Explanation of the assumption the ant data is normally distributed for proper order statistic analysis. from Multi-robot replication of ant collective towing behaviours

In this work, teams of small mobile robots are used to test hypotheses about cooperative transport by ants. This study attempts to explain a decrease in steady-state transport speed with increasing team size that was previously observed in the ant <i>Novomessor cockerelli</i>. Two models of one-dimensional collective towing are compared: one in which transporters with different maximum speeds pull the payload with continuous, variable forces, and another in which transporters with identical speeds pull with intermittent, unsynchronized forces. A statistical analysis of ant data supports the hypothesis that ants behave according to the first model, in which the steady-state transport speed is the maximum speed of the slowest teammate. By contrast, the ant data are not consistent with the second model, which predicts constant speed regardless of team size. To verify these predictions, the ant behaviours in each model are translated into decentralized controllers and implemented on teams of two to four robots. The controller for the first model incorporates a real-time reinforcement learning algorithm that successfully reproduces the observed relationship between ant team size and transport speed. The controller for the second model yields the predicted invariance of transport speed with team size. These results show the value of robotic swarms for testing mechanistic hypotheses about biological collectives.