On Stochastic Broadcast Control of Swarms

We present a model for controlling swarms of mobile agents via a broadcast control, detected by a random number of agents in the swarm. The agents that detect the control signal become the ad-hoc leaders of the swarm, while they detect the exogenous control. The agents are assumed to be velocity controlled, identical, anonymous, oblivious units with unlimited visibility. Assuming unlimited visibility decouples the problem of emergent behavior in a swarm from that of keeping the visibility graph complete, which has been thoroughly discussed in [10]. Each agent applies a linear local gathering control, based on the relative position of its neighbors. The detected exogenous control is superimposed by the leaders on the local gathering control. We show that in each time interval of a piecewise constant system, where the system evolves as a time-independent dynamic linear system, the swarm asymptotically aligns on a line in the direction of the exogenous control and all the agents move with identical speed. The speed of the swarm is set by the ratio between the numbers of agents receiving the control signal and the total number of agents in the swarm. A new time interval is triggered by a change in the broadcast control signal or in the agents detecting it, i.e. the “leadership team”.