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

这个职业奖将支持算法的研究，为机器人和其他机械系统设计运动策略。 其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自动化制造的更可靠工具的设计。 有一些基本的未决问题。 给定一个需要保存的资源，如时间、能量、精度或感知机会，两种配置之间的最佳轨迹是什么？ 如何规划运动高度约束的机械系统，这是很难自动生成可行的配置？ 机械装置能否被设计成使所有的运动都可靠地导向目标，而不管传感和控制方面的误差？这些挑战跨越了运动问题的几个方面，但有一个基本的主题。 由于对最优性、机构的运动学或摩擦接触力学的要求而产生的约束在系统的可能配置的空间上强加了全局结构。 通常，配置空间可以被描述为相对均匀的区域的集合，由系统行为改变的尖锐边界分开。 基本目标是使用任何最合适的分析技术，包括庞特里亚金最大值原理、莫尔斯理论和数学规划工具，提取尽可能多的关于位形空间结构的信息。 一旦确定了这个结构，下一步就是找到自动表示空间和推理的方法。 该研究计划将通过开发机器人和几何推理算法的强大课程来补充。 该奖项将支持一个研究生研究小组，开发一个核心课程组，为本科生和研究生进行机器人研究做好准备，并为K-12学生举办机器人夏令营。

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.