Linear constraints for ensuring k‐hop connectivity using mixed‐integer programming for multi‐agent systems

This note concerns the problem of k$$ k $$‐hop connectivity in a network of mobile agents, which is achieved if any pair of agents can communicate with each other through a link of k−1$$ k-1 $$ or fewer intermediate nodes. We propose linear constraints involving binary optimization variables to ensure k$$ k $$‐hop connectivity. Such constraints are then integrated into a mixed‐integer linear programming (MILP) trajectory planning model. Simulation results illustrate the application of the proposed method and the effect of varying k$$ k $$ in the context of a mission involving the visitation of multiple targets.