Abstract
The Pattern Formation problem is one of the most important coordination problem for robotic systems. Initially the entities are in arbitrary positions; within finite time they must arrange themselves in the space so to form a pattern given in input. In this chapter, we will mainly deal with the problem in the \(\mathcal{OBLOT}\) model.
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Notes
- 1.
Note that, since at this time the robots still do not have a common agreement on the direction of the X axis, for some robots \({\mathcal M} _\mathbb D \) and \({\mathcal L} _\mathbb D \) might be different. All of them, however, agree on \(K _m\).
- 2.
Note that, since \(\mathbb P _R\) is symmetric, nothing changes if the topmost point on the leftmost vertical axis tangent to \(\mathbb P\) is mapped onto \({ Out} \), and the topmost point on the rightmost vertical axis tangent to \(\mathbb P\) is mapped onto \({ Out}' \).
- 3.
Equivalently, the position of the landmarks is known a priori to all robots.
- 4.
For a plane graph, the periphery is the boundary of the exterior face.
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Prencipe, G. (2019). Pattern Formation. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_3
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