Integration of communication and control using discrete time Kuramoto models for multivehicle coordination over broadcast networks

This paper considers the integration of communication and control with respect to the task of coordinated heading control for a group of N vehicles with the energy efficiency of communications in mind. The heading control employed on each vehicle is a discretization of the well-known Kuramoto model of nonlinearly coupled oscillators over a sequence of logical graphs. Stability for both all-to-all and random one- to-all broadcasts is shown to be dependent on the coupling strength, K, and the time discretization, DeltaT. For desired system performance characteristics, DeltaT imposes a tight deadline by which the state information (M bits) must be propagated through the communication network. Routing optimization with respect to minimizing energy consumption is formulated considering the DeltaT deadline. Due to the tight time deadline, a one-to-all single- hop broadcasting scheme is shown to be more energy efficient for practical choices of M/DeltaT. The proposed modularization is illustrated via a set of simulations where the overall communication energy to reach alignment is optimized.