Laplacian Sheep: A Hybrid, Stop-Go Policy for Leader-Based Containment Control

The problem of driving a collection of mobile robots to a given target location is studied in the context of partial difference equations. In particular, we are interested in achieving this transfer while ensuring that the agents stay in the convex polytope spanned by dedicated leader-agents, whose dynamics will be given by a hybrid Stop-Go policy. The resulting system ensures containment through the enabling result that under a Laplacian, decentralized control strategy for the followers, these followers will converge to a location in the convex leader polytope, as long as the leaders are stationary and the interaction graph is connected. Simulation results testify to the viability of the proposed, hybrid control strategy.