Geodesic complexity of motion planning

We introduce the geodesic complexity of a metric space, inspired by topological space. Both them are numerical invariants, but, while TC only depends on homotopy type, GC is an invariant under isometries. show that in many cases they coincide but we also develop tools to distinguish two range examples. To this end, study what denote total cut locus, which does not appear have been explicitly considered literature. knowledge author, new Furthermore, just like TC, has potential applications field robotics.