Forming Large Patterns with Local Robots in the OBLOT Model
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914740503052288 |
|---|---|
| author | Hahn, Christopher Harbig, Jonas Kling, Peter |
| author_facet | Hahn, Christopher Harbig, Jonas Kling, Peter |
| contents | In the arbitrary pattern formation problem, $n$ autonomous, mobile robots must form an arbitrary pattern $P \subseteq \mathbb{R}^2$. The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to communicate. An important distinction is whether robots have memory and/or a limited viewing range. Previous work managed to form $P$ under a natural symmetry condition if robots have no memory but an unlimited viewing range [22] or if robots have a limited viewing range but memory [25]. In the latter case, $P$ is only formed in a shrunk version that has constant diameter.
Without memory and with limited viewing range, forming arbitrary patterns remains an open problem. We provide a partial solution by showing that $P$ can be formed under the same symmetry condition if the robots' initial diameter is $\leq 1$. Our protocol partitions $P$ into rotation-symmetric components and exploits the initial mutual visibility to form one cluster per component. Using a careful placement of the clusters and their robots, we show that a cluster can move in a coordinated way through its component while drawing $P$ by dropping one robot per pattern coordinate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02771 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Forming Large Patterns with Local Robots in the OBLOT Model Hahn, Christopher Harbig, Jonas Kling, Peter Robotics Data Structures and Algorithms In the arbitrary pattern formation problem, $n$ autonomous, mobile robots must form an arbitrary pattern $P \subseteq \mathbb{R}^2$. The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to communicate. An important distinction is whether robots have memory and/or a limited viewing range. Previous work managed to form $P$ under a natural symmetry condition if robots have no memory but an unlimited viewing range [22] or if robots have a limited viewing range but memory [25]. In the latter case, $P$ is only formed in a shrunk version that has constant diameter. Without memory and with limited viewing range, forming arbitrary patterns remains an open problem. We provide a partial solution by showing that $P$ can be formed under the same symmetry condition if the robots' initial diameter is $\leq 1$. Our protocol partitions $P$ into rotation-symmetric components and exploits the initial mutual visibility to form one cluster per component. Using a careful placement of the clusters and their robots, we show that a cluster can move in a coordinated way through its component while drawing $P$ by dropping one robot per pattern coordinate. |
| title | Forming Large Patterns with Local Robots in the OBLOT Model |
| topic | Robotics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2404.02771 |