Distance-Based Formation Tracking of Single- and Double-Integrator Agents

This article studies the distance-based formation tracking problem of a group of agents with a leader–follower topology. It is assumed that the desired formation is minimally infinitesimally rigid and the agents in the formation are classified as leaders and followers. The leaders are moving in the space and their positions determine a time-varying target formation, which may differ from the desired formation by a translation and a rotation. The followers, which can sense the local displacements with regard to their neighboring agents, track the moving target formation by controlling several interagent distance constraints. In case the followers are modeled by single integrators and the leaders are moving with bounded uniformly continuous velocities, we propose formation tracking control laws for followers with and without information on the exact upper bound of the leaders' velocities. Furthermore, another formation tracking law is proposed for double-integrator followers when the leaders are moving with the same constant velocity. In all cases, we provide sufficient conditions on the bound of the initial conditions so that the time-varying target formation is asymptotically achieved. Simulation results are then given to support the mathematical analysis.