Parametrized topological complexity of poset-stratified spaces

In this paper, parametrized motion planning algorithms for a fiberwise space X → P over a poset P are studied. Such an algorithm assigns paths in a space X decomposed into subspaces with the index set P, that do not cross the boundaries of the separated regions. We compute the parametrized topological complexity of X → P , which is one less than the minimal number of local parametrized motion planning algorithms used for designing non-cross-border robot motions in X.