Forming Large Patterns with Local Robots in the OBLOT Model
<|reference_start|>Forming Large Patterns with Local Robots in the OBLOT Model: 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.<|reference_end|>
@article{hahn2024forming,
    title={Forming Large Patterns with Local Robots in the OBLOT Model},
    author={Christopher Hahn, Jonas Harbig, Peter Kling},
    journal={arXiv preprint arXiv:2404.02771},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.02771},
    primaryClass={cs.RO cs.DS}
}