3.2.2. Return Hormone

The return hormone equation is as follows:

$$H\_r(t) = \lambda\_r H\_r(t-1) + \gamma\_r \mathcal{C} \tag{3}$$

where *t* is the current time step *Hr* is the return hormone, *λ<sup>r</sup>* is the decay for the system and *γ<sup>r</sup>* is the stimuli weighting. The return hormone has a single stimulus, *C*, for collision detection. Although it does not regulate speed, it does feed into the speed hormone. The primary function of the Return Hormone is to identify the frequency of collisions detected by a robot, between walls or other robots. This information can then be used to decide if an individual robot should return to the nest having been unsuccessful, typically by exceeding either a fixed or similarly adaptive threshold. At this stage the threshold for returning was set to 50, with any value of *Hr* exceeding that resulting in a given robot changing behaviour state and travelling back to the nest site.
