The central problem of robotics is the analysis and replication of patterns of movement required to accomplish useful tasks. Physicists have found that deeper examination of the physical world often reveals inadequacies in the vocabulary and mathematics used to describe it; in much the same way, roboticists have found it quite awkward to give precise, succinct descriptions of effective movements using the syntax and semantics in common use. What is needed to produce general purpose robots is a more expressive means for discussing movement. This volume focuses on some of the ways that mathematics can be used to address problems in this area.

Focusing on some of the important mathematical questions arising in the field of robotics, this book conveys a sense for the effectiveness of mathematics in capturing the essence of robotics problems. In addition, the book will make readers aware of the way in which computer control interacts with geometry. The first four papers deal with kinematics and control, relying on realistic models for kinematic processes. The last two papers have more of the flavor of computer science and are concerned with the symbolic descriptions of motion, including the treatment of uncertainty.

The book is directed toward mathematically literate readers interested in finding out about the questions that arise in robotics and how mathematics can help answer them. A mathematical background at the level of an undergraduate degree in mathematics and some knowledge of basic mechanics is assumed.