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

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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.