Representation and planning for complex physical tasks involving spatial relationships are key challenges facing the robotics community. This project proposes to develop new theoretical and algorithmic approaches to important cases of these challenges. The researchers will apply a new, general geometric and topological approach to the study of system parameterization, constraint formulation, and configuration space structures of linkage systems. They will also develop and perform benchmark evaluations of motion planning algorithms. While this project focuses on manipulation systems and knots, the addressed issues and developed techniques will be applicable to a wide range of linkages including both physical linkages (such as articulated robots or protein molecules) and virtual linkages (such as groups of points or swarms of mini-robots) under various kinds of geometric constraints. The project will also contribute to the development of human infrastructure in science and technology, by allowing the researchers to continue and expand their successful training and involvement of undergraduate students in mathematical and algorithmic aspects of robotics research.
