Fully-Implicit Time Stepping Methods with Integrated Proximity Queries for Accurate Simulation of Multi-Rigid-Body Systems with Intermittent Contact

为了自动规划涉及物体之间接触的任务，物体运动的准确预测是必不可少的。应用包括协作式人机操作、工业自动化、工程设计和计算机游戏的物理引擎。接触和粘滑行为的间歇性给稳定、准确地模拟多体系统带来了困难。商业上可用的多体模拟软件即使是简单的有接触的系统也很难模拟。因此，用户必须通过反复试验来找到能够产生可信但不一定准确的结果的模拟参数。本研究项目中开发的算法将改进未来版本的仿真产品，如ADAMS和Working Model。多体仿真中稳定性和精度问题的主要来源是光滑物体的多面体表示、碰撞检测与动态时间步进子问题求解的解耦、库仑摩擦模型的线性化以及模型参数的误差。为了消除前三个误差源，本研究着重于时间步进器的公式、算法开发和分析。其结果将是一种完全隐式的、稳定的、准确的、优化的方法来模拟经历间歇接触的刚性对象的系统；对象将使用隐式和参数曲面表示来建模。以前还没有开发出以完全隐式的方式组合动力学和几何约束的通用方法。通过使用新的时间步进器作为“地面真理”模型，可以比较所有以前的模型，从而第一次可以量化最常见的近似的误差影响。这项研究将包括研究生和本科生。结果将被纳入我们的模拟包中，并在RPI的机器人课程中介绍。推广活动包括为中学生举办的夏季乐高机器人活动。

To automatically plan tasks involving contact between objects, accurate prediction of object motions is essential. Applications include collaborative human-robot manipulation, industrial automation, engineering design, and physics engines for computer games. The intermittency of contact and stick-slip behavior make it difficult to simulate multibody systems stably and accurately. Commercially available multibody simulation software has difficulty simulating even simple systems with contacts. As a result, users must resort to trial-and-error to find simulation parameters that yield believable, not necessarily accurate, results. The algorithms developed in this research project will lead to improved future versions of simulation products such as Adams and Working Model.The primary sources of stability and accuracy problems in multibody simulation are polyhedral representations of smooth objects, decoupling of collision detection from the solution of the dynamic time-stepping subproblem, linearization of Coulomb friction model, and errors in model parameters. This research focuses on formulations, algorithm development and analysis of time-steppers to eliminate the first three error sources. The result will be a fully-implicit, stable, accurate, optimization approach to simulating systems of rigid objects undergoing intermittent contact; the objects will be modeled using implicit and parametric surface representations. No previous general method has been developed that combines dynamics and geometric constraints in a fully-implicit manner. By using the new time-stepper as a ``ground truth" model, all previous models can be compared, so that for the first time, the error effects of the most common approximations can be quantified. This research will involve graduate and undergraduate students. The results will be incorporated into our simulation package and introduced in the robotics courses at RPI.Outreach activities include summer Lego robotics activities for middle school students.