Abstract
We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move cycles and communicate with other robots using colored lights following the robots with lights model. We study the fundamental Complete Visibility problem of repositioning N autonomous robots on a plane so that each robot is visible to all others in this model. We assume obstructed visibility where a robot cannot see another robot if a third robot is positioned between them on the straight line connecting them. There exists an \(\mathcal{O}(\log N)\) time, \(\mathcal{O}(1)\) color algorithm for this problem in the asynchronous setting. In this paper, we provide the first, asymptotically optimal, \(\mathcal{O}(1)\) time, \(\mathcal{O}(1)\) color algorithm for this problem in the asynchronous setting. The proposed algorithm is collision-free – robots do not share positions and their paths do not cross. We also introduce a technique, called Beacon-Directed Curve Positioning, for moving robots in an asynchronous setting, that may be of independent interest.
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Notes
- 1.
The simulation technique of Das et al. [7] shows that any algorithm (for any problem) in the robots with lights model with \(k>1\) colors in the semi-synchronous setting can be simulated in the asynchronous setting with 5k colors (without a time bound on the simulation).
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Sharma, G., Vaidyanathan, R., Trahan, J.L. (2017). Constant-Time Complete Visibility for Asynchronous Robots with Lights. In: Spirakis, P., Tsigas, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2017. Lecture Notes in Computer Science(), vol 10616. Springer, Cham. https://doi.org/10.1007/978-3-319-69084-1_18
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