  In this paper, we propose a novel decentralized control method to maintain
Line-of-Sight connectivity for multi-robot networks in the presence of
Guassian-distributed localization uncertainty. In contrast to most existing
work that assumes perfect positional information about robots or enforces
overly restrictive rigid formation against uncertainty, our method enables
robots to preserve Line-of-Sight connectivity with high probability under
unbounded Gaussian-like positional noises while remaining minimally intrusive
to the original robots' tasks. This is achieved by a motion coordination
framework that jointly optimizes the set of existing Line-of-Sight edges to
preserve and control revisions to the nominal task-related controllers, subject
to the safety constraints and the corresponding composition of
uncertainty-aware Line-of-Sight control constraints. Such compositional control
constraints, expressed by our novel notion of probabilistic Line-of-Sight
connectivity barrier certificates (PrLOS-CBC) for pairwise robots using control
barrier functions, explicitly characterize the deterministic admissible control
space for the two robots. The resulting motion ensures Line-of-Sight
connectedness for the robot team with high probability. Furthermore, we propose
a fully decentralized algorithm that decomposes the motion coordination
framework by interleaving the composite constraint specification and solving
for the resulting optimization-based controllers. The optimality of our
approach is justified by the theoretical proofs. Simulation and real-world
experiments results are given to demonstrate the effectiveness of our method.
