Invitation to Topological Robotics
Topological robotics is a new mathematical field inspired by recent problems in robotics - for instance the problem of the number of solutions of certain problems, obstacle avoidance and singularity free regions. The quality of a solution of such a problem depends on the topological structure of the configuration space of the considered mechanism. In this book, sophisticated topological methods are used to study topological properties of configuration spaces of planar linkages. The author presents some very interesting results about connections between linkages and their configuration spaces. To illustrate the nature of such results let us cite one: the relative size of bars of a linkage is determined (up to an equivalence) by the cohomology algebra of its configuration space.
The material of the book is based on lectures given by the author on topics of topological robotics at ETH Zürich in 2006. The exposition of material is very simple on the engineering side but requires a good knowledge of algebraic topology and other modern mathematical techniques. It is therefore readable for mathematicians who are interested in applications of topology in other fields of mathematics. Proofs of statements are either given or cited. The author himself says: “The book is intended as an appetizer and will introduce the reader to many fascinating topological problems motivated by engineering”. The book is clearly written and gives a good number of examples. The author provides 103 references. This will help the reader to orient himself in the subject.