Multi-Agent Control Using Coverage Over Time-Varying Domains

Swarm Herding: A Leader-Follower Framework For Multi-Robot Navigation

“…A coverage control algorithm naturally offers the ability to coordinate the motion of robots in a team. In this section, we will employ a coverage control law which is decentralized and can efficiently capture the evolution of the time-varying domain by extending ideas from our previous work [16]. The advantage of coverage control is that the individual controller for each robot in a team is synthesized such that the team can be controlled as a whole with time-varying densities [20] and time-varying domains [16].…”

“…In this section, we will employ a coverage control law which is decentralized and can efficiently capture the evolution of the time-varying domain by extending ideas from our previous work [16]. The advantage of coverage control is that the individual controller for each robot in a team is synthesized such that the team can be controlled as a whole with time-varying densities [20] and time-varying domains [16]. For completeness, we begin this section with briefly introducing the coverage algorithm over convex time-varying domains.…”

“…It is known that a necessary condition to minimize the locational cost defined in ( 6) is the centroidal Voronoi tessellation (CVT) configuration, i.e., p i (t) = C i (p, t) ∀i, where C i (p, t) is the cener of mass (centroid) of ith Voronoi cell. A control law is proposed for time-varying densities and time-varying domains to exponentially converge to a centroidal Voronoi configuration in [20,16],…”

“…by truncating the Neumann series for the matrix inverse to make the control law decentralized. The expressions of the centroids C i (p, t), and matrices ∂C ∂p and ∂C ∂t in ( 7) and ( 8) can be found in [16]. The matrix ∂C ∂p is a block matrix with sparsity structure encoding the adjacency information in the Voronoi tessellation [20], and the matrix ∂C ∂t captures the evolution of time-varying densities and time-varying domains.…”

“…The third layer provides control for a team of follower robots which stay in the time-varing domain defined by leader robots and perform coverage over it [16]. This layer of controller allows the followers to distributed in the domain defined by the leaders, to coordinates with each other to avoid collision (in point particle case), and to efficiently capture the motion of leaders.…”