Collaborative Research: Ergodic Trajectories in Discrete Mechanics

协作研究：离散力学中的遍历轨迹

• 批准号: 1334609
• 负责人: Todd Murphey
• 金额: $ 23.5万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1334609&HistoricalAwards=false
• 关键词: Collaborative; Research; Ergodic; Trajectories; Discrete

The objective of this research project is to develop efficient and robust numerical methods for searching and exploring an environment using a mechanical system, while ensuring that the average temporal coverage reproduces a prescribed spatial distribution. This is achieved by developing methods for controlling mechanical systems so that they are ergodic with respect to the given spatial distribution, and combining them with geometric structure-preserving numerical integrators which have good backward error properties, and preserve geometric invariants like the symplectic structure, energy, and momentum. Furthermore, these methods preserve the nonlinear structure of the configuration manifold, such as the Lie group or homogeneous space structure. The key technical goals include: (i) the development and analysis of structured integrators to accurately predict ergodic properties of a given system; (ii) the development of simulation-based optimization of system parameters, and controls to maximize efficiency of ergodic search; (iii) the generalization of these techniques to Lie groups and homogeneous spaces, enabling ergodic search for a rich class of robotic systems; (iv) experimental validation on realistic systems.These techniques will directly be applicable to a broad range of real-world industrial applications, including joint space exploration for robotic systems, fault detection in manufacturing, and optimal search, coverage, and information extraction for autonomous sensor networks. This industrial outreach will be facilitated by the release of public-domain software that will lower the barrier to adapting geometric numerical integration techniques in a variety of applications. Furthermore, we will engage in public outreach activities by teaming up with the Museum of Science and Industry in Chicago to develop an interactive exhibit demonstrating search algorithms for mechanical systems. These concrete applications serve to inspire high-school students (in particular, underrepresented minorities and women) to pursue STEM degrees, and this in turn will help to secure the long-term economic innovation and competitiveness of American industry.

该研究项目的目的是开发使用机械系统搜索和探索环境的有效且鲁棒的数值方法，同时确保平均时间覆盖范围再现了规定的空间分布。这是通过开发用于控制机械系统的方法来实现的，使它们相对于给定的空间分布具有崇高，并将它们与具有良好向后误差属性的几何结构的数值积分器相结合，并保留几何不变性，例如符号结构，能量，能量和动量。此外，这些方法保留了构型歧管的非线性结构，例如谎言组或均匀的空间结构。关键技术目标包括：（i）结构化集成剂的开发和分析，以准确预测给定系统的千古特性； （ii）开发基于模拟的系统参数的优化，以及最大程度地提高ergodic搜索效率的控制； （iii）将这些技术概括为谎言组和均匀空间，从而使人们能够搜索丰富的机器人系统； （iv）对现实系统的实验验证。这些技术将直接适用于广泛的现实世界应用，包括用于机器人系统的联合空间勘探，制造业中的故障检测以及自治传感器网络的最佳搜索，覆盖范围和信息提取。公共域软件的发布将促进这种工业外展，该软件将降低在各种应用中适应几何数值集成技术的障碍。此外，我们将通过与芝加哥科学和工业博物馆合作开发互动展览，展示机械系统的搜索算法，从事公共宣传活动。这些具体的应用有助于激发高中生（尤其是代表性不足的少数民族和妇女）来攻读STEM学位，这反过来又有助于确保美国工业的长期经济创新和竞争力。