Higher topological complexity of subcomplexes of products of spheres and related polyhedral product spaces

Abstract

We construct ``higher'' motion planners for automated systems whose spaces of states are homotopy equivalent to a polyhedral product space $Z(K,\{(S^{k_i},\star)\})$, {e.g. robot arms with restrictions on the possible combinations of simultaneously moving nodes.} Our construction is shown to be optimal by explicit cohomology calculations. The higher topological complexity of other {families of} polyhedral product spaces is also determined.