A Macroscopic Probabilistic Model of Adaptive Foraging in Swarm Robotics Systems

In this paper, we have extended a macroscopic probabilistic model of a swarm of homogeneous foraging robots to a swarm of heterogeneous foraging robots. Each robot is capable of adjusting its searching time threshold and resting time threshold following the rules described in our previous paper. In order to model the difference between robots, private resting time and searching time thresholds are introduced. The robots resting at home are divided into two subsets according to which states they are transferred from, either state Deposit or state Homing. For each subset of robots, private resting time and searching time thresholds are used to calculate the effect of social and internal cues. The transition between state Resting and state Searching is then decided by the corresponding private resting time threshold. Corresponding to private resting time thresholds, a public resting time threshold is used to track the contribution of the social cues, internal cues and environmental cues for the whole swarm, which is a global property owned by all robots. Although the public resting time threshold doesn’t affect the behaviours for the individual robots directly, it affects the private resting time threshold and vice versa. Similarly, a public searching time threshold is introduced to track the contributions of the adaptation cues. The behaviours for the robots searching for food in the arena are constrained with the corresponding private searching time threshold, which is “inherited” from the public searching time threshold but will affect it as well. With these considerations, a number of equations are then developed to work out the relationship between these private time thresholds and public time thresholds based on previously developed difference equations. The resting time and searching time thresholds are dealt with separately because each of them has its own valid scope. The extended macroscopic probabilistic model has been tested using the simulation tools Player/Stage. A set of randomly chosen adjustment factors which are presented in our previous paper are used to validate the macroscopic model. Different environmental conditions are also considered. The results from the macroscopic probabilistic model match with those from the simulation with reasonable accuracy, not only in the final net energy of the swarm but also in the instantaneous net energy. Although the model is specific to adaptive foraging, it can be extended to other systems in which the heterogeneity of the system is coupled with its time parameters.