Min-Sum Uniform Coverage Problem by Autonomous Mobile Robots

2026-02-11

AI Summary

This study addresses the problem of coordinating memoryless, anonymous, and homogeneous robots—without communication—to achieve a uniform distribution on either a finite line segment or a given circle while minimizing the total movement distance. Operating under the Look-Compute-Move paradigm with non-rigid fair asynchronous scheduling, the work proposes distributed algorithms that attain geometric optimality. The main contributions include the first complete characterization of initial configurations for which deterministic algorithms are impossible on a circle, and the design of deterministic distributed algorithms that achieve both uniform coverage and optimal total movement distance for all solvable instances on the line segment and on the circle.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study the \textit{min-sum uniform coverage} problem for a swarm of $n$ mobile robots on a given finite line segment and on a circle having finite positive radius, where the circle is given as an input. The robots must coordinate their movements to reach a uniformly spaced configuration that minimizes the total distance traveled by all robots. The robots are autonomous, anonymous, identical, and homogeneous, and operate under the \textit{Look-Compute-Move} (LCM) model with \textit{non-rigid} motion controlled by a fair asynchronous scheduler. They are oblivious and silent, possessing neither persistent memory nor a means of explicit communication. In the \textbf{line-segment setting}, the \textit{min-sum uniform coverage} problem requires placing the robots at uniformly spaced points along the segment so as to minimize the total distance traveled by all robots. In the \textbf{circle setting} for this problem, the robots have to arrange themselves uniformly around the given circle to form a regular $n$-gon. There is no fixed orientation or designated starting vertex, and the goal is to minimize the total distance traveled by all the robots. We present a deterministic distributed algorithm that achieves uniform coverage in the line-segment setting with minimum total movement cost. For the circle setting, we characterize all initial configurations for which the \textit{min-sum uniform coverage} problem is deterministically unsolvable under the considered robot model. For all the other remaining configurations, we provide a deterministic distributed algorithm that achieves uniform coverage while minimizing the total distance traveled. These results characterize the deterministic solvability of min-sum coverage for oblivious robots and achieve optimal cost whenever solvable.

Problem

• min-sum uniform coverage
• autonomous mobile robots
• uniform deployment
• oblivious robots
• total movement minimization

Innovation

• min-sum uniform coverage
• deterministic distributed algorithm
• oblivious robots
• asynchronous scheduler
• optimal movement cost