Effect of Network Size on Fractional-Order Dynamics in Large, Scale-Free Robotics Swarms and Platoons

This paper studies the effect of the size of a large scale robot network on the fractional order of the dynamics of the step response of the system. We show that, for a scale free network with certain parameter values, as the number of robots increases the fractional order also increases up to certain size network, after which the order plateaus. In contrast, for a much more structured platoon network, the opposite happens. This paper presents those results and discusses some hypotheses attempting to resolve the apparent contradiction. We are interested in investigating the presence of fractional order dynamics in systems of this type because they are becoming increasingly common for large scale engineered systems. Very large scale systems can be difficult to design, analyze and control and understanding various approaches to determine effective and accurate reduced order models is important. A concise fractional order description of the dynamics offers insight into the nature of the system that may not otherwise be available through either the full, very large scale system dynamics or other types of reduced order models.