The Computational Landscape of Autonomous Mobile Robots: The Visibility Perspective

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 $\{ \mathcal{OBLOT},\ \mathcal{FSTA},\ \mathcal{FCOM},\ \mathcal{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 $\{ \mathcal{OBLOT},\ \mathcal{FSTA},\ \mathcal{FCOM} \}$ models and to synchronous schedulers only. The results in $\mathcal{LUMI}$ model is yet to be determined.