A Framework Based on Control Barrier Functions for Time-Varying Connectivity Maintenance

Connectivity maintenance is one of the fundamental properties that must be guaranteed in networked Multi-Agent Systems (MASs). Existing approaches assume static constraints on the algebraic connectivity of the graph. However, in dynamic and unstructured operational settings, such as in agricultural scenarios, the possibility to dynamically vary the minimum algebraic connectivity is desirable, for instance, to avoid deadlocks or adapt to dynamic occlusions. In this work, we propose a framework to ensure connectivity maintenance with time-varying constraints. To this aim, we resort to a Control Barrier Function (CBF) formulation and assume that a target minimum algebraic connectivity value is externally provided to the team. Then, we ensure that the MAS smoothly adapts to the updated constraints. Additionally, a simple strategy to map human inputs into reference values of the minimum algebraic connectivity is presented as an example of operating scenario. Numerical simulations in the context of precision agriculture and laboratory experiments are provided to validate the proposed approach.