Continuum Evolution of a System of Agents with Finite Size

In this paper, considered is the evolution of a multi agent system (MAS) where every agent of the MAS is a ball in with radius ε. Evolution of the MAS occurs with n+1 agents, called leader agents, moving independently, with rest of the agents of the MAS, called follower agents, updating their positions through communication with n+1 local neighboring agents with weights of communication of follower agents assigned based only on the initial positions of agents of the MAS. When weights of communications are all positive, it is assured that final formation of the MAS is a homogenous transformation of its initial configuration. During transition however, the follower agents will deviate from the state specified by the homogenous transformation. This deviation from the state corresponding to that of the homogenous transformation during transition from the initial configuration to the final configuration can be controlled by imposing a limit on leaders’ velocities. This velocity limit depends on (i) the norm of the network matrix (specified based on initial positions of the agents), (ii) maximum allowable deviation from the state of homogenous transformation, and (iii) a control parameter . Thus, if the velocities of the leader agents don’t exceed an assigned maximum value, deviation of followers from the state of homogenous transformation is limited to a maximum value throughout the transient motion.