A Computational Framework for Multi-Rigid-Body Dynamics with Contact and Friction

这项研究调查了创建多刚体模拟环境的基本挑战，这些环境对于一大类配置和交互具有健壮和逼真的行为。这一建议特别针对的问题是，由于结果模型显然缺乏解，当涉及库仑摩擦时，很难一致地建立和有效地求解约束牛顿力学定律。部分由作者发展的最新结果表明，在脉冲-速度互补公式中，可以采用定义明确的数值方法。建议的研究满足了将摩擦模型研究的最新发展与先进的数值积分和优化技术相结合的需要。互补性公式将在该项目中发挥核心作用，但也将探索替代方法。开发的算法将适应在互补环境中很少处理的数值问题，如刚度和约束漂移控制。一些专门的优化方法将被设计来解决约束模拟中出现的特殊问题，如接触退化时的约束稳定。这项研究将克服所有研究领域的基本困难，这些领域依赖于正确模拟接触摩擦的物体的运动，如机器人、虚拟现实、生物力学、制造设计。在所有这些领域，与摩擦的接触都是一个基本的组成部分，无论是与用户在虚拟现实中推动或拉出一堆相互摩擦接触的虚拟物体有关，还是与机器人抓取和操纵负载有关，还是与正确模拟人类行走有关，在那里需要摩擦以防止滑动。然而，尽管接触和摩擦在日常生活中无处不在，但事实证明，它的模拟非常困难，部分原因是缺乏一致和有效的理论和计算框架。这项提议的目的是将摩擦接触建模的最新成果向满足高质量、高性能多刚体动力学仿真的方向发展，用于机器人、虚拟现实、制造设计和其他领域。这将使软件开发成为未来制造基础设施的重要组成部分。

This research investigates fundamental challenges in creatingmulti-rigid-body simulation environments that have a robust andrealistic behavior for a large class of configurations andinteractions. The problem specifically targeted by this proposal isthe difficulty, due to the apparent lack of solutions of the resultingmodel, in consistently formulating and efficiently solving theconstrained Newton laws of mechanics when Coulomb friction isinvolved. Recent results, partly developed by the author have shownthat a well-defined numerical approach is possible in animpulse-velocity complementarity formulation. The proposed researchaddresses the need to integrate recent developments in the study ofmodels of friction with advanced numerical integration andoptimization techniques. The complementarity formulation will play acentral part in this project but alternative methods will also beexplored. The algorithms developed will accommodate numerical issuesrarely approached in a complementarity setting such as stiffness andconstraint drift control. Several specialized optimization methodswill be designed to address distinguished problems that appear in aconstrained simulation, such as constraint stabilization in presenceof contact degeneracy.This research will overcome essential difficulties in all areas ofinvestigation that depend on the correct simulation of the motion ofobjects in contact with friction such as robotics, virtual reality,biomechanics, manufacturing design. In all these areas, contact withfriction is a fundamental component, whether it is related to the userpushing or pulling a stack of virtual objects in frictional contactwith one another in virtual reality, to a robot grasping andmanipulating a load, or to the correct simulation of human walkingwhere friction is necessary to prevent slipping. Yet in spite of theomni presence of contact and friction in everyday life its simulationhas proved to be very difficult, partly because of the lack of aconsistent and efficient theoretical and computational framework. Itis the aim of this proposal to extend the recent results in frictionalcontact modeling in directions that will answer the requirements ofhigh-quality, high-performance multi-rigid-body dynamics simulation for use in robotics, virtual reality, manufacturing design and other fields.This will enable the development of software that will become an important component of the manufacturing infrastructure of the future.