Rigidity, Flexibility, Stress and Motion: Foundations of Reconfiguration Problems in Computational Geometry

刚性、柔性、应力和运动：计算几何中重构问题的基础

• 批准号: 0728783
• 负责人: Ileana Streinu
• 金额: $ 20万
• 依托单位: Smith College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0728783&HistoricalAwards=false
• 关键词: Rigidity; Flexibility; Stress; Motion; Foundations

Reconfiguration problems underlie modern mathematical investigations in robotics, mechanical design, structural engineering, and bio-geometry, and have the potential of impacting computational biology, especially the problems emerging from modeling protein folding or, more generally, protein flexibility and motion.This research is focused on fundamental mathematical properties and algorithms for reconfiguration problems (in particular, motion planning) of linkages and other flexible structures made from rigid parts connected together with various types of joints and hinges. The research builds upon the principal investigator's previous work on 2-dimensional robot arm reconfiguration (the Carpenter's Rule problem and pointed pseudo-triangulations), as well as on her current work in Combinatorial Rigidity (generalizations of Pebble Game algorithms for 2-dimensional-rigidity to other classes of sparse graphs, computation of rigid and stressed clusters) and Motion generation (for pseudo-triangulations in the plane, and for molecular structures with many loops in 3-dimensions). The goal of this research is furthering the general understanding of a notorious 140-old open problem in the Combinatorial Rigidity of bar-and-joint frameworks, expansive motions and pseudo-triangulations in 3-dimensions, as well as motion and reconfiguration for other 3d-structures (linkages, panel-and-hinge and polyhedral structures). These problems transcend application domains, but they are motivated by and may lead to developing models and techniques for addressing questions that arise in other areas of science and engineering.

重新配置问题是机器人技术，机械设计，结构工程和生物几何的现代数学研究的基础，并且具有影响计算生物学的潜力，尤其是从建模蛋白质折叠中出现的问题，或者更普遍地，蛋白质柔韧性和运动均集中在蛋白质折叠。由刚性零件与各种类型的关节和铰链连接在一起。这项研究基于主要研究者先前关于二维机器人臂重新配置（木匠的规则问题和尖锐的伪三角形）的工作，以及她当前在组合刚性方面的工作平面中的伪三角剖分，对于三维中许多环的分子结构）。这项研究的目的是进一步了解臭名昭著的140岁的开放问题，这是在3次降低中的酒吧和关节框架，宽泛的动议和伪三角仪的组合刚性中，以及其他3D结构的运动和重新配置（其他3D结构（链接，面板和面板挂钩和多面体结构））。这些问题超越了应用程序领域，但它们是受到动机的动机，并可能导致开发模型和技术来解决在科学和工程其他领域中出现的问题。