Mover problems

Abstract

Leo Moser asked what is the region of largest area that can be moved around a right-angled corner in a corridor of unit width? Similarly, what is the region of largest area that can be reversed in a T junction made up of roads of unit width? Can a specific 3-dimensional object pass through a given door? Our survey aims at showing that mover problems are no less challenging even if there are no obstacles other than the objects themselves, but there are many objects to move. We survey some recent results on motion planning and reconfiguration for systems of multiple objects and for modular systems with applications in robotics, and collect some open problems coming out of this line of research.