Multi-agent formation control and trajectory tracking via singular perturbation

We study the problem of formation control and trajectory tracking for a group of robotic systems modeled as second order linear dynamics. The objective is to achieve and maintain a stable formation for a group of multi-agent systems, while guaranteeing tracking of a specified trajectory. The group should appear to the external operator that steers the fleet as a rigid body. We partition the state space for the collective system into coordinates of the geometric center of mass of the team and coordinates that describe the relative position of each robot with respect to the center of mass, thus defining the formation shape. The resulting dynamics are in general coupled. By imposing holonomic constraints between the subsystems (i.e. configuration constraint) and hence reducing the system's dimension, we guarantee the group behaving as a rigid body. Using high gain feedback we achieve asymptotic decoupling between the center of mass and the shape dynamics and the analysis is performed using singular perturbation method. In fact, the resulting system is a singularly perturbed system where the shape dynamics describe the boundary layer while the center of mass dynamics describes the reduced system. After an initial fast transient in which the robots lock to the desired shape, a slower tracking phase follows in which the center of mass converges to the desired trajectory while maintaining a stable formation.