# Collective Memory: Transposing [PERSON]'s Experiment to Robot Swarms
## 4 Results  
We start by analyzing the mean field model as defined by Equation (3) and their steady-states (see [18] for details). The model possesses four types of solutions:  
* a homogeneous solution (referred to in the sequel as a mixed configuration), in which all four variables are equal (\(X_{S,1}=X_{O,1}=X_{S,2}=X_{O,2}\)),
* four semi-homogeneous solutions defined by \(X_{S,1}=X_{O,1}\) (referred to in the sequel as a default mixed configuration) and by \(X_{S,1}=X_{O,2}\) (referred to in the sequel as a segregation configuration),
* and four inhomogeneous solutions defined by \(x_{1}\
eq x_{2}\
eq y_{1}\
eq y_{2}\). Figure 9A shows a bifurcation diagram of the steady solutions of Equation (3) with fixed \(\kappa\) and \(\rho\) values and varying \(\alpha\). As noticed, for increasing values of \(\alpha\), the system switches from a segregated configuration, where each team \(X_{S}\) and \(X_{O}\) aggregates respectively in one area, to a mixed configuration, where robots of each team are equally distributed either in both areas, or all in a single area (default mixed configuration). As a side note, the default mixed configuration may seem to be an artifact of the mathematical model since the division of the aggregation zone in two areas is abstract and only serves the purpose of mathematical description. However, this particular solution can be interpreted as the result of competition between different early aggregates. If, by chance, robots from the opposite team encounter and start forming an aggregate earlier than robots of the same team, they offer an alternative aggregation site that may eventually capture all the robots of each team, thereby producing a mixed configuration by default. Notice that this state may only be observed when \(\alpha>0\), which is not the case when robots are segregating in our experiments. Figure 9B shows a state diagram against parameters \(\kappa\) and \(\alpha\) for a particular value of \(\rho\) where all the available states are available. In particular, we see that increasing the carrying capacity \(\kappa\) (the size of the aggregation zone) favors the mixed configurations for large values of \(\alpha\). For small values of \(\alpha\) and \(\kappa\), the segregated configuration dominates. Finally, when \(alpha\) is small but \(\kappa\) is large, we observe a simultaneous coexistence of mixed and segregated configurations. All in all, the model depicted by Equation (3) shows non-trivial features like different aggregation configurations and coexistence between them. Of special interest is the segre  
Figure 8: Decision tree describing the reactive behavior implemented by the robots. In circles are the signals that can be perceived by the robot, with \(B\) the beacon signal of the aggregating device, \(US\) the unconditional stimulus, and \(CS\) the conditional stimulus (\(B\), \(US\), and \(CS\) are implemented in simulation as acoustic messages that can be perceived by all robots at once). In rounded rectangles are the subroutines that can be executed, with mainly the random walk, the quorum, and the decision to stop any motion with a probability that can either depend on any (self or opposite team) nearby robots (\(P_{mix}\)) or on the nearby robots of the same team only (\(P_{seg}\)). This behavior does not require memory at the individual level as it is only based on the execution of different subroutines controlled by the current perception of the robots. gated configuration that is not induced by any agonistic behaviors but only by the finite size of aggregation zone, the individuals of the two teams interacting the same way. In the following, we focus on results obtained with individual based simulations. Figure 10 shows snapshots of simulated experiments. In the training phase, two different conditions are tested: the robots are either exposed to the unconditional and the conditional stimuli together, or the unconditional stimulus alone.