An Alignment Strategy for Evolution of Multi-Agent Systems

Developed in this paper is the notion that the collective behavior of swarms can be achieved without explicit peer-to-peer communication among agents. It is based on a recently proposed continuum framework for studying swarms where homogeneous maps are the key. The paper focuses on 2D evolution of a multi-agent system (MAS) that consists of N agents with Nl leaders at the two ends of m lines called leading segments, that are on the boundary of a moving convex domain Ωt. Rest of the (N-Nl) agents, the followers, are distributed along the m leading segments while lying inside the convex domain Ωt. Every follower i is initially located at the intersection of two line segments whose end points define four agents that are adjacent to i. Under this setup if the domain Ωt is transformed under a homogenous mapping and if every follower agent moves in such a way to reach the point of intersection of the two line segments connecting the adjacent agents, then the final formation of the MAS will satisfy the same homogenous map. This alignment strategy has the distinct advantage that the followers do not need the exact positions of the adjacent local agents to stay aligned.