## Supporting material for the article:

# The k-Unanimity Rule for Self-organized Decision Making in Swarms of Robots

by Alexander Scheidler, Arne Brutschy, Eliseo Ferrante, and Marco Dorigo

October 2011

## Abstract

In this paper we propose a collective decision making method for swarms of
robots. The method enables a robot swarm to select, from a set of possible
actions, the one that has the fastest mean execution time. By means of
positive feedback the method achieves consensus on the
fastest action from the initially heterogeneous beliefs of the robots. We study two analytical models of the decision making
method to understand the dynamics of the consensus formation process. Moreover,
we verify the applicability of the method in a real swarm robotics scenario. To
this end, we conduct three sets of experiments that show that a robotic swarm can
collectively select the shortest of two paths. Finally, we use a Monte Carlo
simulation model to study and predict the influence of different parameters on
the method.

## Analytical model, continuum approach

**Figure S1. **Example trajectories of the continuum model for different memory sizes k. The upper trajectories start at x=0.5 (unbiased swarms) and the lower start at x=0.3. The dashed line marks the critical fraction 0.4.

## Analytical model, Master Equation approach

**Figure S2. **Probability E(x) to converge to action A depending on the difference in action execution times for different memory sizes k and swarm sizes N.

## Real robot experiments

Example run of Experiment I:

## Simulation model

**Figure S3.** Probability to converge to action A depending on the memory size k for different swarm sizes.