One-Dimensional Discrete-Time Swarm

Abstract

The simplest case which can be considered in a discrete-time setting is the case in which a swarm moves in one-dimensional space. In this chapter we will consider this case. First, we describe the model of a single agent. Then, we present the one-dimensional swarm model (i.e., when many agents are arranged next to each other on a line). The model we consider also allows for asynchronous operation and time delays in neighbor position sensing. Therefore, the analysis of the swarm dynamics is relatively difficult. For this reason, we first analyze the dynamics of the swarm under the assumption of synchronous operation and perfect sensing (without time delays). Then, we build on the results obtained for this case and investigate the dynamics of the asynchronous swarm with sensing delays.