Summary
Methods of algebraic topology are used to analyze the structure of motion planning algorithms in robotics. Navigational complexity of a mechanical system is measured by a numerical invariant TC(X) depending on the homotopy type of the configuration space X. Computations of TC(X) use various topological tools including cohomology algebras and cohomology operations. This paper is a brief survey introducing these topics to the community of applied and industrial mathematicians. The method is illustrated by applications to problems of simultaneous control of multiple moving objects.