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We are given $N$ autonomous mobile robots inside a bounded region. The robotsare opaque which means that three collinear robots are unable to see each otheras one of the robots acts as an obstruction for the other two. They operate inclassical \emph{Look-Compute-Move} (LCM) activation cycles. Moreover, therobots are oblivious except for a persistent light (which is why they arecalled \emph{Luminous robots}) that can determine a color from a fixed colorset. Obliviousness does not allow the robots to remember any information frompast activation cycles. The Uniform Partitioning problem requires the robots topartition the whole region into sub-regions of equal area, each of whichcontains exactly one robot. Due to application-oriented motivation, we, in thispaper consider the region to be well-known geometric shapes such as rectangle,square and circle. We investigate the problem in \emph{asynchronous} settingwhere there is no notion of common time and any robot gets activated at anytime with a fair assumption that every robot needs to get activated infinitelyoften. To the best of our knowledge, this is the first attempt to study theUniform Partitioning problem using oblivious opaque robots working underasynchronous settings. We propose three algorithms considering three differentregions: rectangle, square and circle. Robots partition the region in adistributed way and reach their respective positions in the partitions. Thealgorithms proposed for rectangular and square regions run in $O(N)$ epochswhereas the algorithm for circular regions runs in $O(N^2)$ epochs, where anepoch is the smallest unit of time in which all robots are activated at leastonce and execute their LCM cycles.

Distributed Uniform Partitioning of a Region using Opaque ASYNC Luminous Mobile Robots