A continuum based approach for multi agent systems under local inter-agent communication

In this paper we develop an approach for the control of evolution of a multi agent system (MAS) based on a new local inter-agent communication protocol. The agents of the MAS occupy a compact region, have n-D dynamics, and are guided by n+ 1 special leader agents that can move independently. The rest of the agents, called followers, have the ability to update their positions via local communication with some adjacent agents. The special communication protocol is brought about by certain distance ratios that must be satisfied by points of a set that transforms as a homogeneous map. It is assumed that the leaders can and will determine on-line, in real time the desired intermediate configurations of the MAS. It is further assumed that the leaders cannot directly communicate such information to the follower agents in the MAS. The followers are expected to acquire that information through communication with n+ 1 local agents. The followers by moving in such a way to preserve, at all times, certain pre-computed distance ratios corresponding to the initial configuration of the MAS will learn the desired homogeneous maps. The proposed technique allows the MAS to (i) deform like a flexible body and/or (ii) undergo rigid body translations by satisfying certain key properties of homogeneous maps guaranteed by the special local inter-agent communication protocol.