, finding a proper set of contact points (and defining their Φ i distance functions) is not always trivial [3,4]. In fact, there could be multiple contact points, or it could even happen that defining a differentiable signed distance function is not possible, as in the case of concave shapes [3].…”

“…Nevertheless, since we are interested in enforcing non-penetration, what truly matters is that a signed distance function be defined up to some value of the penetration [4]. We thus assume that Φ(q, Ω) can be differentiably defined at least on a neighborhood of the set Φ(q, Ω) ≥ 0.…”

GPU-Based Parallel Computing for the Simulation of Complex Multibody Systems with Unilateral and Bilateral Constraints: An Overview

“…The 1 h © i (q (l) ) term is introduced to ensure contact stabilization, and its effect is discussed in [3]. Similarly, the term 1 h ª i (q (l) ) achieves stabilization for bilateral constraints.…”

“…The solution of the modified time stepping scheme approaches the solution of the original differential inclusion for h ! 0 just as the original scheme [3]. Most importantly, the modified scheme becomes a Cone Complementarity Problem (CCP), which can be solved efficiently by an iterative numerical method that relies on projected contractive maps.…”

“…In terms of the former, sequential computing appears to lose momentum at a time when the microprocessor industry ushers in commodity many-core hardware. In terms of internal factors, contributions made in understanding and handling frictional contact [1][2][3][4][5][6][7][8][9][10][11], have led to robust numerical algorithms that can tackle sizeable granular dynamics problems. This paper discusses how the interplay of these two factors will enable in the near future a discrete approach to investigating the dynamics of systems with hundreds of millions of rigid bodies.…”