CAREER: Finding and using global structure in state-space planning problems

该职业奖将支持机器人和其他机械系统运动策略设计算法的研究。应用包括移动机器人控制，药物设计的蛋白质结构分析，以及为自动化制造设计更可靠的工具。有许多基本的未解决问题。给定要节省的资源，例如时间、能源、精度或传感机会，两种配置之间的最佳轨迹是什么？对于难以自动生成可行构型的高约束机械系统，应该如何规划运动？机械装置是否可以被设计成使所有的运动都可靠地导向目标，尽管在传感和控制上有错误？这些挑战跨越了运动问题的几个方面，但有一个潜在的主题。由于对最优性的要求、机构的运动学或摩擦接触力学的约束，在系统可能配置的空间上施加了一个全局结构。通常，构型空间可以被描述为相对均匀区域的集合，由系统行为变化的明显边界分隔。基本目标是使用任何最合适的分析技术（包括Pontryagin的最大值原理、Morse理论和数学规划工具）提取关于组态空间结构的尽可能多的信息。一旦确定了这种结构，下一步就是找到表示空间的方法，并自动对其进行推理。该研究计划将由机器人和几何推理算法方面的强大课程的发展来补充。该奖项将支持一个由研究生研究人员组成的小团队，开发一个核心小组，为本科生和研究生的机器人研究做准备，并为K-12学生举办一个夏季机器人训练营。

This CAREER award will support research in algorithms to design motion strategies for robots and other mechanical systems. Applications include mobile-robot control, analysis of protein structure for drug design, and design of more reliable tools for automated manufacturing. There are a number of fundamental open problems. Given a resource to conserve, such as time, energy, precision, or opportunities for sensing, what is the optimal trajectory between two configurations? How should motions be planned for highly-constrained mechanical systems, for which it is difficult to automatically generate feasible configurations? Can mechanical devices be designed so that all motions lead reliably to the goal, in spite of errors in sensing and control?These challenges span several facets of the motion problem, but there is an underlying theme. Constraints due to the requirement for optimality, kinematics of the mechanism, or frictional contact mechanics impose a global structure on the space of possible configurations of the system. Often, the configuration space can be described as a collection of relatively homogeneous regions, separated by sharp boundaries at which the behavior of the system changes. The basic goal is to extract as much information as possible about the structure of the configuration space using whatever analytical techniques are most appropriate, including Pontryagin's Maximum Principle, Morse Theory, and tools from mathematical programming. Once this structure has been determined, the next step is to find ways to represent the space and reason about it automatically. The research program will be complemented by the development of a strong curriculum in robotics and geometric-reasoning algorithms. The award will support a small team of graduate student researchers, the development of a core group of classes to prepare undergraduate and graduate students for robotics research, and a summer robotics camp for K-12 students.