Collaborative Research: A Complementarity-Free Contact Model for Robotics Applications

这一合作研究项目的主要目标是通过开发合理准确的刚体动力学接触模型来提高现实机器人模拟的技术水平，这些模型既健壮又高效地可解。自牛顿和莱布尼茨时代以来，刚体动力学建模取得了巨大的成功。然而，当刚体接触时，当接触包括库仑摩擦时，标准力-加速度模型有时会失效。在这种情况下，理论上甚至不可能有一个平稳的解决方案。从著名的斯诺里尼-菲切拉(S-F)互补条件出发，发展了一套解决这个问题的接触模型。但是，有一些证据表明，这些条件对于碰撞(而不是平滑接触)刚体来说并不准确。这个项目将调查互补性条件受到质疑的情况，并将开发一种新的方法来解决在现有接触模型中存在的不同程度的三个关键缺陷：(I)他们的指数最坏情况解决时间；(Ii)即使有解决办法，也无法找到解决办法；(3)它们在数量上的脆弱性。该项目将调查和评估新的接触模型，这些模型由于消除了互补性条件，可能不会受到这些缺点的影响；同时，该项目将使用弹性动力有限元分析和物理实验来评估撞击刚体的模型精度。该项目将影响包括航空航天、制造和土木工程在内的广泛技术。在短期内，该项目将能够模拟复杂的机器人环境，帮助机器人专家微调机械设计和控制算法。开发的计算模型将通过开源的莫比动态库公开。此外，通过辅导学生，扩大了对STEM的参与。

The main goal in this collaborative research project is to advance the state of the art in realistic robot simulation by developing reasonably accurate contact models for rigid body dynamics that are both robustly and efficiently solvable. Since the times of Newton and Leibniz, the modeling of rigid body dynamics has been a tremendous success story. However, when rigid bodies come into contact and when that contact includes Coulomb friction, standard force-acceleration models sometimes fail. In such cases, a smooth solution is theoretically not even possible. A set of contact models that address this problem has been developed, derived from the well-established Signorini-Fichera (S-F) complementarity conditions. However, there is some evidence that these conditions are not accurate for impacting (rather than smoothly contacting) rigid bodies. This project will investigate situations in which the complementarity conditions are called into question, and will develop a new approach to address three critical shortcomings, present in varying degrees in state of the art contact models: (i.) their exponential worst-case solution times; (ii.) their inability to find solutions even though one exists; (iii.) their numerical brittleness. This project will investigate and evaluate new contact models that, by virtue of eliminating complementarity conditions, may not suffer from these shortcomings; in tandem, the project will use elastodynamic finite element analysis and physical experimentation in order to evaluate model accuracy for impacting rigid bodies.This project will impact a broad range of technologies, including aerospace, manufacturing, and civil engineering. In the near term, the project will enable the simulation of complex robot environments that help roboticists fine-tune both mechanical design and control algorithms. The computational models developed will be made public via the open-source Moby dynamics library. Additionally, participation in STEM is broadened through mentoring of students.