Distributed planar formation maneuvering of leader-follower networked systems via a barycentric coordinate-based approach

This paper presents a distributed planar leader-follower formation maneuver control strategy for multi-agent systems with different agent dynamic models. This method is based on the barycentric coordinate-based (BCB) control, which can be performed in the local coordinate frame of each agent with required local measurements. By exploring the properties of BCB Laplacians, a time-varying target formation can be BCB localizable by a sufficient number of leaders uniquely, and this formation is converted from a given nominal formation with geometrical similarity transformation. The proposed control laws can continuously maneuver collective single- and double-integrator agents to achieve a translation, scale, rotation, or even their compositions in various directions. For the formation shape control problem of multi-car systems with/without saturation constraints, the obtained control performance can preserve good robustness. Global stability is also proven by mathematical derivations and verified by numerical simulations.