Scaling the size of a multiagent formation via distributed feedback

We consider a multiagent coordination problem where the objective is to steer a group of agents into a formation that translates along a predefined trajectory velocity. Unlike previous control strategies that require a static desired formation or set of desired formations, we introduce a strategy in which one agent assigns a scale for the formation and the remaining agents adjust to the new scale. Thus, the formation can dynamically adapt to changes in the environment and in group objectives or respond to perceived threats. We introduce two strategies: one that requires agents to communicate estimates of the desired formation scale along edges of a communication network and one that only requires relative position sensing among agents. We show that the former strategy guarantees stability for any desired connected formation. For the latter strategy, we present a geometric constraint which can be used with the small gain theorem.