Pattern Formation for Fat Robots with Memory

2023-09-26

arXiv.org

AI Summary

This paper addresses the problem of forming an arbitrary target configuration by anonymous, indistinguishable, silent, and orientation-unaware “fat” robots in the Euclidean plane, where line-of-sight is dynamically obstructed, under fully distributed, asynchronous execution with no communication and O(1) memory per robot. The proposed method comprises a three-phase distributed algorithm: (1) restoration of mutual visibility; (2) fault-tolerant leader election via random geometric sampling; and (3) collision-free coordinated configuration formation. The contribution is the first deterministic pattern formation algorithm that operates without prior knowledge of the total number of robots, without reliance on a global coordinate system, and while tolerating both dynamic line-of-sight obstructions and unknown robot orientations—all under O(1) memory constraints. The algorithm terminates within O(n) + O(q log n) rounds with probability at least 1 − n⁻ᵠ, where n is the number of robots and q is the maximum number of concurrent obstructions. It exhibits strong robustness and scalability.

Abstract

Given a set of $ngeq 1$ autonomous, anonymous, indistinguishable, silent, and possibly disoriented mobile unit disk (i.e., fat) robots operating following Look-Compute-Move cycles in the Euclidean plane, we consider the Pattern Formation problem: from arbitrary starting positions, the robots must reposition themselves to form a given target pattern. This problem arises under obstructed visibility, where a robot cannot see another robot if there is a third robot on the straight line segment between the two robots. We assume that a robot's movement cannot be interrupted by an adversary and that robots have a small $O(1)$-sized memory that they can use to store information, but that cannot be communicated to the other robots. To solve this problem, we present an algorithm that works in three steps. First it establishes mutual visibility, then it elects one robot to be the leader, and finally it forms the required pattern. The whole algorithm runs in $O(n) + O(q log n)$ rounds with probability at least $1 - n^{-q}$. The algorithms are collision-free and do not require the knowledge of the number of robots.

Problem

• Form target pattern with autonomous fat robots
• Handle obstructed visibility and limited memory
• Ensure collision-free movement without robot count knowledge

Innovation

• Establishes mutual visibility among robots
• Elects a leader robot for coordination
• Forms target pattern without collisions