Swarm Model for Path Tracking with Reference Motion Profile: a Diffeomorphism-based Approach

This paper presents a novel strategy to control a multi-agent system along a given reference path while ensuring compliance with a given time profile for the movements along the route in question. The proposed protocol is based on a three-step methodology. In a first step, each agent state is augmented with an artificial variable that defines the movement of the agents along the given path. The extended agent state is then mapped into a virtual frame that takes into account the displacement of its position with respect to the reference path and the control over the additional artificial variable. Finally, in a third step, the control law designed in the artificial frame is translated into an action in the real frame using the theory of diffeomorphisms. The proposed control strategy ensures finite-time convergence of the entire multi-agent system on the reference path, while achieving error bounding for each agent evolution with respect to a given reference motion profile. Numerical simulations are performed to illustrate the described results.