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

本研究探讨了创建多刚体仿真环境的基本挑战，这些环境对大量配置和相互作用具有鲁棒性和逼真性。这个建议特别针对的问题是，由于所得到的模型明显缺乏解，当涉及库仑摩擦时，难以一致地表述和有效地求解受约束的牛顿力学定律。最近的结果（部分由作者开发）表明，在脉冲速度互补公式中，可以有一个定义良好的数值方法。提出的研究解决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。互补性配方将在这个项目中发挥核心作用，但也将探索替代方法。所开发的算法将适应很少在互补设置中接近的数值问题，如刚度和约束漂移控制。将设计几个专门的优化方法来解决约束仿真中出现的突出问题，例如存在接触退化的约束稳定。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与摩擦接触的物体的运动，如机器人、虚拟现实、生物力学、制造设计。在所有这些领域中，摩擦接触是一个基本组成部分，无论是与用户在虚拟现实中推或拉一堆虚拟物体相互摩擦接触有关，还是与机器人抓取和操纵负载有关，或者与人类行走的正确模拟有关，其中摩擦是防止滑动所必需的。然而，尽管接触和摩擦在日常生活中无处不在，但其模拟已被证明是非常困难的，部分原因是缺乏一致和有效的理论和计算框架。本提案的目的是扩展摩擦接触建模的最新成果，以满足机器人，虚拟现实，制造设计和其他领域中使用的高质量，高性能多刚体动力学仿真的要求。这将使软件的开发成为未来制造业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.