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Forming Large Patterns with Local Robots in the OBLOT Model

3 April 2024
Christopher Hahn
Jonas Harbig
Peter Kling
ArXiv (abs)PDFHTML
Abstract

In the arbitrary pattern formation problem, nnn autonomous, mobile robots must form an arbitrary pattern P⊆R2P \subseteq \mathbb{R}^2P⊆R2. 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 PPP 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, PPP 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 PPP can be formed under the same symmetry condition if the robots' initial diameter is ≤1\leq 1≤1. Our protocol partitions PPP 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 PPP by dropping one robot per pattern coordinate.

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