English

Sequential parametrized motion planning and its complexity, II

Robotics 2022-12-05 v1 Algebraic Topology

Abstract

This is a continuation of our recent paper 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 the previous publication we analysed the sequential parametrized topological complexity of the Fadell - Neuwirth fibration which in relevant to the problem of moving multiple robots avoiding collisions with other robots and with obstacles in the Euclidean space. Besides, in the preceeding paper we found the sequential parametrised topological complexity of the Fadell - Neuwirth bundle for the case of the Euclidean space Rd\Bbb R^d of odd dimension as well as the case d=2d=2. In the present paper we give the complete answer for an arbitrary d2d\ge 2 even. Moreover, we present an explicit motion planning algorithm for controlling multiple robots in Rd\Bbb R^d having the minimal possible topological complexity; this algorithm is applicable to any number nn of robots and any number m2m\ge 2 of obstacles.

Keywords

Cite

@article{arxiv.2212.01091,
  title  = {Sequential parametrized motion planning and its complexity, II},
  author = {Michael Farber and Amit Kumar Paul},
  journal= {arXiv preprint arXiv:2212.01091},
  year   = {2022}
}
R2 v1 2026-06-28T07:20:19.369Z