Going in Circles: Collaborative Multi-Robot Treasure Hunting

2026-08-12

AI Summary

This study addresses the problem of minimizing the total completion time for a team of $n$ robots to collaboratively search for and visit $k$ hidden treasures located on the unit circle in an unknown environment. Starting from the origin and leveraging real-time information sharing, the robots must collectively ensure that all treasures are eventually visited by every robot. The work innovatively introduces an auxiliary problem under full prior knowledge—namely, the optimal trajectory of a single robot—and derives its exact solution. Building upon this, the authors establish tight upper and lower bounds on the total completion time for the multi-robot system operating without prior knowledge of treasure locations. By integrating geometric analysis with scheduling theory, the proposed approach provides a theoretical benchmark and performance guarantees for cooperative search strategies.

Abstract

This paper investigates a multi-robot search-and-visit problem involving $n$ robots starting at the origin and $k$ unknown treasures hidden on the unit circle $\mathcal{C}$. The robots move independently anywhere in the plane with a maximum speed of 1 and instantly share discovery information. The goal is to determine an algorithm that minimizes the total time needed for all robots to individually visit every treasure. To establish the foundational limits of this task, we first solve an auxiliary optimal routing problem for a single robot on $\mathcal{C}$ that possesses complete prior knowledge of the treasure locations. The exact analysis of this auxiliary problem yields explicit upper and lower bounds for the original search problem.

Problem

• multi-robot
• search-and-visit
• treasure hunting
• unit circle
• collaborative

Innovation

• multi-robot collaboration
• search-and-visit problem
• optimal routing
• information sharing
• theoretical bounds