Forming Large Patterns from Widespread Swarms of Oblivious Robots with Limited Visibility / Jonas Harbig ; Reviewers Prof. Dr. Friedhelm Meyer auf der Heide, (Paderborn University), Prof. Dr. Christian Scheideler, (Paderborn University). Paderborn, 2025
Inhalt
- 1 Introduction
- 1.1 Introduction into Pattern Formation Problems
- 1.2 Outline of the Thesis and Main Results
- 1.2.1 Near-Gathering (chapter:near-gathering)
- 1.2.2 Symmetricity Preservation (chapter:symmetry-preservation)
- 1.2.3 Large Pattern Formation from Contracted Swarms (chapter:symmetry-preservation)
- 1.2.4 / for Widespread Swarms (Combined Main Result)
- 1.3 Model
- 1.4 Notation
- 1.4.1 Configuration
- 1.4.2 Target Position
- 1.4.3 Characterizing Protocols via their Evolution Function
- 1.4.4 Pattern
- 1.4.5 Geometrical Notations
- 1.5 Further Related Work
- 2 A Class of Near-Gathering Strategies
- 2.1 A Class of Contracting Protocols
- 2.2 Analysis of lambda-contracting Near-Gathering Protocols
- 2.3 From Contracting Protocols to Near-Gathering
- 2.4 Proofs for Near-Gathering Protocols Pcl(P, , )
- 3 Near-Gathering with Symmetry Preservation
- 3.1 Preserving Symmetries via Local Invertibility
- 3.2 Preserving Symmetries via Averaging
- 3.3 Preserving Symmetries via Contracting Waves
- 4 Forming Large Patterns from Contracted Swarms
- 4.1 Forming Patterns via Drawing
- 4.1.1 Drawing Formations & Movement
- 4.1.2 States of a Drawing Formation
- 4.1.3 Drawing a Pattern via a Drawing Path
- 4.1.4 Full Pattern via Many Drawing Formations
- 4.1.5 Putting Everything Together
- 4.1.6 Illustration of Drawing Path Traversal
- 4.2 Existence of Suitable Drawing Paths
- 4.2.1 Constructing a Drawing Tree
- 4.2.2 Appending a Tail
- 4.2.3 Illustration of the Drawing Path Construction
- 4.2.4 Auxiliary Result
- 4.3 Description of the Pattern-Formation Protocol
- 5 Conclusion and Outlook