A Review of Topological Perspectives in Robotic Manipulation

Topology is an important area of study in mathematics, which is mainly concerned with qualitative properties of objects or spaces. It is broad and well developed. Current research interests are to explore the possibilities to integrate topological perspectives in various practical engineering problems. Robotics contains many challenging tasks and provides an ideal playground for topological tools. In this thesis, we select several topics of interdisciplinary research from topology and robotic manipulation and summarize some interesting topological insights and approaches. In the introductory chapter, several selected aspects of topological perspectives in robotics are briefly reviewed. In the second chapter, we give a detailed account of widely used topological modeling methods that are used for robotic manipulation, revealing the common ground to involve topology. In the third chapter, topological considerations about configuration spaces and topological reasoning on the problems such as finding a global inverse kinematic solution or dealing with singularities are presented. In the fourth chapter, we concentrate on topological properties of kinematic maps of redundant manipulators and discuss methods that potentially enable an efficient exploration of redundancy resolution. Finally, we mention some open problems for future research.