A discrete grid abstraction for formation control in the presence of obstacles

In this paper we present a formation reconfiguration methodology designed for controlling groups of autonomous agents in environments densely populated with obstacles. Our approach is based on abstracting the group of agents by a discrete rectangular grid. Agent and obstacle positions are mapped onto the formation grid. Then, collision free formation transition trajectories are computed using discrete event scheduling techniques that have been well-established in the manufacturing systems domain. The main contribution of this paper is a unified formation control framework that explicitly takes obstacles into account. Using discrete event system analysis tools we show that our approach guarantees convergence to the desired formation while avoiding obstacles and inter-agent collisions.