2018 **Abstract:** Given any multiset F of points in the Euclidean plane and a set R of robots such that |R| = |F|, the Arbitrary Pattern Formation (APF) problem asks for a distributed algorithm that moves robots so as to reach a configuration similar to F. Similarity means that robots must be disposed as F regardless of translations, rotations, reflections, uniform scalings. Initially, each robot occupies a distinct position. When active, a robot operates in standard Look-ComputeMove cycles. Robots are asynchronous, oblivious, …

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“…The ability to make circular moves is crucial to our algorithm. Although the standard model for mobile robots in the plane assumes rectilinear robot movement, it is not completely uncommon to allow the robots to move along circular trajectories (e.g., [7,17]). It would be interesting to see if the same result can be achieved without the ability to make circular moves.…”

confidence: 99%

“…The ability to make circular moves is crucial to our algorithm. Although the standard model for mobile robots in the plane assumes rectilinear robot movement, it is not completely uncommon to allow the robots to move along circular trajectories (e.g., [7,17]). It would be interesting to see if the same result can be achieved without the ability to make circular moves.…”

confidence: 99%

“…A robot infers that it is in Phase 1 if ¬(C 1 ∧C 2 ) ∧ ¬(C 3 ∧C 4 ) is true 3 . In this case, the tail will move to the right and all other robots will remain static.…”

confidence: 99%

“…When active, a robot operates in standard Look-Compute-Move (LCM) computational cycles, see e.g. [8], [39], [52]. Within one cycle, a robot acquires a snapshot of the current global positioning of the other robots (Look phase) with respect to its own coordinate system.…”

confidence: 99%

“…This, of course, extraordinarily affects also the arguments necessary to provide the proofs of correctness of the proposed algorithms. To this respect, see [11] for an extended discussion related to the difficulties encountered when dealing with ASYNC.…”

confidence: 99%