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

该职业奖将支持为机器人和其他机械系统设计运动策略的算法研究。应用包括移动机器人控制，用于药物设计的蛋白质结构分析，以及设计更可靠的自动化制造工具。有许多根本性的公开问题。在给定需要节约的资源(例如时间、能量、精度或感知机会)的情况下，两种配置之间的最佳轨迹是什么？对于很难自动生成可行配置的高度受限的机械系统，应该如何规划运动？机械设备的设计是否能让所有运动都可靠地通向目标，尽管存在传感和控制方面的错误？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。由于机构的最优性、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构型的空间上施加了全局结构。通常，配置空间可以被描述为相对同质的区域的集合，这些区域由系统行为发生变化的尖锐边界分隔。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，尽可能多地提取关于配置空间结构的信息。一旦确定了这种结构，下一步就是找到自动表示空间和推理的方法。这项研究计划将由开发一门强大的机器人学和几何推理算法课程来补充。该奖项将支持一小批研究生研究人员，开发一组核心课程，为本科生和研究生进行机器人研究做准备，以及为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.