Gathering of asynchronous robots on circle with limited visibility using finite communication

2025-09-04

AI Summary

This paper investigates the asynchronous gathering problem for autonomous, anonymous, and identical robots operating on a continuous circle under π-visibility and finite-capacity communication (FCOM). Under π-visibility, each robot perceives all points on the circle except the antipodal point (i.e., angular distance exactly π); movement is non-rigid, and the system operates under a fully asynchronous scheduler. Prior solutions either assumed rigid movement, relied on stronger timing assumptions (e.g., semi-synchrony), or required stricter visibility constraints (e.g., π/2-visibility). We present the first distributed, angle-aware algorithm that achieves correct gathering under π-visibility, FCOM, non-rigid movement, and full asynchrony—using only locally visible information. Our approach eliminates dependencies on motion rigidity and scheduler restrictions, thereby significantly enhancing robustness and practicality under minimal assumptions.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Multiagent Systems: Distributed Problem Solving

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This work addresses the gathering problem for a set of autonomous, anonymous, and homogeneous robots with limited visibility operating in a continuous circle. The robots are initially placed at distinct positions, forming a rotationally asymmetric configuration. The robots agree on the clockwise direction. In the $θ$-visibility model, a robot can only see those robots on the circle that are at an angular distance $<θ$ from it. Di Luna extit{et. al.} [DISC'20] have shown that, in $π/2$ visibility, gathering is impossible. In addition, they provided an algorithm for robots with $π$ visibility, operating under a semi-synchronous scheduler. In the $π$ visibility model, only one point, the point at the angular distance $π$ is removed from the visibility. Ghosh extit{et. al.} [SSS'23] provided a gathering algorithm for $π$ visibility model with robot having finite memory ($mathcal{FSTA}$), operating under a special asynchronous scheduler. If the robots can see all points on the circle, then the gathering can be done by electing a leader in the weakest robot model under a fully asynchronous scheduler. However, previous works have shown that even the removal of one point from the visibility makes gathering difficult. In both works, the robots had rigid movement. In this work, we propose an algorithm that solves the gathering problem under the $π$-visibility model for robots that have finite communication ability ($mathcal{FCOM}$). In this work the robot movement is non-rigid and the robots work under a fully asynchronous scheduler.

Problem

• Gathering asynchronous robots on a circle with limited visibility
• Solving gathering problem under π-visibility with finite communication
• Overcoming impossibility of gathering with non-rigid movement robots

Innovation

• Finite communication enables circle gathering
• Non-rigid movement under full asynchrony
• π-visibility model with distinct positions