Uniform Robot Relocation Is Hard in only Two Directions Even Without Obstacles

Abstract

Given n robots contained within a square grid surrounded by four walls, we ask the question of whether it is possible to move a particular robot a to a specific grid location b by performing a sequence of global step operations in which all robots move one grid step in the same cardinal direction (if not blocked by a wall or other blocked robots). We show this problem is NP-complete when restricted to just two directions (south and west). This answers the simplest fundamental problem in uniform global unit tilt swarm robotics. We then consider a relaxed version of this problem in which the goal is to move a robot a to a specific row regardless of its horizontal placement. We show that if asking about the bottom-most row of the square grid, then this version of the problem is solvable in polynomial time. Finally, we discuss several areas for future research and open problems.

Uniform Robot Relocation is Hard in only two Directions even without Obstacles

“…This work is an extension of a conference version with the hardness proof [13], and of a 2-page abstract outlining the first row relocation problem [12]. The journal has extended these in several ways with full details and proofs of the positive result as well as additional future work and open problems.…”