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

该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推进逼真机器人仿真的最新技术，这些模型既可靠又有效地可解。自牛顿和莱布尼茨时代以来，刚体动力学的建模一直是一个巨大的成功故事。然而，当刚体接触时，当这种接触包括库仑摩擦时，标准的力-加速度模型有时会失效。在这种情况下，平滑的解决方案在理论上甚至是不可能的。根据公认的sigorini - fichera （S-F）互补条件，开发了一套解决这一问题的接触模型。然而，有一些证据表明，这些条件是不准确的冲击（而不是顺利接触）刚体。该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三个关键缺陷，这些缺陷在最先进的接触模型中不同程度地存在：(i)它们的指数最坏情况解决时间；（ii）即使存在解决方案，他们也无法找到解决方案；（iii）其数值脆性。这个项目将调查和评价新的接触模式，这些模式由于消除了互补性条件，可能不会有这些缺点；同时，该项目将使用弹性动力学有限元分析和物理实验来评估撞击刚体的模型精度。该项目将影响广泛的技术领域，包括航空航天、制造业和土木工程。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Moby dynamics库公开。此外，通过对学生的指导，拓宽了STEM的参与范围。

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.