On the Problem of Representing and Characterizing the Dynamics of Multi-Robot Systems

In the recent years, there has been a growing interest in the design and programming of multi-robot systems. This is mainly due to the potential advantages of these systems, such as physical deployment, redundancy and parallelism in sensing and actuation. The interest of the collective robotics community has focused on the development of technology to support the interaction among single robots to achieve common goals, such as methods for inter-robot communication, kin recognition, sensor fusion, and information sharing. The outcomes of this research are seen to be of direct relevance to other fields involving the inter-operation of various software and physical components, such as sensor networks and ubiquitous computing. In spite of all the progress made in collective robotics in the last years, a lot of work remains to be done both in describing and understanding the behavior of multi-robot systems without regard to their internal mechanisms. However, theoretical descriptions of the dynamics of multi-robot systems pose a considerable challenge to robot designers because they do not rely on well-established and quantitative laws of behavior. As a matter of fact, collective robotics suffers from a lack of descriptive and analytical tools for estimating the tendencies and evolution of the dynamics of multi-robot systems under a variety of conditions. Some efforts have been made towards the theoretical understanding of multi-robot systems, such as the introduction of metrics for measuring specific aspects of multi-robot systems, e.g. diversity (Balch, 2000) and fluctuations from a steady state (Lerman et al., 2006), as well as attempts to describe the dynamics of multi-robot systems by using formal and semi-formal methodologies, e.g. ergodic dynamics (Shell et al., 2005). In this work, various attempts to describe the dynamics of multi-robot systems are presented and discussed. Two large-scale measures, average flow and average activity, are namely introduced and applied in experiments of simulated foraging robots, in order to characterize the systems limits. These measures are supported on parameters of crowd behavior applied in mechanical statistics. In addition, based on a set of selected case studies we provide experimental evidence about the quantification of the performance of multi-robot systems. This research aims at contributing to understand and characterize multi-robot dynamics, in order to generate a favorable framework to detect strengths and weaknesses in current designs. 27