Problem
Research questions and friction points this paper is trying to address.
pattern formation
hardwired pattern
mobile robots
oblivious robots
synchronization
Hardwired Pattern Formation by Mobile Robots with Common Unit Distance
🤖 AI Summary
This study addresses the hardwired pattern formation (HwPTF) problem, wherein mobile robots must form a target pattern with exact geometric dimensions under strict constraints that prohibit translation, rotation, and scaling. The work formally defines this size-constrained pattern formation task for the first time and establishes its solvability by two memoryless semi-synchronous robots in the absence of multiplicity detection. It further introduces a luminous asynchronous robot model to solve HwPTF and proposes a scalable resizing algorithm applicable to systems with four or more robots. By integrating distributed coordination theory with synchronous models, finite-state machines, and light-based communication, the paper delineates the solvability boundaries of HwPTF across multiple robot models, thereby providing both theoretical foundations and practical algorithms for multi-robot cooperative tasks requiring precise dimensional control.
📝 Abstract
The pattern formation (PTF) problem requires mobile robots to form a specified target pattern. Existing papers investigated the PTF problem and revealed the effect of obliviousness and synchronization on distributed coordination of mobile robots. However, the PTF problem allows translation, rotation, and scaling of the target pattern. In this paper, we introduce a novel pattern formation problem, called the hardwired pattern formation (HwPTF) problem that requires the robots to form a given target pattern in a specified size. Although two oblivious semi-synchronous robots cannot solve the HwPTF problem of multiplicity two (i.e., the rendezvous problem), we show that they can solve the HwPTF problem without multiplicity. We also show that two oblivious asynchronous robots equipped with lights can solve the HwPTF problem, while oblivious asynchronous robots cannot. We finally present a size-adjusting algorithm for more than four oblivious semi-synchronous robots, that yields a HwPTF algorithm when combined with some existing pattern formation algorithms.
Innovation
Methods, ideas, or system contributions that make the work stand out.
hardwired pattern formation
oblivious robots
asynchronous robots with lights
size-adjusting algorithm
semi-synchronous coordination
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