On the Sequential topological complexity of directed (parametrized) motion planning algorithms

Abstract

We introduce sequential analogues of directed (parametrized) topological complexity, in the context of motion planning problems requiring a system to traverse a prescribed sequence of intermediate states while respecting directed dynamics and varying external parameters. We develop their basic theory, establish fundamental properties, and compute them for several classes of examples. Our computations show, in particular, that distinct directed structures on the same underlying space can have different values of this invariant.