Clustering and coverage control for systems with acceleration-driven dynamics

In this technical note, we consider the dynamic coverage control problem from a clustering perspective, to which we apply control-theoretic methods to identify and track the cluster center dynamics. To the authors' knowledge, this is the first work to consider tracking cluster centers when the dynamics of the system elements involve acceleration fields. We show that a dynamic control design is necessary to achieve dynamic coverage under these acceleration fields. We pose the goal of maximizing the instantaneous coverage as a combinatorial optimization problem, and propose a framework that extends the concepts of the deterministic annealing algorithm to the dynamic setting. The resulting Lagrangian is used as a control Lyapunov function for designing coverage control. The algorithms we propose guarantee asymptotic tracking of cluster group dynamics, and we further establish continuity and boundedness of the corresponding control laws. Simulations are provided to corroborate these results.