The Computational Landscape of Autonomous Mobile Robots: The Visibility Perspective
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Consider a group of autonomous mobile computational entities called robots. The robots move in the Euclidean plane and operate according to synchronous Look-Compute-Move cycles. The computational capabilities of the robots under the four traditional models {𝒪ℬℒ𝒪𝒯, ℱ𝒮𝒯𝒜,ℱ𝒞𝒪ℳ, ℒ𝒰ℳℐ} have been extensively investigated both when the robots had unlimited amount of energy and when the robots were energy-constrained. In both the above cases, the robots had full visibility. In this paper, this assumption is removed, i.e., we assume that the robots can view up to a constant radius V_r from their position (the V_r is same for all the robots) and, investigates what impact it has on its computational capabilities. We first study whether the restriction imposed on the visibility has any impact at all, i.e., under a given model and scheduler does there exist any problem which cannot be solved by a robot having limited visibility but can be solved by a robot with full visibility. We find that the answer to the question in general turns out to be positive. Next we try to get an idea that under a given model, which of the two factors, Visibility or Synchronicity is more powerful and conclude that a definite conclusion cannot be drawn. We restrict our investigations to {𝒪ℬℒ𝒪𝒯, ℱ𝒮𝒯𝒜, ℱ𝒞𝒪ℳ} models and to synchronous schedulers only. The results in ℒ𝒰ℳℐ model is yet to be determined.
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