Continuum evolution of multi agent systems under a polyhedral communication topology

In this paper, evolution of a multi agent system (MAS) in n-D space where n+1 or more leader agents located on the boundary guide the MAS is studied. We consider the MAS as a deformable body whose motion can be prescribed by a homogeneous map determined by the initial and current positions of the leaders. Each follower agent learns this leader prescribed motion plan by local communication with adjacent agents. In previous work we assumed that each follower communicates with n+1 adjacent agent [1-7]. Here we relax that constraint to include more than 3 adjacent agents by choosing a polyhedral communication topology where the vertices are local agents that are adjacent to a follower agent i. The polytope encloses the follower agent i and is the union of m_i sub-polyhedra, with one of the n+1 vertices occupied by agent i. m_i volume weights are defined based on the initial position of follower i and the set of adjacent agents to. The motion proceeds by updating the position of every follower agent such that volume weights in intermediate configurations of the MAS are close to the initial volume weights. This update strategy maneuvers the MAS to its final desired formation as a homogenous map of its initial configuration.