Rational sequential parametrized topological complexity

Abstract

Sequential parametrized topological complexity is a numerical homotopy invariant of a fibration, which arose in the robot motion planning problem with external constraints. In this paper, we study sequential parametrized topological complexity in view of rational homotopy theory. We generalize results on topological complexity, and in particular, give an explicit algebraic upper bound for sequential parametrized topological complexity when a fibration admits a certain decomposition, which is a generalization of the result of Hamoun, Rami and Vandembroucq on topological complexity.