Controlling the Relative Agent Motion in Multi-Agent Formation Stabilization

In this technical note, we propose a novel technique to control the relative motion of multiple mobile agents as they stabilize to a desired configuration. In particular, we focus on the agents' relative velocities and the rate of change of their pairwise distances, and employ constructs from classic navigation functions (NFs) to control these quantities. Controlling agent velocities requires nontrivial extensions of the NF methodology to second-order models. Although in this work we propose a centralized framework to control the relative agent velocities, it adds a new dimension to the control of multi-agent systems with several advantages. In particular, we provide a novel approach to control the transient dynamics of a network that may facilitate the integration of continuous motion planing with discrete topology control. The result is verified theoretically and via computer simulations.