REU: CAREER: Motion Strategy Algorithms for Geometry-Intensive Applications

该奖项支持一个以几何密集型应用中的计算运动策略为中心的综合研究和教育计划。通过平衡核心问题和专门应用之间的努力，将取得健康的协同效应。该研究计划的核心是机器人运动规划，它建立在一个更广泛的统一数学框架上，该框架结合了最优控制理论、计算几何、统计决策理论和动态博弈论的概念。这导致了对三个核心算法问题的研究：1)搜索具有代数和微分约束的高维空间，2)响应不可预测的变化和在线信息，3)求解基于传感器的任务和处理不完全信息。与传统的路径规划相比，重点要广泛得多。核心研究是由几个应用领域的努力指导的，例如具有主动传感功能的移动机器人、虚拟原型-危险环境。这些研究工作被纳入一项教育计划：1)建立一个跨学科的研究生小组，他们在教育和研究过程中得到仔细的指导；ii)介绍本科生从事研究，特别是通过移动机器人和图形模拟项目；iii)采取步骤，开设几何算法的跨学科课程；以及iv)帮助那些处于不利背景的人实现他们的潜力并在他们的职业生涯中脱颖而出。

This award supports an integrated research and education program that is centered on computing motion strategies in geometry-intensive applications. A healthy synergy will be obtained by balancing efforts between both core issues and specialized applications. The core of this research program is rooted in robot motion planning, and it is built on a broader unified mathematical framework that incorporates concepts from optimal control theory, computational geometry, statistical decision theory, and dynamic game theory. This leads to the proposed investigation of three core algorithmic issues: 1) searching high-dimensional spaces that have algebraic and differential constraints, 2)responding to unpredictable changes and on-line information, and 3) solving sensor-based tasks and processing incomplete information. The focus is significantly broader than traditional path planning. The core research is guided by efforts in several applications, such as mobile robotics with active sensing, virtual prototyping-hazardous environments. These research efforts are incorporated into an education plan that: 1)builds an interdisciplinary group of graduate students who are carefully guided through the education and research process, ii) introduces undergraduates to research, particularly through mobile robotics and graphical simulation projects, iii) takes steps towards an interdisiplinary curriculum in geometric algorithms, and iv) helps those from disadvantaged backgrounds to realize their potential and excel in their careers.