  Inter-robot communication enables multi-robot systems to coordinate and
execute complex missions efficiently. Thus, maintaining connectivity of the
communication network between robots is essential for many multi-robot systems.
In this paper, we present a trajectory planner for connectivity maintenance of
a multi-robot system. We first define a weighted undirected graph to represent
the connectivity of the system. Unlike previous connectivity maintenance works,
we explicitly account for robot motion and sensing uncertainties while
formulating the graph edge weights. These uncertainties result in uncertain
robot positions which directly affect the connectivity of the system. Next, the
algebraic connectivity of the weighted undirected graph is maintained above a
specified lower limit using a trajectory planner based on a distributed
alternating direction method of multipliers (ADMM) framework. Here we derive an
approximation for the Hessian matrices required within the ADMM optimization
step to reduce the computational load. Finally, simulation results are
presented to statistically validate the connectivity maintenance of our
trajectory planner.
