Formation control with size scaling using relative displacement feedback

We study a multiagent formation control problem where the objective is to steer a team of double integrator agents evolving in Euclidean space of arbitrary dimension into a desired formation. The size scaling of the desired formation is known only to a subset of the agents, and we present two decentralized strategies by which the agents can accomplish the formation task using only relative displacement feedback. A variable formation size allows the team of agents to adjust to changes in the environment or in group objectives, or respond to perceived threats, and control laws using only relative displacement information enables these strategies to be implemented using only local sensors and no interagent communication. We demonstrate the proposed strategies through several examples with simulations.