A Study of Marginal Performance Properties in Robotic Teams

In this paper we describe how the productivity of homogeneous robots scales with group size. Economists found that the addition of workers into a group results in their contributing progressively less productivity; a concept called the Law of Marginal Returns. We study groups that differ in their coordination algorithms, and note that they display marginal returns only until a certain group size. After this point the groups' productivity drops with the addition of robots. However, the group size where this phenomenon occurs varies between groups. To determine the cause for the differences between coordination algorithms, we define a measure of interference that enables comparison, and find a high negative correlation between interference and productivity. Effective coordination algorithms maintain marginal productivity over larger groups by reducing the team's interference levels. Using this result we are able to examine the productivity of robotic groups in several simulated domains in thousands of trials. We find that groups in theory always produce marginally, but that spatial limitations within domains cause robots to deviate from this ideal.