Computational and Algorithmic Representations of Geonetric Objects - CARGO: Folding and Unfolding Processes for Polygonal Linkages, with Applications to Robotics and Biology

几何对象的计算和算法表示 - CARGO：多边形链接的折叠和展开过程，及其在机器人和生物学中的应用

• 批准号: 0138374
• 负责人: Ileana Streinu
• 金额: $ 10万
• 依托单位: Smith College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0138374&HistoricalAwards=false
• 关键词: Computational; Algorithmic; Representations; Geonetric; Objects

Abstract for DMS - 0138374This incubation project plans to start an interdisciplinary collaborationwhose goal is the understanding of folding and unfolding processes forpolygonal linkages and other related structures.We plan to investigate the topology and the algebraic-geometric structureof configuration spaces of two- and three-dimensional serial linkages, viageneralizations of recent successful rigidity-theoretic approaches basedon pseudo-triangulation mechanisms, and to advance the understanding ofthe global structure of the associated configuration spaces. Therigidity-theoretic techniques have allowed the definition of 2-d motionsthat are purely expansive or contractive: the former can guarantee that achain will not self-collide. We plan to extend these techniques to threedimensions and subsequently develop efficient data structures andalgorithms for planning, analyzing, approximating, tracking and queryingsuch motions.We expect that folding problems, beyond their intrinsic mathematicalinterest, will lead to techniques that will impact areas such as molecularbiology, where the protein folding problem is of central significance, aswell as robotics and micromechanics, where modular kinematic mechanisms(with possibly large numbers of links) are often employed. The commondenominator of these endeavors, and our main theme, is the generalquestion of planning and reasoning about collision free motions for seriallinkages of various kinds.

这个孵化项目计划启动一个跨学科的合作，其目标是了解多边形连杆和其他相关结构的折叠和展开过程。我们计划研究二维和三维串联机构构型空间的拓扑结构和代数几何结构，通过对最近成功的基于伪三角化机构的刚度理论方法的推广，并推进对相关构型空间整体结构的理解。他们的刚性理论技术允许定义纯膨胀或收缩的二维运动：前者可以保证链不会自碰撞。我们计划将这些技术扩展到三维，并随后开发有效的数据结构和算法，用于规划，分析，近似，跟踪和查询这些运动。我们期望折叠问题，超越其固有的数学兴趣，将导致技术将影响诸如分子生物学等领域，其中蛋白质折叠问题具有核心意义，以及机器人和微力学，其中模块化运动机制（可能有大量链接）经常被采用。这些努力的共同点，以及我们的主题，是关于各种类型的串行连接的无碰撞运动的规划和推理的一般问题。