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In this paper, we consider a team of mobile robots executing simultaneouslymultiple behaviors by different subgroups, while maintaining global andsubgroup line-of-sight (LOS) network connectivity that minimally constrains theoriginal multi-robot behaviors. The LOS connectivity between pairwise robots ispreserved when two robots stay within the limited communication range and theirLOS remains occlusion-free from static obstacles while moving. By using controlbarrier functions (CBF) and minimum volume enclosing ellipsoids (MVEE), wefirst introduce the LOS connectivity barrier certificate (LOS-CBC) tocharacterize the state-dependent admissible control space for pairwise robots,from which their resulting motion will keep the two robots LOS connected overtime. We then propose the Minimum Line-of-Sight Connectivity ConstraintSpanning Tree (MLCCST) as a step-wise bilevel optimization framework to jointlyoptimize (a) the minimum set of LOS edges to actively maintain, and (b) thecontrol revision with respect to a nominal multi-robot controller due to LOSconnectivity maintenance. As proved in the theoretical analysis, this allowsthe robots to improvise the optimal composition of LOS-CBC control constraintsthat are least constraining around the nominal controllers, and at the sametime enforce the global and subgroup LOS connectivity through the resultingpreserved set of pairwise LOS edges. The framework thus leads to robots stayingas close to their nominal behaviors, while exhibiting dynamically changingLOS-connected network topology that provides the greatest flexibility for theexisting multi-robot tasks in real time. We demonstrate the effectiveness ofour approach through simulations with up to 64 robots.

Minimally Constrained Multi-Robot Coordination with Line-of-sight Connectivity Maintenance