Discovery of Dynamic Mechanical Structures through Modeling and Analysis of Closed Chains using Homotopy-Based Optimization

该项目通过加速腿式机器人技术的创新，促进了科学的进步，促进了国家的繁荣和福利。在过去的几年里，有腿机器人的使用和能力随着工业/建筑环境的应用而增加，最近，在医疗场所对病人进行分类。机器人肢体可以组合成封闭链结构，在速度、力和刚度方面具有潜在的变革性优势。然而，由于封闭链结构运动建模和分析的计算复杂性，这些优点迄今尚未充分实现。这项拨款支持基础研究，以提出、开发和展示一类新的优化技术，这些技术可以处理这些复杂性。新技术将结合同伦寻根程序，目的是解决比当前最先进的系统大许多数量级的问题。这项研究涉及将有腿机器人的工程与新的数学技术相结合。这种多学科的方法将以独特的跨学科教育经验对工程教育产生积极影响，并有助于扩大代表性不足群体的参与。由闭链机构组成的机器人肢体在探索其定义的运动参数变化时发生的退化阻碍了建模。这些退化包括工作空间崩溃、锁定配置、零链接长度和移动性的变化。它们的存在阻碍了分析导致有用的动态行为的运动学参数模式的努力。为了克服这些挑战，优化技术被用于发现有用的机制。特别是，本项目将开发利用数值同伦延拓算法的新的优化技术。由此产生的技术旨在以有效和协调的方式收集几乎完整的最小集合，以提供全局最小值，以及通过探索运动学参数变化提供的有用结构的调查。研究小组计划开发优化算法，并将其应用于相关的机器人肢体问题。建模和分析技术将通过仿真、原型和测试进行验证。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project promotes the progress of science and advances national prosperity and welfare, by accelerating innovation in legged robotics. The usage and capability of legged robots has increased over the past years with applications in industrial/construction settings and, more recently, to triage patients at healthcare sites. Robotic limbs can be composed to incorporate closed chain structures with potentially transformative benefits on their speed, force, and stiffness capabilities. However, these benefits have so far not been fully realized due to the computational complexity involved with the modeling and analysis of the motions of closed chain structures. This grant supports foundational research to propose, develop, and demonstrate a new class of optimization techniques that are equipped to deal with these complexities. The new techniques will incorporate homotopy root finding routines with the aim of solving systems many orders of magnitude larger than the current state-of-the-art. This research involves blending the engineering of legged robots with new mathematical techniques. This multi-disciplinary approach will positively impact engineering education with a unique interdisciplinary educational experience and will help broaden participation of underrepresented groups. The modeling of robotic limbs composed of closed chain mechanisms is hindered by degeneracies that occur when exploring variations in their defining kinematic parameters. These degeneracies include workspace break-downs, locked configurations, zero link lengths, and changes in mobility. Their existence thwarts efforts to analyze patterns of kinematic parameters that lead to useful dynamic behaviors. To overcome these challenges, techniques in optimization are used to discover useful mechanisms. In particular, this project will develop new optimization techniques that leverage the algorithms of numerical homotopy continuation. The resulting techniques aim to gather nearly complete sets of minima in an efficient and coordinated manner to provide both a global minimum, as well as a survey of useful structures provided by exploring kinematic parameter variations. The research team plans to develop the optimization algorithms and apply them to relevant robot limb problems. The modeling and analysis techniques will be verified through simulation, prototyping, and testing.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.