Stabilizing and Maneuvering Angle Rigid Multiagent Formations With Double-Integrator Agent Dynamics

This article studies 2-D formation stabilization and maneuvering of mobile agents governed by double-integrator dynamics. The desired formation is described by a set of triple-agent interior angles. A carefully chosen such set of angle constraints guarantees that the desired formation is angle rigid. To achieve the desired angle rigid formation, a stabilization control law is proposed using only local velocity and direction measurements. We show that the closed-loop dynamics of the formation, when each agent is modeled by a double-integrator, are closely related to the corresponding one in single-integrator agent dynamics. Sufficient conditions are constructed to guarantee the closed-loop stability for identical and distinct velocity damping gains, respectively. To guide an angle rigid formation to move with the desired translational velocity, orientation, and scale, formation maneuvering laws are then proposed. Simulation examples are also provided to validate the results.