  In this paper, we consider a team of mobile robots executing simultaneously
multiple behaviors by different subgroups, while maintaining global and
subgroup line-of-sight (LOS) network connectivity that minimally constrains the
original multi-robot behaviors. The LOS connectivity between pairwise robots is
preserved when two robots stay within the limited communication range and their
LOS remains occlusion-free from static obstacles while moving. By using control
barrier functions (CBF) and minimum volume enclosing ellipsoids (MVEE), we
first introduce the LOS connectivity barrier certificate (LOS-CBC) to
characterize the state-dependent admissible control space for pairwise robots,
from which their resulting motion will keep the two robots LOS connected over
time. We then propose the Minimum Line-of-Sight Connectivity Constraint
Spanning Tree (MLCCST) as a step-wise bilevel optimization framework to jointly
optimize (a) the minimum set of LOS edges to actively maintain, and (b) the
control revision with respect to a nominal multi-robot controller due to LOS
connectivity maintenance. As proved in the theoretical analysis, this allows
the robots to improvise the optimal composition of LOS-CBC control constraints
that are least constraining around the nominal controllers, and at the same
time enforce the global and subgroup LOS connectivity through the resulting
preserved set of pairwise LOS edges. The framework thus leads to robots staying
as close to their nominal behaviors, while exhibiting dynamically changing
LOS-connected network topology that provides the greatest flexibility for the
existing multi-robot tasks in real time. We demonstrate the effectiveness of
our approach through simulations with up to 64 robots.
