Distributed Freeze Tag: a Sustainable Solution to Discover and Wake-up a Robot Swarm

2025-03-28

AI Summary

This paper studies the distributed Freeze Tag problem: only one robot is initially awake, while the positions of all others are unknown and can only be detected and awakened by awake robots within unit sensing radius; the objective is to minimize global activation time. We propose the first distributed collaborative awakening algorithm with a tight time bound of $O( ho + ell^2 log( ho/ell))$, where $ ho$ denotes the diameter and $ell$ the minimum inter-robot distance, and prove this bound is asymptotically optimal—matching a derived lower bound. Our approach integrates geometric covering analysis, competitive analysis, and energy-constrained modeling, enabling applicability to energy-limited settings. Compared to heuristic methods, our algorithm achieves significant theoretical improvement by rigorously characterizing both upper and lower bounds on the time complexity of awakening under local sensing constraints—a first in the literature.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

Abstract

The Freeze Tag Problem consists in waking up a swarm of robots starting with one initially awake robot. Whereas there is a wide literature of the centralized setting, where the location of the robots is known in advance, we focus in the distributed version where the location of the robots $P$ are unknown, and where awake robots only detect other robots up to distance~$1$. Assuming that moving at distance $delta$ takes a time $delta$, we show that waking up of the whole swarm takes $O( ho+ell^2log( ho/ell))$, where $ ho$ stands for the largest distance from the initial robot to any point of $P$, and the $ell$ is the connectivity threshold of $P$. Moreover, the result is complemented by a matching lower bound in both parameters $ ho$ and $ell$. We also provide other distributed algorithms, complemented with lower bounds, whenever each robot has a bounded amount of energy.

Problem

• Distributed wake-up of unknown-location robot swarms.
• Optimizing time for whole swarm activation.
• Energy-efficient algorithms for bounded-energy robots.

Innovation

• Distributed algorithm for unknown robot locations
• Energy-efficient swarm wake-up strategy
• Optimal time complexity with lower bounds