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. Finally, 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.

翻译：考虑一组称为“机器人”的自主移动计算实体。这些机器人在欧几里得平面中移动，并遵循同步的“观察-计算-移动”周期运行。在四种传统模型 $\{ \mathcal{OBLOT},\ \mathcal{FSTA},\ \mathcal{FCOM},\ \mathcal{LUMI} \} $ 下，机器人的计算能力已在机器人拥有无限能量和能量受限两种情况下得到广泛研究。在上述两种情形中，机器人均具备完全可见性。本文去除了这一假设，即我们假设机器人只能从自身位置观察到恒定半径 $V_r$ 范围内的环境（$V_r$ 对所有机器人相同），并研究该限制对其计算能力的影响。我们首先探究可见性限制是否会产生任何影响，即在给定模型和调度器下，是否存在某些有限可见性机器人无法解决而完全可见性机器人可以解决的问题。我们发现，该问题的答案在一般情况下是肯定的。最后，我们试图了解在给定模型下，可见性和同步性这两个因素中哪一个更具影响力，并得出结论：无法得出确定性的结论。