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

Abstract

Abstract. 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.

Motion probes for fault detection and recovery in networked control systems

“…This analogy enables the connection to traditional boundary-value problems. In particular, it has been showed in [5], [12] that the introduction of single anchor nodes, i.e., a single, immobile agent, results in a rendezvous at the location of that agent, provided that the underlying graph remains connected. Similarly, with multiple anchor nodes, the remaining agents converge to the convex hull spanned by the anchor nodes [5].…”

A Leader-based Containment Control Strategy for Multiple Unicycles

“…The second objective is containment of the followers in the convex hull of the leaders' final positions. A similar problem was treated in [7] for multiple agents with single integrator kinematics. Unlike the strategy proposed in [7], the followers do not have to stay in the convex hull of the leaders' positions at each time instant.…”

Steering a Leader-Follower Team Via Linear Consensus

“…It has already been shown ( [3]) that, in the equilibrium, the followers are contained in the convex hull defined by the positions of the leaders, and hence in R L . However, if the motion of the leaders is not properly controlled, some followers could exit the region R L during the process.…”

“…To this purpose, we refer to a leader-follower structure, whereby a (small) subset of agents is assumed to have access to global information, and to lead through local consensus interactions the remaining agents. We adopt the team structure proposed in [3], which is particularly suitable when the goal is to steer a group of agents while maintaining certain geometric properties. For instance, if the agents transport some dangerous materials, it is important to keep them inside a proper area, not to contaminate the outer region.…”

“…For instance, if the agents transport some dangerous materials, it is important to keep them inside a proper area, not to contaminate the outer region. In [3], authors investigate properties such as controllability, containment and optimal control of leader -follower consensus structure for steering a group of mobile agents. Containment techniques rely on the use of sensors to detect the movements of the driven agents, and to trigger hybrid control actions by the team leaders.…”