Sequential parametrized motion planning and its complexity, II

This is a continuation of our recent paper [6] in which we developed the theory of sequential parametrized motion planning. A sequential parametrized motion planning algorithm produced a motion of the system which is required to visit a prescribed sequence of states, in a certain order, at specified moments of time. In [6] we analysed the sequential parametrized topological complexity of the Fadell - Neuwirth fibration which is relevant to the problem of moving multiple robots avoiding collisions with other robots and with obstacles in the Euclidean space. In [6] we found the sequential parametrised topological complexity of the Fadell - Neuwirth bundle for the case of the Euclidean space R-d of odd dimension as well as the case d >= 2. In the present paper we give the complete answer for an arbitrary d > 2 even. Moreover, we present an explicit motion planning algorithm for controlling multiple robots in R-d having the minimal possible topological complexity; this algorithm is applicable to any number n of robots and any number m > 2 of obstacles. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).