Pattern Formation by Mobile Robots with Limited Visibility
We investigate the pattern formation problem by mobile robots with limited visibility that can observe the positions of robots within limited distance. For robots with unlimited visibility, Fujinaga et al. (DISC 2012) showed that asynchronous oblivious robots have the same formation power as fully-synchronous non-oblivious robots, that is, starting from any initial configuration I, target pattern F is formable if and only if ρ(I) divides ρ(F) where ρ(·) is the geometric symmetricity. We first show that fully-synchronous oblivious robots with limited visibility cannot form F even when ρ(I) divides ρ(F). Hence, limited visibility substantially weakens the formation power of oblivious robots. Secondly, we show that despite limited visibility, semi-synchronous robots with rigid moves, and fully-synchronous robots with non-rigid moves have the same formation power as robots with unlimited visibility. Consequently, local memory is necessary and sufficient for these robots.
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