The min-move mutual visibility problem for disoriented asynchronous robots

We consider a distributed system of n≥3 autonomous robots in the Euclidean plane under the obstructed visibility model. In the obstructed visibility model, robots are considered opaque, and if three robots lie on a straight line, the mid- dle robot blocks the vision of the two other robots. The mutual visibility problem requires the robots to coordinate their movements in such a way that all the robots in the system become mutually visible. This paper studies a constrained version of the mutual visibility problem, namely the min-move mutual visibility problem. The min-move mutual visibility problem asks to solve the mutual visibility problem by moving each robot at most once. One of the major implications of this constrained version of the mutual visibility problem is that it also addresses the issue of energy efficiency for the robots. We study the min-move mutual visibility problem for disoriented robots (i.e., robots not having any form of local axis agreement or common chirality). We study the problem under two of the strongest adversarial models, namely asynchronous scheduler and non- rigid movements. We first show that the min-move mutual visibility problem is not solvable for disoriented asynchronous robots with non-rigid movements in the absence of externally visible lights. Then, we analyze different characteristics of a min-move mutual visibility algorithm for disoriented robots with non-rigid movements. We use these properties to present a distributed algorithm that solves the problem for disoriented asynchronous robots with non-rigid movements and having externally visible lights (FALL light model). The algorithm uses only 7 colors for the lights. The proposed algorithm is collision-free and runs in O(n) epochs. © 2025 Elsevier B.V.