Hierarchic social entropy: An information theoretic measure of robot group diversity

As research expands in multiagent intelligent systems, investigators need new tools for evaluating the artificial societies they study. It is impossible, for example, to correlate heterogeneity with performance in multiagent robotics without a quantitative metric of diversity. Currently diversity is evaluated on a bipolar scale with systems classified as either heterogeneous or homogeneous, depending on whether any of the agents differ. Unfortunately, this labeling doesn't tell us much about the extent of diversity in heterogeneous teams. How can it be determined if one system is more or less diverse than another? Heterogeneity must be evaluated on a continuous scale to enable substantive comparisons between systems. To enable these types of comparisons, we introduce: (1) a continuous measure of robot behavioral difference, and (2) hierarchic social entropy, an application of Shannon's information entropy metric to robotic groups that provides a continuous, quantitative measure of robot team diversity. The metric captures important components of the meaning of diversity, including the number and size of behavioral groups in a society and the extent to which agents differ. The utility of the metrics is demonstrated in the experimental evaluation of multirobot soccer and multirobot foraging teams.