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Capturing a Moving Target by Two Robots in the F2F Model

Khaled Jawhar, Evangelos Kranakis

TL;DR

This work studies capturing a moving target on an infinite line using two robots under face-to-face (F2F) communication. It analyzes four knowledge models (Full Knowledge, No Distance, No Speed, No Knowledge) and distinguishes target motion toward or away from the origin, deriving competitive-ratio bounds and showing that capture can be achieved with a constant number of turns (at most 3 in most schemes). Key contributions include tight or near-tight CRs for each model, explicit strategies such as ZigZag and NonZigZag variants, and demonstration that certain problems remain inherently difficult under information absence (yielding high or optimal CRs like 3 for Toward in No Speed and No Knowledge Toward). The results provide a detailed map of how input knowledge affects capture efficiency and turn costs, with implications for energy-efficient multi-robot pursuit and evacuation tasks in continuous domains.

Abstract

We study a search problem on capturing a moving target on an infinite real line. Two autonomous mobile robots (which can move with a maximum speed of 1) are initially placed at the origin, while an oblivious moving target is initially placed at a distance $d$ away from the origin. The robots can move along the line in any direction, but the target is oblivious, cannot change direction, and moves either away from or toward the origin at a constant speed $v$. Our aim is to design efficient algorithms for the two robots to capture the target. The target is captured only when both robots are co-located with it. The robots communicate with each other only face-to-face (F2F), meaning they can exchange information only when co-located, while the target remains oblivious and has no communication capabilities. We design algorithms under various knowledge scenarios, which take into account the prior knowledge the robots have about the starting distance $d$, the direction of movement (either toward or away from the origin), and the speed $v$ of the target. As a measure of the efficiency of the algorithms, we use the competitive ratio, which is the ratio of the capture time of an algorithm with limited knowledge to the capture time in the full-knowledge model. In our analysis, we are mindful of the cost of changing direction of movement, and show how to accomplish the capture of the target with at most three direction changes (turns).

Capturing a Moving Target by Two Robots in the F2F Model

TL;DR

This work studies capturing a moving target on an infinite line using two robots under face-to-face (F2F) communication. It analyzes four knowledge models (Full Knowledge, No Distance, No Speed, No Knowledge) and distinguishes target motion toward or away from the origin, deriving competitive-ratio bounds and showing that capture can be achieved with a constant number of turns (at most 3 in most schemes). Key contributions include tight or near-tight CRs for each model, explicit strategies such as ZigZag and NonZigZag variants, and demonstration that certain problems remain inherently difficult under information absence (yielding high or optimal CRs like 3 for Toward in No Speed and No Knowledge Toward). The results provide a detailed map of how input knowledge affects capture efficiency and turn costs, with implications for energy-efficient multi-robot pursuit and evacuation tasks in continuous domains.

Abstract

We study a search problem on capturing a moving target on an infinite real line. Two autonomous mobile robots (which can move with a maximum speed of 1) are initially placed at the origin, while an oblivious moving target is initially placed at a distance away from the origin. The robots can move along the line in any direction, but the target is oblivious, cannot change direction, and moves either away from or toward the origin at a constant speed . Our aim is to design efficient algorithms for the two robots to capture the target. The target is captured only when both robots are co-located with it. The robots communicate with each other only face-to-face (F2F), meaning they can exchange information only when co-located, while the target remains oblivious and has no communication capabilities. We design algorithms under various knowledge scenarios, which take into account the prior knowledge the robots have about the starting distance , the direction of movement (either toward or away from the origin), and the speed of the target. As a measure of the efficiency of the algorithms, we use the competitive ratio, which is the ratio of the capture time of an algorithm with limited knowledge to the capture time in the full-knowledge model. In our analysis, we are mindful of the cost of changing direction of movement, and show how to accomplish the capture of the target with at most three direction changes (turns).

Paper Structure

This paper contains 21 sections, 18 theorems, 73 equations, 4 tables, 10 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Notation
  3. Related Work
  4. Outline and Results of the Paper
  5. Full Knowledge Model
  6. No Distance Model
  7. No Speed Model
  8. No Knowledge Model
  9. Full Knowledge Model
  10. Target moving away from the origin
  11. Target moving toward the origin
  12. No Distance Model
  13. Target moving away from the origin
  14. Target Moving Toward the Origin
  15. No Speed Model
  16. ...and 6 more sections

Key Result

theorem 1

For the full knowledge away model, the competitive ratio of Algorithm FKGoTogetherAwayAlgorithm is at most $\frac{3-v}{1-v}$

Theorems & Definitions (36)

  • theorem 1
  • proof
  • theorem 2
  • proof
  • theorem 3
  • proof
  • theorem 4
  • proof
  • theorem 5
  • proof
  • ...and 26 more