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Separation of Unconscious Robots with Obstructed Visibility

Prajyot Pyati, Navjot Kaur, Saswata Jana, Adri Bhattacharya, Partha Sarathi Mandal

TL;DR

The paper addresses the separation problem for unconscious, opaque mobile robots with obstructed visibility in the Look-Compute-Move model. It introduces Con-SemCirc-Separation, a staged, collision-free algorithm that achieves separation into concentric semicircles in $O(n)$ epochs under the $SSYNC$ scheduler without knowledge of $n$, using axis agreement and a grid-point signaling framework. A key novelty is handling opacity, where robots can block visibility, and yet the algorithm ensures coordinated progression through triangular, semicircular, grid-point, and sector configurations to reach the final separated state. The work broadens the scope of formation tasks for unconscious autonomous swarms, with potential extensions to concentric circles under stronger color constraints and implications for robust swarm coordination under obstructed visibility.

Abstract

We study a recently introduced \textit{unconscious} mobile robot model, where each robot is associated with a \textit{color}, which is visible to other robots but not to itself. The robots are autonomous, anonymous, oblivious and silent, operating in the Euclidean plane under the conventional \textit{Look-Compute-Move} cycle. A primary task in this model is the \textit{separation problem}, where unconscious robots sharing the same color must separate from others, forming recognizable geometric shapes such as circles, points, or lines. All prior works model the robots as \textit{transparent}, enabling each to know the positions and colors of all other robots. In contrast, we model the robots as \textit{opaque}, where a robot can obstruct the visibility of two other robots, if it lies on the line segment between them. Under this obstructed visibility, we consider a variant of the separation problem in which robots, starting from any arbitrary initial configuration, are required to separate into concentric semicircles. We present a collision-free algorithm that solves the separation problem under a semi-synchronous scheduler in $O(n)$ epochs, where $n$ is the number of robots. The robots agree on one coordinate axis but have no knowledge of $n$.

Separation of Unconscious Robots with Obstructed Visibility

TL;DR

The paper addresses the separation problem for unconscious, opaque mobile robots with obstructed visibility in the Look-Compute-Move model. It introduces Con-SemCirc-Separation, a staged, collision-free algorithm that achieves separation into concentric semicircles in epochs under the scheduler without knowledge of , using axis agreement and a grid-point signaling framework. A key novelty is handling opacity, where robots can block visibility, and yet the algorithm ensures coordinated progression through triangular, semicircular, grid-point, and sector configurations to reach the final separated state. The work broadens the scope of formation tasks for unconscious autonomous swarms, with potential extensions to concentric circles under stronger color constraints and implications for robust swarm coordination under obstructed visibility.

Abstract

We study a recently introduced \textit{unconscious} mobile robot model, where each robot is associated with a \textit{color}, which is visible to other robots but not to itself. The robots are autonomous, anonymous, oblivious and silent, operating in the Euclidean plane under the conventional \textit{Look-Compute-Move} cycle. A primary task in this model is the \textit{separation problem}, where unconscious robots sharing the same color must separate from others, forming recognizable geometric shapes such as circles, points, or lines. All prior works model the robots as \textit{transparent}, enabling each to know the positions and colors of all other robots. In contrast, we model the robots as \textit{opaque}, where a robot can obstruct the visibility of two other robots, if it lies on the line segment between them. Under this obstructed visibility, we consider a variant of the separation problem in which robots, starting from any arbitrary initial configuration, are required to separate into concentric semicircles. We present a collision-free algorithm that solves the separation problem under a semi-synchronous scheduler in epochs, where is the number of robots. The robots agree on one coordinate axis but have no knowledge of .
Paper Structure (12 sections, 13 theorems, 4 equations, 8 figures, 1 table)

This paper contains 12 sections, 13 theorems, 4 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Model, Preliminaries and Problem Definition
  3. Notations and Terminologies:
  4. Algorithm to Separate Opaque Colored Robots
  5. A high-level Idea of the Algorithm:
  6. Stage: Arbitrary-To-Triangular
  7. Stage: Triangular-To-Semicircular
  8. Stage: Semicircular-To-GridPoint
  9. Stage: GridPoint-To-SectorPartitioning
  10. Stage: SectorPartitioning-To-ConcenSemiCirc
  11. Analysis of the Algorithm Con-SemCirc-Separation
  12. Conclusion

Key Result

Lemma 1

Starting from an arbitrary initial configuration, all the robots reach a triangular configuration in $O(n)$ epochs using stage Arbitrary-To-Triangular.

Figures (8)

  • Figure 1: Represents the eventual configuration to be attained, while executing the respective subroutines, based on some specific view.
  • Figure 2: The diameter robots $r$ and $r'$ find their respective $\theta < \pi/4$, and move to their target point.
  • Figure 3: The diameter robots $r$ and $r'$ find their respective $\theta \geq \pi/4$, and move to the target point on $L_{r_b}$.
  • Figure 4: Illustration of Case B, first stage and all the sub-cases of the second stage.
  • Figure 5: Leader repositioning with different inward distances.
  • ...and 3 more figures

Theorems & Definitions (21)

  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • Lemma 6
  • proof
  • ...and 11 more