Maintaining limited-range connectivity among second-order agents

In this paper we consider ad-hoc networks of robotic agents with double integrator dynamics. For such networks, the connectivity maintenance problems are: (i) do there exist control inputs for each agent to maintain network connectivity, and (ii) given desired controls for each agent, can one compute the closest connectivity-maintaining controls in a distributed fashion. The proposed solution is based on three contributions. First, we define and characterize admissible sets for double integrators to remain inside disks. Second, we establish an existence theorem for the connectivity maintenance problem by introducing a novel state-dependent graph, called the double-integrator disk graph. Finally, we design a distributed "flow-control" algorithm to compute optimal connectivity-maintaining controls.