Hierarchic social entropy: An information theoretic measure of robot groupdiversity

As research expands in multiagent intelligent systems, investigators need n ew tools for evaluating the artificial societies they study. It is impossib le, 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 heterogeneo us or homogeneous, depending on whether any of the agents differ. Unfortuna tely, this labeling doesn't tell us much about the extent of diversity in h eterogeneous 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 o f comparisons, we introduce: (1) a continuous measure of robot behavioral d ifference, and (2) hierarchic social entropy, an application of Shannon's i nformation entropy metric to robotic groups that provides a continuous, qua ntitative measure of robot team diversity. The metric captures important co mponents of the meaning of diversity, including the number and size of beha vioral groups in a society and the extent to which agents differ. The utili ty of the metrics is demonstrated in the experimental evaluation of multiro bot soccer and multirobot foraging teams.