Flocking while preserving network connectivity

Coordinated motion of multiple agents raises fundamental and novel problems in control theory and robotics. In particular, in applications such as consensus seeking or flocking by a group of mobile agents, a great new challenge is the development of robust distributed motion algorithms that can always achieve the desired coordination. In this paper, we address this challenge by embedding the requirement for connectivity of the underlying communication network in the controller specifications. We employ double integrator models for the agents and design nearest neighbor control laws, based on potential fields, that serve a twofold objective. First, they contribute to velocity alignment in the system and second, they regulate switching among different network topologies so that the connectivity requirement is always met. Collision avoidance among neighboring agents is also ensured and under the assumption that the initial network is connected, the overall system is shown to asymptotically flock for all initial conditions. In particular, it is shown that flocking is achieved even in sparse communication networks where connectivity is more prone to failure. We conclude by illustrating a class of interesting problems that can be achieved while preserving connectivity.