A Cascades Approach to Formation-Tracking Stabilization of Force-Controlled Autonomous Vehicles

We present a cascades-based controller for the problem of formation-tracking control in a group of autonomous vehicles. We consider general models composed of a velocity kinematics equation and a generic force-balance equation. For each vehicle, a local controller ensures tracking of a reference generated by a leader vehicle. One or many vehicles may have access to the reference trajectories; each robot has one leader only, but may have several followers (spanning-tree topology). We establish uniform global asymptotic stability in a closed loop for a wide class of controllers. Our analysis relies on the construction of an original strict Lyapunov function for the position tracking error dynamics and an inductive argument based on the cascades-systems theory.