Self-triggered best-response dynamics for mobile sensor deployment

The coordination of large numbers of autonomous agents has lead to the development of novel theoretical tools for the analysis and design of practical control algorithms with performance guarantees. Aligned with this research, this paper investigates the adaptation of classical best-response dynamics to achieve coverage control by a mobile sensor network subject to communication constraints. To do this, we first formulate a 1-D deployment scenario as a continuous-time-space potential game with a componentwise concave potential function. Making use of the stability theory for non-smooth dynamical systems, we characterize how the set-valued, best-response dynamics can converge to the set of Nash equilibria under some general conditions. This allows us to guarantee that sensor trajectories converge toward positions that maximize the covered area. We then modify the best-response dynamics to account for a self-triggered communication strategy that decreases the multi-agent communication effort while ensuring convergence to the equilibrium set. Finally, we present some simulations that demonstrate the performance of the proposed strategy.