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This paper considers the problem of maintaining global connectivity of amulti-robot system while executing a desired coordination task. Our approachbuilds on optimization-based feedback design formulations, where the nominalcost function and constraints encode desirable control objectives for theresulting input. Our solution uses the algebraic connectivity of themulti-robot interconnection topology as a control barrier function andcritically embraces its nonsmooth nature. We take advantage of theunderstanding of how Laplacian eigenvalues behave as their multiplicitieschange, in combination with the flexibility provided by the concept of controlbarrier function, to carefully design additional constraints that guarantee theresulting optimization-based controller is continuous and maintains networkconnectivity. The technical treatment combines elements from set-valued theory,nonsmooth analysis, and algebraic graph theory to imbue the proposedconstraints with regularity properties so that they can be smoothly combinedwith other control constraints. We provide simulations and experimental resultsillustrating the effectiveness and continuity of the proposed approach in aresource gathering problem.

Nonsmooth Control Barrier Function Design of Continuous Constraints for Network Connectivity Maintenance