In this paper we study a notion of topological complexity TC(X) for the motion planning problem. TC(X) is a number which measures discontinuity of the process of motion planning in the configuration space X. More precisely, TC(X) is the minimal number k such that there are k different “motion planning rules”, each defined on an open subset of X×X, so that each rule is continuous in the source and target configurations. We use methods of algebraic topology (the Lusternik Schnirelman theory) to… CONTINUE READING