# Pattern Formation Problem for Synchronous Mobile Robots in the Three Dimensional Euclidean Space

- 2016

#### Abstract

We investigate the pattern formation problem that requires a swarm of autonomous mobile robots to form a given target pattern in the three-dimensional Euclidean space. We show a necessary and sufficient condition for synchronous robots to form a given target pattern from an initial configuration. We give a pattern formation algorithm for solvable instances that does not need any local memory at each robot.

**DOI:**10.1145/2933057.2933063

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