Distributed Containment Control with Multiple Dynamic Leaders for Double-Integrator Dynamics Using Only Position Measurements

TLDR: Analysis of the distributed containment control problem for a group of autonomous vehicles modeled by double-integrator dynamics with multiple dynamic leaders shows that the followers will move into the convex hull spanned by the dynamic leaders if the network topology among the followers is undirected.

Abstract: This note studies the distributed containment control problem for a group of autonomous vehicles modeled by double-integrator dynamics with multiple dynamic leaders. The objective is to drive the followers into the convex hull spanned by the dynamic leaders under the constraints that the velocities and the accelerations of both the leaders and the followers are not available, the leaders are neighbors of only a subset of the followers, and the followers have only local interaction. Two containment control algorithms via only position measurements of the agents are proposed. Theoretical analysis shows that the followers will move into the convex hull spanned by the dynamic leaders if the network topology among the followers is undirected, for each follower there exists at least one leader that has a directed path to the follower, and the parameters in the algorithm are properly chosen. Numerical results are provided to illustrate the theoretical results.